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CK-12 Physics - Intermediate
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iii

Contents www.ck12.org
Contents
1 What is Science? Worksheets 1
1.1 Scientific Inquiry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Fundamental Units and Standard Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Measurement and Recording Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Working with Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 One-Dimensional Motion Worksheets 15
2.1 Locating an Object: Distance and Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Speed and Velocity in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Average Speed, Velocity, and Instantaneous Velocity . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Uniform Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 The Kinematic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 Two-Dimensional Motion Worksheets 32
3.1 Independence of Motion Along Each Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Vector Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Inertial Frames and Relative Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Newton’s Three Laws Worksheets 48
4.1 Newton’s First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Newton’s Third Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 Forces in Two Dimensions Worksheets 57
5.1 Normal Force and Friction Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Inclined Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Circular Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.4 Forces in Translational Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 Work and Energy Worksheets 68
6.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.3 Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.4 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7 Momentum Worksheets 79
7.1 Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.2 Conservation of Momentum in One Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.3 Conservation of Momentum in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 84
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7.4 Collisions and Conservation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8 Statics Worksheets 88
8.1 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.2 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.3 Two Conditions of Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.4 Applications of Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
9 Newton’s Universal Law of Gravity Worksheets 97
9.1 Kepler’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
9.2 Newton’s Universal Law of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.3 Circular Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
10 Periodic Motion Worksheets 105
10.1 Simple Harmonic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
10.2 Mass on a Spring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
10.3 Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
10.4 Waves and Wave Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
11 Vibrations and Sound Worksheets 115
11.1 Transmission of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
11.2 Wave Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
11.3 Resonance with Sound Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
11.4 Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
12 Fluid Mechanics Worksheets 128
12.1 Pressure in Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
12.2 Measuring Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
12.3 Pascal’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
12.4 Archimedes’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
12.5 Bernoulli’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
13 Heat Worksheets 139
13.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
13.2 Kinetic Theory of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
13.3 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
13.4 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
13.5 Specific Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
14 Thermodynamics Worksheets 149
14.1 The Ideal Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
14.2 First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
14.3 Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
15 Electrostatics Worksheets 156
15.1 Static Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
15.2 Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
15.3 Electrostatic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
16 Electric Potential Worksheets 165
16.1 Reviewing Gravitational Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
16.2 Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
16.3 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
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Contents www.ck12.org
16.4 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
16.5 Electrical Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
17 Circuits Worksheets 175
17.1 Electric Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
17.2 Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
17.3 Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
17.4 Resistors in Series and Parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
17.5 Measuring Current and Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
18 Magnetism Worksheets 189
18.1 Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
18.2 The Magnetic Force acting on a Current-Carrying Wire . . . . . . . . . . . . . . . . . . . . . . 193
18.3 Magnetic Force on Moving Electric Charges . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
18.4 A Practical Application of Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
19 Electromagnetism Worksheets 200
19.1 Electromagnetic Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
19.2 The Electric Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
19.3 Electrical Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
19.4 The Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
20 Geometric Optics Worksheets 210
20.1 Light as a Ray and the Law of Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
20.2 Concave and Convex Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
20.3 Index of Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
20.4 Thin Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
21 CK-12 Physics IH-Chapter-Physical Optics Worksheets 235
21.1 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
21.2 The Double-Slit Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
21.3 Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
21.4 Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
22 The Special Theory of Relativity 242
22.1 The Special Theory of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
23 CK-12 Physics IH-Chapter-Quantum Physics Worksheets 246
23.1 Quantum Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
24 CK-12 Physics IH-Chapter-Atomic Physics Worksheets 250
24.1 Atomic Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
25 Nuclear Physics 254
25.1 Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
25.2 Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
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www.ck12.org Chapter 1. What is Science? Worksheets
CHAPTER
1 What is Science?
Worksheets
Chapter Outline
1.1 SCIENTIFIC INQUIRY
1.2 FUNDAMENTAL UNITS AND STANDARD UNITS
1.3 UNIT CONVERSIONS
1.4 MEASUREMENT AND RECORDING DATA
1.5 WORKING WITH ERROR
1.6 REFERENCES
1

1.1. Scientific Inquiry www.ck12.org
1.1 Scientific Inquiry
Worksheet
Name___________________ Class______________ Date________
Answer each of the questions below to show your achievement of the lesson objectives.
Lesson Objective: Explain the role of using postulates in science.
1. Why is your friend incorrect when they state, "But that is only a scientific theory"?
2. Choose two important steps in a scientific investigation and describe them below.
Lesson Objective: Explain the role of mathematics in science.
3. Give an example in which we use numbers to describe something in the physical world around us.
4. Why do you think scientists record their experimental data as numbers instead of drawing representative
pictures?
Lesson Objective: Explain how scientists investigate nature by ensuring their models can be proven incorrect
(falsifiable) and are tested by many independent researchers.
5. Develop a scientific investigation to address the following question: "Does heating a cup of water allow it to
dissolve more salt?"
6. Is there only one correct way to develop a scientific explanation?
Lesson Objective: Describe the difference between a hypothesis, theory, and law.
7. What is a hypothesis? Give an example.
8. What is a scientific theory? Give an example.
2

9. What is a scientific law? Give an example.
Lesson Objective: Explain that new theories explain phenomena more accurately than preexisting theories,
and such theories are consistent with the correct predictions of previous theories.
10. Why is it important that scientific theories are able to change?
11. Why does science involve repeating experiments and examining sources of error?
Lesson Objective: Describe the scientific method.
FIGURE 1.1
12. List three observations regarding the image 1.1.
13. Pick one observation from your list above and develop a hypothesis. Be sure to include your reasoning for this
prediction.
Answer Key
1. Theories are not guesses or opinions, they are broad explanations supported by an enormous amount of
evidence.
2. Answers may vary. Sample answers may describe how scientists make observations, ask questions, form
hypotheses, test hypotheses, draw conclusions, and communicate results.
3. Answers will vary. Sample Answer: We use numbers to describe height and weight.
3

1.1. Scientific Inquiry www.ck12.org
4. Answers will vary. Sample Answers: Recording numerical data allows scientists to be more precise and
accurate when collecting evidence to support their hypothesis. Numbers are easier to analyze than pictures
and can be represented in graphs, tables and charts. Numbers allow scientists to easily see the effect of one
variable on another. Numbers are objective and pictures are subjective.
5. Answers will vary. Sample Answer: Develop a Hypothesis such as, "If you increase the heat of water, then
more salt will dissolve". Test the hypothesis by increasing the heat of water by 25°C and measuring the amount
of salt that dissolves (repeat at least three times). Keep the amount of water, amount of salt, and the pot that
the salt and water are in constant.
6. The process for developing a scientific explanation can go in different orders, but must meet the following
requirements: it must be logically consistent, it must make predictions, and it must be potentially disprovable.
7. A scientific hypothesis is a proposed explanation for an observation based on logic. Examples will vary.
8. A scientific theory is the best explanation for a broad range natural phenomena based on many lines of
evidence. Examples will vary.
9. A scientific law is a specific mathematical relationship that can describe experimental data. Examples will
vary.
10. Scientific theories are not absolute truths; they are simply the best explanation based on evidence at the time.
Therefore, if new evidence arises, theories must be edited or overturned.
11. Scientists test their explanations by repeating the experiment and examining sources of error in order to ensure
the validity of their conclusions.
12. Answers may vary. Sample Answers: The man is trying to lift the weights. The man is holding his breath. The
man is at the gym.
13. Answers may vary. Sample Answers: If the amount of weight decreases, the man will be able to lift the weight
more quickly. Rationale: it will be easier for the man to lift a lighter load, so he will be able to lift the weight
faster. I could test this by decreasing the amount of weight by 10 lbs and measuring the amount of time it takes
the man to lift the weight in seconds.
4

1.2 Fundamental Units and Standard Units
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: List and use fundamental units in the study of mechanics.
1. What is a fundamental unit?
2. What is an example of a fundamental unit?
3. Give an example of how fundamental units can be used to derive another units.
4. Force is measured in Newtons. If the equation for Force is F = ma, how can you express Newtons in
fundamental units?
Lesson Objective: List and use standard units in the study of mechanics.
5. The standard unit for mass is_________________.
6. The standard unit for temperature is _______________________.
7. Make the following metric conversions:
a. 7.64 g to kg
b. 987 cm to m
c. 65 ms to s
8. Describe how the kilometer, centimeter and millimeter relate to the base unit of the meter.
Lesson Objective: Use dimensional analysis.
9. What is dimensional analysis? Give an example.
10. It is best to use dimensional analysis when:
a. making scientific observations
b. recording experimental data
c. deriving the units of a number
5

1.2. Fundamental Units and Standard Units www.ck12.org
d. none of the above
11. Explain why the following equation does not correctly convert 5 centimeters into meters using dimensional
analysis:
5 cm× 100 cm
1 m = 500cm2
m
12. Use dimensional analysis to calculate how many dozen donuts you would need to order to feed a school of
456 students.
13. Use dimensional analysis to calculate how many quarters are in 50 dollars.
Answer Key
1. A set of units for physical quantities that can be used to derive all other units.
2. Answers will vary. Sample Answers: Mass (kg), length (m), time (s), temperature (°C)
3. Answers may vary. Sample Answer: Velocity is derived from the fundamental units of length (m) and time (s);
Velocity (m/s) = distance (m) / time (s)
4. N = kg x (m/s2)
5. Kilogram (Kg)
6. Degree Celsius (°C)
7.
a. 0.00764 kg
b. 9.87 m
c. 0.065 s
8. These prefixes relate to the meter by some power of ten:
• The prefix kilo means 103 , so 1 km = 1000 m
• The prefix centi means 10−2, so 1 cm = 0.01 m
• The prefix milli means 10−3, so 1 mm = 0.001 m
9. Dimensional analysis involves finding a numerical quantity with its corresponding units. This allows you to
check mathematical equations and predict units based on the relation of other units. Examples will vary.
10. C
11. When we multiple these units together, we get cm2
m . These are not the correct units we are looking for. The
correct equation would be:
5 cm× 1 m
100 cm = 0.05 m
12. You would need to order 38 dozen.
456 donuts× 1 dozen
12 donuts = 38 dozen
13. There are 200 quarters in 50 dollars.
50 quarters× 4 quarters
1 dollar = 200 quarters
6

1.3 Unit Conversions
Worksheet
Name___________________ Class______________ Date________
Perform unit conversions.
1. What is a conversion factor?
2. Provide two examples of conversion factors.
3. Explain how a conversion factor is different from a measurement.
4. How many hours are there in 3 days?
5. An NFL linebacker weighs 252 lbs. What is his weight in kg if 1 lb=0.454 kg?
Properly use scientific notation.
6. When writing an extremely small number is scientific notation, the exponent will be:
a. Positive
b. Negative
c. Zero
d. None of the above
7. When writing an extremely large number is scientific notation, the exponent will be:
a. Positive
b. Negative
c. Zero
8. Convert the following numbers to scientific notation.
a. 7000
b. 0.000 087
c. 543
d. 254000
9. Convert the following numbers out of scientific notation.
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1.3. Unit Conversions www.ck12.org
a. 5.32 x 10−3
b. 6.35 x 105
c. 4.2 x 104
d. 3.5 x 10−4
10. Solve the following problems and write your answer in scientific notation.
a. (9.0 x 109) x (2.7 x 10−4)
b. (5.0 x 10−6) ÷ (3.5 x 102)
Answer Key
1. A ratio used to convert one unit of measurement into another unit.
2. Answers will vary. Sample Answers: 1 m = 100 cm; 1 kg = 1000 g; 1 s = 1000 ms
3. When measuring a quantity, a scientist uses an instrument to determine the size or amount of something. A
conversion factor is not a measurement itself, but a ratio of units that can be used to change the units of a
measurement.
4. Conversion factor: 1 day = 24 hours
3 days× 24 hrs
1 day = 72 hrs
5. Conversion factor: 1 lb=0.454 kg
252 lbs× 0.454 kg
1 lb = 114 kg
6. B
7. A
8.
a. 7000 = 7.0 x 103
b. 0.000 087 = 8.7 x 10−5
c. 543 = 5.43 x 102
d. 254000 = 2.54 x 105
9.
a. 5.32 x 10−3 = 0.00532
b. 6.35 x 105 = 635,000
c. 4.2 x 104 = 42,000
d. 3.5 x 10−4 = 0.00035
10.
a. (9.0 x 109) x (2.7 x 10−4) = 2.43 x 106
b. (5.0 x 10−6) ÷ (3.5 x 102) = 1.43 x 10−8
8

1.4 Measurement and Recording Data
Worksheet
Name___________________ Class______________ Date________
Describe measurement.
1. A measurement is based on
a. qualitative observations
b. quantitative observations
c. hypotheses
d. none of the above
2. Which one of the following is a reasonable measurement for the height of a coconut palm tree?
a. 250 m
b. 25 m
c. 2.5 m
d. 0.25 m
Explain what is meant by significant digits.
3. What are significant figures?
4. What are significant figure rules involving zero?
5. What is a right-end zero?
6. What is a left-end zero?
Determine the number of significant digits in a measurement.
7. Round the following numbers to 3 significant figures:
a. 8.666
b. 123,456,789
c. 5.363
d. 0.00632
e. 407.5
8. Determine the number of significant figure in each of the following:
9

1.4. Measurement and Recording Data www.ck12.org
a. 15.42
b. 0.0000000000078
c. 9.06
d. 1.5 x 105
e. 909,000
f. 909,000.00
9. Apply the rule of zeros to determine the amount of significant figures in the following measurements:
a. 900 m
b. 0.00000053 mm
c. 89,000 kg
d. 6,000,000,000,000.0 g
Add, subtract, multiply, and divide with significant digits.
10. Solve each of the following, keeping the correct number of significant figures in the answer:
a. 2.4 + 13.5 + 3.38 =
b. 0.050 x 0.000080 =
c. 0.025/0.00755 =
11. When doing math with significant figures, what determines the number of significant figures in the answer?
Use scientific notation.
12. Convert the following numbers to scientific notation.
a. 765000
b. 87
c. 0.0000543
d. 5500
13. Convert the following numbers out of scientific notation.
a. 5.67 x 10−3
b. 6.0 x 105
c. 2.456 x 104
d. 3.29 x 104
Answer Key
1. B
2. B
3. Significant figures are the certain digits in a measurement plus one uncertain or estimated digit.
4.
a. All non-zero numbers are significant
b. Zeros that appear between other non-zero digits are always significant
c. Left-end zeros are never significant
d. Right-end zeros in a number that lacks a decimal point are not significant
e. Right-end zeros in a number with a decimal point are significant
10

5. For any zero written after the non-zero digits. For example, the number 6300 has right end zeros. If there is
a decimal, these zeros are significant. If there is no decimal, these zeros are insignificant. In the example of
6300, the right-end zeros are insignificant.
6. Any zero that is before all of the non-zero digits. For example, the number 0.0063 has left-end digits. All
left-end zeros are always insignificant.
7. a. 8.67; b. 1.23 x 108; c. 5.36; d. 6.32 x 10−3; e. 408
8. a. 4; b. 2; c. 3; d. 2; e. 3; f. 8
9. a. 1; b. 2; c. 2; d. 14
10. a. 19; b. 4.0 x 10−6; c. 3.3
11. The LEAST number of significant figures in any number of the problem determines the number of significant
figures in the answer.
12. a. 7.65 x 105; b. 8.7 x 101; c. 5.43 x 10−5; d. 5.5 x 103
13. a. 0.00567; b. 600,000; c. 24,560; d. 32,900
11

1.5. Working with Error www.ck12.org
1.5 Working with Error
Worksheet
Name___________________ Class______________ Date________
Describe systematic and random error.
1. What is a systematic error?
2. What is a random error?
3. What is an example of a systematic error?
4. What is an example of a random error?
5. When using a force probe, a physics student forgets to calibrate the instrument. This will most likely result in:
a. A systematic error
b. A random error
c. Both A B
Explain precision and accuracy as they relate to error.
6. What is accuracy?
7. What is precision?
8. The mass of a particular red clay brick is 3 kg.
a. Provide an example of a data set that is both accurate and precise.
b. Provide an example of a data set that is not accurate and but is precise.
12

Answer Key
1. An error of constant value that is made repeatedly, usually due to the measuring instrument. This type of error
can be easily corrected.
2. An error that varies within the inherent uncertainty of a measurement and cannot be corrected by a calculation.
3. Examples will vary. Sample Answer: The scale reads 1 g lower than the actual weight of an object, each time
the object it is measured.
4. Examples will vary. Sample Answer: Using 0.1mL less of a solution than required due to difficulty using
syringe.
5. A
6. Accuracy is how close a measurement is to the correct value of the quantity being measured.
7. Precision is how close a series of measurements are to each other.
a. Answers will vary. Sample Answers: If the correct mass of a red clay brick is 3kg, a data set with the
following measurements: 3.01kg, 3.02kg, 3.03kg, 2.99kg would be both accurate (close to the correct
value) and precise (the series of measurements are close to each other).
b. Answers will vary. Sample Answers: If the correct mass of a red clay brick is 3kg, a data set with the
following measurements: 5.01kg, 5.02kg, 5.03kg, 4.99kg would be precise (the series of measurements
are close to each other) but not accurate (these numbers are not close to the actual mass of the brick,
3kg).
13

1.6. References www.ck12.org
1.6 References
1. Jon Clegg. http://www.flickr.com/photos/jonclegg/4457694598/ . CC-BY 2.0
14

www.ck12.org Chapter 2. One-Dimensional Motion Worksheets
CHAPTER
2 One-Dimensional Motion
Worksheets
Chapter Outline
2.1 LOCATING AN OBJECT: DISTANCE AND DISPLACEMENT
2.2 SPEED AND VELOCITY IN ONE DIMENSION
2.3 AVERAGE SPEED, VELOCITY, AND INSTANTANEOUS VELOCITY
2.4 UNIFORM ACCELERATION
2.5 THE KINEMATIC EQUATIONS
15

2.1. Locating an Object: Distance and Displacement www.ck12.org
2.1 Locating an Object: Distance and Dis-
placement
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Define scalar and vector.
1. In your own words, explain why displacement is a vector.
2. In your own words, explain why distance is scalar.
3. How do we use positive and negative signs to communicate the direction of a vector?
Lesson Objective: Define distance and displacement.
Lisa traveled 7 miles to the nearest movie theater. She watched a movie and drove back home.
4. What total distance did Lisa travel?
5. What is Lisa’s displacement?
Describe a real-life example for each of the following scenarios:
6. The distance an object travels is larger than its displacement.
7. The distance an object travels is equal to its displacement.
8. An object travels a positive distance but has zero displacement.
Lesson Objective: Distinguish between distance and displacement.
Joe hits a home run 200 ft over left field.
16

9. Is 200 feet the ball’s distance or displacement?
10. Which is greater, the ball’s distance or displacement?
11. If the bases are 90 ft apart, what is the distance Joe travels if he hits a home run and runs around all 4 bases?
12. What is Joe’s displacement after his run around the bases?
Lesson Objective: Graphically model distance and displacement.
While relaxing on a blanket in the park, Sonia observes a lizard moving quickly about. She immediately gets out her
notebook and creates the following data table of the lizard’s movements:
TABLE 2.1: Lizard movements
Time (s) Position (m)
0 0
2 12
4 12
6 0
13. Graphically model the distance the lizard has traveled.
14. Graphically model the displacement the lizard has traveled.
Answer Key
1. When calculating displacement, you have to consider both magnitude and direction.
2. When calculating the distance traveled by an object, the direction of the object does not matter.
17

2.1. Locating an Object: Distance and Displacement www.ck12.org
3. Usually, a positive number indicates a vector quantity is moving rightward or upward. A negative number
indicates a vector quantity is moving leftward or downward.
4. 14 miles
5. Zero. The difference between her final position and initial position is zero.
6. Answers will vary. Sample Answer: My friend’s house is 5 miles west of my house. The grocery store is 10
miles west of my house. I first drive to the grocery and the stop at my friend’s house on the way back. I’ve
traveled a distance of 15 miles. My displacement from my starting location (my house) to my ending location
(my friends house) is 5 miles west.
7. Answers will vary. Sample Answer: The shopping mall is 25 miles northeast of my house. When I drive to the
mall, I have traveled a distance of 25 miles and also have a displacement of 25 miles northeast.
8. Answers will vary. Sample Answers: My job is 15 miles from my house. I drive my car to work and back. The
distance I have traveled is 30 miles, but my displacement is zero.
9. Distance because it does not include a direction. Displacement is a vector and requires magnitude and
direction.
10. They both have the same magnitude of 200 ft.
11. 4 x 90 = 360 feet
12. Displacement is zero because his final position is the same as his initial position.
13. See distance-time graph below.
14. See displacement-time graph below.
18

2.2 Speed and Velocity in One Dimension
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Define constant speed and velocity.
1. In your own words, define constant speed and provide an example of an object moving with a constant speed.
2. When calculating the velocity of a moving object, do you need to consider the distance traveled or the object’s
displacement? Explain.
3. You are flying 2586 miles from San Francisco to New York. An hour into the flight, you are 600 miles from
San Francisco. What is your speed in m/s?
4. The pilot looks at the speedometer on the plane and it reads 615 mph. This is a measure of the:
a. Average speed
b. Instantaneous speed
c. Average velocity
d. Instantaneous velocity
Lesson Objective: Distinguish between speed and velocity.
You get in your car to drive to school at 7:33 am and drive 10 miles north at a constant speed until 7:45 am, when you
realize you left your homework on the kitchen table. You turn around and drive 10 miles south back to your house
and retrieve your homework at 8:00 am. You get back in the car and drive 15 miles north to school at a constant
speed arriving at school at 8:29 am sharp, just in time to make it before the bell rings.
TABLE 2.2: Driving distance
Time (min) Distance (miles)
0 0
12 10
15 10
29 15
5. What is your average speed in m/s?
6. What is your average velocity?
19

2.2. Speed and Velocity in One Dimension www.ck12.org
7. If you looked at your speedometer on your drive to school and it read 30mph, this value describes your
a. Instantaneous speed
b. Average speed
c. Instantaneous velocity
d. Average velocity
Lesson Objective: Determine velocity from position-time graphs.
Describe the direction of motion of the following objects based on the slope of their position-time graphs:
8. Positive slope
9. Negative slope
10. Slope equals zero (horizontal line)
11. The following data table depicts the motion of a mouse as it runs rightward across a street. Create a position-
time graph and use your graph to derive the mouse’s velocity.
TABLE 2.3: Mouse velocity
Time (s) Position (m)
0 0
1 1
2 3
3 5
4 7
12.
Answer Key
1. Constant speed is when an object travels an equal distance in any given time period during its motion. For
example: 1 m/s describes the constant speed of a moving object. It means that the object moves 1 meter every
second. After 5 s, the object will have travelled 5 meters.
2. You need to consider an object’s displacement. Velocity is a vector, so the direction the object is moving
matters. Displacement is a vector quantity and takes direction into account. Therefore, to solve for an object’s
velocity you must divide an object’s displacement (change in position) by the change in time.
3. 600 miles
hr × 1600 m
1 mile × 1 hr
60 min × 1 min
60 s = 266.7 m
s
4. B
5. 0.625 miles/min = 16.7 m/s
6. Average speed = total distance/total time = 35 miles/56 minutes = 0.625 miles/min
7. 0.625 miles
min × 1600 m
1 mile × 1 min
60 s = 16.7 m
s
8. 0.27 miles/min = 7.2 m/s north
20

9. Average velocity = change in position/change in time =15 miles north/56 minutes = 0.27 miles/min north
10. 0.27 miles
min × 1600 m
1 mile × 1 min
60 s = 7.2 m
s
11. ?
12. A
13. A positive slope indicates a positive velocity, so the motion is to the right.
14. A negative slope indicated a negative velocity, so the motion is to the left.
15. A horizontal line indicates zero velocity, so the object is not moving.
16. The velocity of the mouse can be derived from the slope of the position-time graph.
(7 m−5 m)
(4 s−3 s) = 2 m
1 s = 2m
s
The slope of this line is +2 m/s, so the velocity is 2 m/s rightward.
21

2.3. Average Speed, Velocity, and Instantaneous Velocity www.ck12.org
2.3 Average Speed, Velocity, and Instanta-
neous Velocity
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Calculate average speed for varying rates.
The data table below describes the motion of a marble. Use the information in the data table to answer questions
#1-6.
TABLE 2.4:
t (s) x (m)
0 11
11 11
15 31
19 61
23 71
29 71
31 61
1. At t = 29 s, what is the position of the marble?
2. Solve for the total distance traveled by the marble.
3. Solve for the average speed of the marble.
4. Solve for the displacement of the marble.
5. Solve for the average velocity of the marble.
6. Create a position-time graph for the marble.
Lesson Objective: Explain what is meant by instantaneous velocity.
The data table below describes the motion of a paper airplane. Use the information in the data table to answer
questions #7-12.
22

TABLE 2.5:
t (s) x (m) v (m/s)
0 0
6 -3.2
11 -5.7
16 -8.5
21 -10.5
26 -13.2
31 -15.7
36 -18.5
7. Complete the table above by solving for the instantaneous velocity of the paper airplane.
8. Solve for the average velocity of the paper airplane.
9. What is the instantaneous velocity of the paper airplane at t=6 s?
10. Explain why the instantaneous velocity at t=6s and the average velocity of the paper airplane are different
values.
11. Create a position-time graph for the paper airplane.
12. Explain how you could use your graph determine the paper plane’s instantaneous velocity at 7 s.
Answer Key
1. The variable for the position of an object is x. According to the chart, at t=29 s, x=71 m.
2. [ |(11-11)| + |(31-11)| + |(61-31)| + |(71-61)|+|(71-71)| + |(61-71)|] = 70 m
3. Average Speed = total distance/total time
70 m/31 s = 2.3 m/s
4. Displacement:∆x = pf − pi; 61 m-11 m=50 m rightward
5. ∆v = ∆x
(tf −ti) ; 50 m/31 s = 1.6 m/s rightward
6.
23

2.3. Average Speed, Velocity, and Instantaneous Velocity www.ck12.org
7. See chart below
8. Example work to complete chart below:
v(6) = (−3.2−0
6−0 ) = −0.53
v(11) = (−5.7−0
11−0 ) = −0.52
9. v = (
pf −pi
tf −ti
); (-18.5-0)/(36-0)= -0.51 m/s leftward
10. v(6) = (−3.2−0
6−0 ) = -0.53 m/s leftward
11. The instantaneous velocity at t=6 s is -0.53 m/s leftward. This is the velocity at that exact moment in time (or
the closest approximation possible). The average velocity for the entire time of travel is -0.51 m/s leftward.
This is the average displacement of the paper airplane over the entire 36 seconds.
12.
A close approximation of the instantaneous velocity can be calculated by finding the slope of a line drawn
tangent to the curve of the position-time graph at 7 s.
24

2.4 Uniform Acceleration
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Define and explain acceleration.
1. Complete the chart below:
TABLE 2.6:
Quantity SI Units Scalar/Vector
Displacement
Speed
Velocity
Acceleration
2. Explain how an object can have a rightward velocity and a leftward acceleration.
3. If an object is moving rightward and speeding up, the sign of the acceleration must be
a. Positive
b. Negative
4. Explain the reason for your answer in question #3.
5. Explain why the following statement is a misconception, "An object does not accelerate if it remains at the
same speed but changes direction".
Provide an example for each of the following scenarios described in #6-7:
6. A moving object with a large velocity and a small acceleration.
7. A moving object with a positive velocity and a negative acceleration.
Use the information in the chart below to answer questions #8-10.
25

2.4. Uniform Acceleration www.ck12.org
TABLE 2.7:
t (s) x (m) v (m/s)
3 19 6.3
10 64 6.4
15 92 6.1
19 120 6.3
23 140 6.1
25 150 6.0
8. What is the average acceleration?
9. Create a v-t graph
10. Describe how you could use the graph to derive acceleration?
Answer Key
1.
2. ~
aavg = ∆~
v
∆t = (
vf −vi
tf −ti
)
So, if an object traveling rightward has a final velocity that is less than its initial velocity, it will have a negative
acceleration. This object is slowing down.
3. A
4. If an objects velocity and acceleration are in the same direction, an object will speed up. In this case, an
object is moving rightward, so its velocity will be positive. Therefore, in order for the object to speed up, its
acceleration must also be positive.
5. This is a misconception because acceleration is the change in velocity over time. Velocity is a vector quantity
and direction matters. If the magnitude of the velocity remains the same but the direction of motion changes,
the object still experiences acceleration.
6. Answers will vary. (Sample Answer: A jet goes from 700 mph to 705 mph in 3 seconds. The magnitude of its
velocity is very large and its acceleration is very small.)
7. Answers will vary. (Sample Answer: A train travels 60 mph north (+60 mph) and slows down to 30 mph
(+30 mph) in 10 seconds as it approaches the station. The acceleration must be negative because the train is
slowing down (30-60)/10 =-3 m/s2)
8. ~
aavg = ∆~
v
∆t = (
vf −vi
tf −ti
)
(6.0-6.3)/(25-3)=-0.01 m/s2
9.
26

10. The slope of the line in a velocity-time graph is the acceleration. You could calculate the slope of the line to
derive the acceleration.
27

2.5. The Kinematic Equations www.ck12.org
2.5 The Kinematic Equations
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Interpret area in an acceleration-time graph.
Use the graph below for questions #1-3.
1. Without doing any calculations, will the velocity at t=3 s be positive, negative or zero?
a. positive
b. negative
c. zero
2. Explain the reason for your choice in question #1:
3. Calculate the instantaneous velocity at t=3 s.
Lesson Objective: Represent motion using a velocity-time graph.
Draw the resulting velocity-time graphs for the given position-time graphs in questions #4-6.
4.
28

5.
6.
Lesson Objective: Interpret slope and area in a velocity-time graph.
Use the velocity-time graph below to answer questions #7-12.
29

2.5. The Kinematic Equations www.ck12.org
7. Without doing any calculations, predict the sign of the displacement according to the graph above.
a. positive
b. negative
c. zero
8. Explain the reason for your choice in question #6.
9. Calculate the displacement at t=10 s.
10. Without doing any calculations, will the average acceleration be positive, negative or zero?
a. positive
b. negative
c. zero
12. Calculate the instantaneous acceleration at t=10 s.
Answer Key
1. Positive
2. Answers will vary. Sample Answer: The velocity can be derived from the area under an acceleration-time
graph. The area bounded by this line is in the positive quadrant.
3. The shape of the area bounded by the line is a triangle and the equation for the area of a triangle is A = 1
2 b×h
. Velocity=(1/2)3 x 12 = +18 m/s rightward
4.
30

5.
6.
7. Positive
8. Answers will vary. Sample Answer: The displacement can be derived from the area under a v-t graph. The
area of this v-t graph is in the positive quadrant.
9. The shape of the area bounded by the line is a triangle and the equation for the area of a triangle is A = 1
2 b×h.
A=(1/2)10 x 20 = +100 m rightward
10. Positive
11. Answers will vary. Sample answers: The acceleration can be derived from the slope of the line in a v-t graph.
The slope of this line is positive.
12. slope = (∆y
∆x ) ; (20-10)/(10-5)= +2 m/s2
31

www.ck12.org
CHAPTER
3 Two-Dimensional Motion
Worksheets
Chapter Outline
3.1 INDEPENDENCE OF MOTION ALONG EACH DIMENSION
3.2 VECTOR REPRESENTATION
3.3 INERTIAL FRAMES AND RELATIVE MOTION
3.4 PROJECTILE MOTION
32

www.ck12.org Chapter 3. Two-Dimensional Motion Worksheets
3.1 Independence of Motion Along Each Di-
mension
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how motion along each axis can be resolved independently
1. Provide a real-world example that supports this concept: Motion in each dimension works independently.
2. A penny is dropped from 2 m high. How long does it take the penny to hit the floor?
3. A penny is pushed horizontally off a desk 2m high. How long does it take the penny to hit the floor?
4. Compare your answers to question #2 and question #3. Provide a reason for any similarities or differences.
5. Create a horizontal position-time (x-t) graph and a vertical position-time (y-t) graph for a penny that is pushed
off a table that is 2 m high with an initial x-velocity of 3.6 m/s.
Lesson Objective: Solve problems involving objects, which are simultaneously under the influence of uniform
acceleration and constant velocity along different dimensions
6. Complete the chart below, describing the two-dimensional motion of a soccer ball that is kicked from the
ground with an initial horizontal velocity of +3 m/s and an initial vertical velocity of +5 m/s.
Answer Key
1. Answers may vary. Sample Answer: A dropped penny and a projected penny released from the same height
will hit the ground at the same time. Although the pennies have different horizontal velocities, their vertical
velocities are the same. They both accelerate at around -10m/s2 due to the force of Earth’s gravity.
33

3.1. Independence of Motion Along Each Dimension www.ck12.org
2.
yf =
1
2
gt2
+yi
0 m =
1
2
(−10)t2
+2 m
t = 0.63 s
3.
yf =
1
2
gt2
+yi
0 m =
1
2
(−10)t2
+2 m
t = 0.63 s
4. X motion and Y motion are independent of each other. Although the pennies have different horizontal
velocities, their vertical velocities are the same. Therefore, they will hit the floor at the same time. Giving the
penny an x-velocity has no affect on the vertical motion. TIME is the only factor that is the same for both
dimensions.
5.
6.
34

3.2 Vector Representation
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain the relationship between coordinates and components.
1. In your own words, describe the components of a two-dimensional vector.
2. Provide an example of a two-dimensional vector and break it up into its components.
3. Explain the relationship between coordinates and components.
Lesson Objective: Use vectors and vector components to add and subtract vectors.
Use the following prompt for questions #4-5:
Vector ~
A has components (15,-2) and Vector ~
B has components (-1,9).
4. Find the sum of ~
A and ~
B; call the result ~
C.
5. Find the difference ~
B−~
A; call the result ~
D.
6. Draw the resultant vector of (~
S+~
T ).
S−~
T ).
35

3.2. Vector Representation www.ck12.org
T −~
S ).
Lesson Objective: Use trigonometric relationships to express vector components.
Use the diagram below of Vector ~
A to answer questions #9-13.
9. Describe how you could use trigonometry to solve for the magnitude of the X and Y components of the
two-dimensional vector ~
A.
10. Use trigonometry to solve for the magnitude of the x-component of Vector ~
A.
11. Use trigonometry to solve for the magnitude of the y-component of Vector ~
A.
36

12. What is the direction of the x-component of Vector ~
A?
a. North
b. South
c. East
d. West
13. What is the direction of the y-component of Vector ~
A?
a. North
b. South
c. East
d. West
Answer Key
1. Answers will vary. Sample Answer: A vector that is directed at an angle is two-dimensional. There is a
horizontal (x) component and a vertical (y) component that make up every two-dimensional vector.
2. Answers will vary. Sample Answer:
3. Answers will vary. Sample Answers: The coordinates (x,y) define a point on a graph. An arrow drawn from
the origin to a point on a graph creates a vector. The first number of a coordinate corresponds to the horizontal
(x) component of the vector and the second number of a coordinate corresponds to the vertical (y) component
of the vector.
4. ~
C = ((15)+(-1),(-2)+(9)) = (14,7)
5. ~
D = ((-1)-(15),(9)-(-2)) = (-16,11)
6.
7.
37

3.2. Vector Representation www.ck12.org
8.
9. Answers will vary. Sample Answer: Trigonometric functions can be used to find the magnitude of the
horizontal and vertical components of two-dimensional vectors.
10. ~
Ax = 15 cos 60 ° = 7.5
11. ~
Ay = 15 sin 60 ° = 7.5
12. D
13. A
38

3.3 Inertial Frames and Relative Motion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain frames of reference and inertial frames..
1. What is a frame of reference? Provide an example
2. What is an inertial frame of reference? Provide an example.
3. Circle the objects below that could be used as a frame of reference.
• A plane traveling at a constant velocity of 500 mph
• Your desk
• The finish line of a race
• A car using cruise control, traveling at 65 mph on the highway
• A ball in the air, accelerating at -10 m/s2 due to the Earth’s gravity
4. Explain the reason for your answer in the question above.
Lesson Objective: Solve problems involving relative motion in one dimension.
Car A is traveling 25 mph east on one side of the road.
Car B is traveling 50 mph west on the other side of the road.
5. What is the velocity of Car B relative to Car A?
a. 25 mph
b. -50 mph
c. 75 mph
d. -75 mph
6. Explain the reason for your choice above.
7. What is the velocity of Car A relative to Car B?
a. 25 mph
b. -50 mph
c. 75 mph
39

3.3. Inertial Frames and Relative Motion www.ck12.org
d. -75 mph
Lesson Objective: Solve problems involving relative motion in two dimensions.
A plane travels with a velocity of +30 m/s north.
Determine the magnitude and direction of the resultant velocity of the plane if it encounters the following:
9. -10 m/s southern headwind
10. +10 m/s northern tailwind
11. +10 m/s eastern crosswind
12. -10 m/s western crosswind
Answer Key
1. A frame of reference is a fixed point that we can use in order to measure relative directions and speeds.
Examples will vary. Sample Answer: If you are a passenger on a train, the ground could serve as a frame of
reference.
2. Objects that are moving with a constant velocity can serve as inertial frames of reference. Examples will vary.
Sample Answer: A train that is traveling at a constant speed of 65 mph could serve as a inertial frame of
reference.
3. All of the following objects could be used as a frame of reference:
• A plane traveling at a constant velocity of 500 mph
• Your desk
• The finish line of a race
• A car using cruise control, traveling at 65 mph on the highway
A ball in the air, accelerating at -10 m/s2 due to the Earth’s gravity could not be used as a frame of reference
because it does not have a constant velocity.
4. A frame of reference is a fixed point that we can use to measure relative motion. So, your desk and the finish
line of a race are fixed points we can use to measure relative motion. An object moving at constant velocity
can also serve as an inertial frame of reference. The plane and car are moving at constant velocities, so they
can be used as inertial frames of reference. The ball is a project and experiences vertical acceleration (does
not have constant velocity). Therefore, it cannot be use as a frame of reference.
5. D
6. The velocity of Car A is +25 mph and the velocity of car B is -50 mph
~
v′
b =~
vb −~
va = −50 mph−25 mph = −75 mph
7. C
40

8. The velocity of Car A is +25 mph and the velocity of car B is -50 mph
~
v′
a =~
va −~
vb = 25 mph−(−50) mph = −75 mph
9. +30 m/s + (-10 m/s) = +20 m/s
10. +30 m/s + 10 m/s= +40 m/s
11. Pythagorean Theorem:
a2
+b2
= c2
(30)2
+(10)2
= c2
31.6 m/s noramp;theast
12. Pythagorean Theorem:
a2
+b2
= c2
(30)2
+(10)2
= c2
31.6 m/s noramp;thwest
41

3.3. Inertial Frames and Relative Motion www.ck12.org
42

3.4 Projectile Motion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Draw and interpret graphs involving two-dimensional projectile motion
Draw a general sketch of the following graphs for a projectile moving rightward. In your own words, describe
what the graph means.
1. X-T: Position in the X direction as a function of time
2. Y-T: Position in the Y direction as a function of time
3. Vx-T: Velocity in the X direction as a function of time
4. Vy-T: Velocity in the Y direction as a function of time
43

3.4. Projectile Motion www.ck12.org
Lesson Objective: Solve for the instantaneous velocity of a projectile
5. You throw a baseball with an initial horizontal velocity of 1 m/s east. What will the final horizontal velocity
be when your teammate catches it 0.4s later?
6. A bowling ball is rolled with an initial horizontal velocity of 12 m/s rightward and hits the pins 1.5 seconds
later. What is the initial vertical velocity of the bowling ball?
Use the following prompt for questions #7-8.
A frog jumps with a velocity of 0.25 m/s at an angle of 30°.
7. What is the magnitude of the frog’s initial horizontal velocity?
8. What is the magnitude of the frog’s initial vertical velocity?
A marble is rolled horizontally off the edge of a 1.5 m table and lands 0.7 m away.
9. At what time did the marble hit the ground?
10. What was the initial horizontal velocity of the marble?
Lesson Objective: Predict a projectile’s range
11. The five darts described below are all thrown from the same initial position. Which will hit the ground first?
a. Dart A, with an initial vertical velocity of 20 m/s upward and an initial horizontal velocity of 0 m/s.
b. Dart B, with an initial vertical velocity of 10 m/s upward and an initial horizontal velocity of 10 m/s.
c. Dart C, with an initial vertical velocity of 15 m/s upward and an initial horizontal velocity of 0 m/s.
d. Dart D, with an initial vertical velocity of 5 m/s upward and an initial horizontal velocity of 20 m/s.
12. Neglecting air resistance, what would happen if you were a passenger in a convertible automobile traveling at
a constant velocity and threw a ball straight up in the air?
a. It would land behind the car
b. It would land in front of the car
c. It would land in the car
44

13. Explain the reasoning for your answer choice to question #12.
14. A tennis ball is hit with an initial velocity of 15 m/s at an angle of 40°. What is the horizontal displacement of
the ball after 2 s?
Answer Key
1. The slope of a position-time graph is velocity. The x-t graph of any projectile must be a straight line because
the horizontal velocity of a projectile is always constant. This graph shows a projectile moving rightward at a
constant speed.
2. The slope of a position-time graph is velocity. The y-t graph of any projectile must be parabolic because the
vertical velocity of a projectile is always changing. This acceleration is due to Earth’s gravity.
45

3.4. Projectile Motion www.ck12.org
3. The slope of a velocity-time graph is acceleration. The Vx-t graph of any projectile must have a slope of 0
because the horizontal velocity of a projectile is constant, and the object has a horizontal acceleration of 0.
4. The slope of a velocity-time graph is acceleration. The Vy-t graph of any projectile must have a slope of
-10m/s2 because this is the acceleration due to Earth’s gravity.
46

5. 1 m/s east; the horizontal velocity of a projectile remains constant
6. 0 m/s; there is no vertical component to the bowling ball’s velocity
7. ~
vx = |v|cosθ
0.25 cos30° = 0.22 m/s
8. ~
vy = |v|sinθ
0.25 sin30° = 0.125 m/s
9.
yf =
1
2
gt2
+(vy−initial)t +yi
0 m = (−5t2
+0+1.5) m
t = 0.55 s
10. xf = (vx)t + xi
0.7 = (vx)(0.55 s) + 0
vx = 1.3 m/s
11. D
12. C.
13. A projectile has constant horizontal motion. Therefore, if you are traveling inside the car and throw the ball,
the horizontal velocity of the ball and the car are the same.
14.
xf = (vcosθ)t +xi
xf = (15cos40◦
)(2)+(0) = 22.98 m
47

www.ck12.org
CHAPTER
4 Newton’s Three Laws
Worksheets
Chapter Outline
4.1 NEWTON’S FIRST LAW
4.2 NEWTON’S SECOND LAW
4.3 NEWTON’S THIRD LAW
48

www.ck12.org Chapter 4. Newton’s Three Laws Worksheets
4.1 Newton’s First Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Describe what force is and different types of forces.
1. In your own words, what is a force?
2. When do forces exist?
3. What are some examples of contact forces?
4. What are some examples of forces that act at a distance?
5. What is the standard metric unit used to measure force?
a. Kilogram (kg)
b. Meter (m)
c. Second (s)
d. Newton (N)
6. Is force a vector or scalar quantity? Circle the correct answer and explain the reason for your choice in the
space provided.
a. Vector
b. Scalar
Explanation:
7. Which of the following statements correctly describes the net force?
a. An upward force acting on an object
b. A force acting at a distance
c. A contact force
d. The sum of all the forces acting on an object
Lesson Objective: Understand the meaning of inertia and Newton’s First Law.
8. How will the same amount of force affect a small rock compared to a giant boulder?
49

4.1. Newton’s First Law www.ck12.org
9. Explain why the following statement is false. "A water bottle is sitting on a table. Since it is not moving, there
are no forces acting on it."
10. An airplane is moving at a constant velocity of 270 m/s (600 mph). What is the net force on the airplane?
Answer Key
1. A force can be simply defined as a push or pull.
2. Forces exist when two objects interact. Whenever there is an interaction between two objects, there is a force
on each of the objects (force-pair). When the objects no longer interact, there is no longer a force between
them.
3. Answers will vary. (Sample Answers: Normal Force, Air Resistance, Friction)
4. Answers will vary. (Sample Answers: Gravitational Force, Electrical Force, Magnetic Force)
5. D
6. Vector. Answer will vary. (Sample Answer: Force is a vector quantity because it has both magnitude and
direction. It can be represented by using an arrow; the length of the arrow represents magnitude and the
direction of the arrow represents the direction of the force).
7. D
8. Answers will vary. Sample answer: The inertia of an object is its resistance to a change in motion and is
directly proportional to its mass. A small rock has less mass than a giant boulder, and therefore less inertia.
As a result, the same amount of force will have a greater effect on a small rock than on a giant boulder.
9. Answers will vary. Sample answer: Forces exist whenever two objects interact. The water bottle and table
are in contact, and therefore interacting. Also, the Earth’s gravity is exerting a force on the water bottle at
a distance. The reason the water bottle is not moving is because all the forces acting on the water bottle are
balanced (the net force is zero). The upward force from the table on the water bottle and the downward force
of gravity on the water bottle are equal in magnitude and opposite in direction. According to Newton’s First
Law of Motion, the water bottle will remain at rest.
10. The airplane is moving at a constant velocity. According to Newton’s first law of motion, all the forces acting
on the airplane must be balanced and the net force must be zero if the airplane’s velocity is constant as a result
of zero acceleration.
50

4.2 Newton’s Second Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Define Newton’s Second Law and net force.
According to Newton’s Second Law of Motion, label each of the statements below as true or false.
1. (True/False): If an object experiences a net force, its velocity will change.
2. (True/False): The more force you apply to an object, the less it will accelerate.
3. (True/False): If all of the forces acting on an object are balanced, its velocity will change.
4. (True/False): A force is required to keep an object moving.
5. (True/False): If all of the forces acting on an object are not balanced, the object will accelerate.
6. (True/False): A force is required in order to slow down a moving object.
7. (True/False): If all the forces acting on an object are unbalanced, then there will be a net force on the object.
8. (True/False): A force is not required to speed up a moving object.
9. (True/False): If no force is applied to an already moving object, it will stop moving.
10. (True/False): The more massive an object, the more force it will take to change its motion.
Lesson Objective: Calculate acceleration from force and mass.
For questions #11-13, determine the resulting acceleration when a +15 N net force is applied to the following objects:
11. A 5 kg massive object
14. In your own words, explain why the same net force results in different accelerations in question #11-13 above.
Lesson Objective: Calculate force from acceleration and mass.
15. A motorcycle with a mass of 200 kg is moving at a constant velocity of +11 m/s. Calculate the magnitude of
the net force on the motorcycle.
51

4.2. Newton’s Second Law www.ck12.org
16. What net force is required to accelerate a 60 g tennis ball +15 m/s2?
17. A runner with a mass of 60 kg begins from rest and increases his speed to 3 m/s in 60 s. What is the net force
on the runner?
Lesson Objective: Calculate mass from force and acceleration.
18. A net force of +100 N was exerted on an object to increase its speed 10 m/s in 5 s.Calculate the mass of the
object.
The mass of an object is 5 kg on Earth.
19. What is the object’s weight on Earth?
a. 5 kg
b. 50 kg
c. 5 N
d. 50 N
20. What is its mass on Mars?
a. 5 kg
b. 50 kg
c. 5 N
d. 50 N
Answer Key
1. True
2. False
3. False
4. False
5. True
6. True
7. True
8. False
9. False
10. True
11. 15 N = (5 kg)(a); a = +3 m/s2
12. 15 N = (15 kg)(a); a = +1 m/s2
13. 15 N = (25 kg)(a); a = 0.6 m/s2
14. The mass of an object is inversely proportional to its acceleration. Therefore, if the net force remains constant
and the mass increases, the acceleration will decrease.
52

15. If the velocity is constant, there is no acceleration. a=0 m/s2. According to Newton’s 2nd Law (Fnet = ma), if
there is no acceleration, there is no net force. All the forces acting on the motorcycle must be balanced.
16. First, convert grams to kg. 60 g = 0.06 kg
Fnet = ma = (0.06 kg)×(+15m/s2)
Fnet = 0.9 N
17. First, solve for the acceleration: a = ∆v
∆t =
3 m
s −0m
s
60 s−0 s = 0.05m
s
2
Then, use Fnet = ma to solve for the net force.
Fnet = (60 kg)(0.05 m/s2)=+3 N
18. First, solve for the acceleration:
Then, use Fnet = ma to solve for the mass.
100 N = (m)(2 m/s2)
m = 50 kg
19. D
20. A
53

4.3. Newton’s Third Law www.ck12.org
4.3 Newton’s Third Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand Newton’s Third Law.
A box is pushed horizontally on the Earth.
For each of the following forces acting on a box, identify the reaction force according to Newton’s third law of
motion and the concept of action-reaction force pairs. Be sure to specify the following:
• the direction of the reaction force
• the type of the reaction force
• the object which the reaction force is acting on
1. Action: A rightward frictional force from the Earth acting on the box.
2. Action: A downward gravitational force from the Earth acting on the box.
3. Action: An upward normal force from the Earth acting on the box.
Lesson Objective: Understand the difference between countering force and action-reaction.
A gravitational force of -100 N from the Earth acts on a box.
4. What is the countering force to the force described above?
a. -100 N gravitational force from the box on the Earth
b. +100 N gravitational force from the box on the Earth
c. -100 N normal force from the Earth on the box
d. +100 N normal force from the Earth on the box
54

6. What is the reaction force according to Newton’s 3rd law of motion?
a. -100 N gravitational force from the box on the Earth
b. +100 N gravitational force from the box on the Earth
c. -100 N normal force from the Earth on the box
d. +100 N normal force from the Earth on the box
Lesson Objective: Use Newton’s three laws to solve problems in one dimension.
Newton’s three laws of motion explain the motion of objects as we observe in our everyday lives. In your own words,
explain each of Newton’s three laws and illustrate each of the laws using the example of the motion of a box on the
Earth.
8. Newton’s 1st Law of Motion:
9. Newton’s 2nd Law of Motion:
10. Newton’s 3rd Law of Motion:
Answer Key
1. Reaction Force: A leftward frictional force from the box acting on the Earth.
2. Reaction Force: A upward gravitational force from the box acting on the Earth.
3. Reaction Force: A downward normal force from the box acting on the Earth.
4. D
5. A countering force is a different type of force than the original force; it acts on the same object as the original
force does and is equal in magnitude but opposite in direction.
6. B
7. A reaction force is the same type of force as the original force; it acts on a different object and is also equal in
magnitude but opposite in direction.
8. Answers will vary. Sample Answer: Newton’s first law of motion addresses an object that is at rest or moving
with a constant velocity. In this situation, all of the forces acting on the object must be balanced (Fnet=0). If
a box is resting on the Earth, the downward force of gravity from the Earth is balanced by the upward normal
force from the Earth. The box will remain at rest until acted upon by another force.
9. Answers will vary. Sample Answer: Newton’s second law of motion addresses the acceleration (change in
motion) of an object. In this situation, the forces acting on the object must be unbalanced (Fnet>0 or <0).
If a person pushes a box rightward across the Earth, the rightward force of the push from the person on the
box must be greater than the leftward force of friction from the Earth on the box, giving the box a rightward
acceleration.
10. Answers will vary. Sample Answer: Newton’s third law of motion addresses action-reaction pairs. In this
situation, every object the box interacts with results in a force and every force has a reaction force pair. The
reaction force is the same type of force, acting on a different object; it is equal in magnitude, and opposite
55

4.3. Newton’s Third Law www.ck12.org
in direction. For example, the reaction force to the upward normal force from the Earth on the box is the
downward normal force from the box on the Earth.
56

www.ck12.org Chapter 5. Forces in Two Dimensions Worksheets
CHAPTER
5 Forces in Two Dimensions
Worksheets
Chapter Outline
5.1 NORMAL FORCE AND FRICTION FORCE
5.2 INCLINED PLANES
5.3 CIRCULAR MOTION
5.4 FORCES IN TRANSLATIONAL EQUILIBRIUM
57

5.1. Normal Force and Friction Force www.ck12.org
5.1 Normal Force and Friction Force
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to solve problems involving the normal force.
Lisa’s mass is 68 kg. She is in an elevator that is moving down and speeding up with an acceleration of -1.5 m/s2
1. Draw a free-body diagram to illustrate all of the forces acting on Lisa.
2. What is the magnitude and direction of the force due to Earth’s gravity acting on Lisa?
3. What is the magnitude and direction of the net force acting on Lisa?
4. What is the magnitude and direction of the normal force acting on Lisa?
5. In your own words, explain how the forces acting on Lisa are responsible for her motion according to Newton’s
laws.
Lesson Objective: Understand how to solve problems involving friction.
A dog pushes a chew toy with a mass of 3 kg horizontally on the kitchen floor. The coefficient of static friction
is 0.8 and the coefficient of kinetic friction is 0.4.
6. What is the normal force acting on the chew toy?
58

7. How much force did it take to get the chew toy to start moving? (Hint: How much force did it take to overcome
the force of static friction?)
8. How much force does it take to get the chew toy to continue sliding across the kitchen floor?
9. Which of the following would help decrease the force of kinetic friction on the chew toy?
a. Pushing down on the chew toy
b. Lifting the chew toy off the floor a little
c. Sliding the chew toy on a carpeted floor (with a coefficient of kinetic friction of 0.8)
Answer Key
1.
2. Fg = mg
(68kg)(-10 m/s2)=-680 N downward
3. FNet = ma
(68 kg)(-1.5 m/s2)= -102 N downward
4.
Fnet = FNormal−Elevator +FGravity−Earth
−102 N = FNormal−Elevator +(−680 N)
FNormal−Elevator = +578 N upward
5. Answers will vary. Sample Answer: The force due to Earth’s gravity is acting from a distance on Lisa and
is constant on Earth. The normal force is due to Lisa’s contact with the floor (surface) of the elevator. The
normal force is less than the force of Earth’s gravity at this instance, creating a net force on Lisa of -102 N
downward. According to Newton’s 2nd law of motion, an unbalanced (net) force of -102 N will cause Lisa to
accelerate downwards at -1.5 m/s2 (Fnet=ma).
59

5.1. Normal Force and Friction Force www.ck12.org
6. FN counters the force due to gravity, or the chew toy’s weight
W = mg = (3 kg)(-10 N/kg)=-3 N downward
FN = + 3 N upwards
7.
Fs = µsFn
Fs = (0.8)(3 N) = −2.4 N le ftward
FA > +2.4 N rightward
8.
Fk = µkFn
Fk = (0.4)(3 N) = −1.2 N le ftward
FA > +1.2 N rightward
9. B
10. Answers will vary. Sample answer: The normal force and the force of kinetic friction are proportional (Fk =
µkFn ). Lifting the chew toy off the floor would decrease the normal force on the chew toy, and simultaneously
decrease the force of kinetic friction.
60

5.2 Inclined Planes
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to analyze and work with forces on inclined planes.
Determine if the following statements are true or false. If false, make the statement true.
1. (True/False) If the weight of a 50 kg box on a flat surface is 500 N, then its weight on an inclined plane will
be smaller than 500 N.
2. (True/False) If the weight of a 50kg box on a flat surface is 500 N, then the normal force exerted on it when
placed on an inclined plane will be smaller than 500 N.
3. (True/False) The direction of the normal force on an object resting on an inclined plane is always opposing
the direction of the force due to gravity.
A 50 kg box is sliding down a hill with an incline of 30 degrees.
4. What is the weight of the box?
5. What is the horizontal (x) component of the weight of the box?
6. What is the vertical (y) component of the weight of the box?
7. What is the normal force on the box?
Lesson Objective: Understand how to apply Newton’s Second Law to the inclined plane problems.
A 50 kg box is sliding down a hill with an incline of 30 degrees.
61

5.2. Inclined Planes www.ck12.org
8. If sliding at a constant speed, what is the force of kinetic friction on the box?
9. If accelerating at -1 m/s2, what is the force of kinetic friction on the box?
10. If accelerating at -3 m/s2, what is the force of kinetic friction on the box?
Answer Key
1. False. The weight of a 50 kg box will be 500 N on Earth no matter what surface it rests on.
2. True. FN=mgcosθ , so the normal force will be a smaller magnitude than the weight (W = mg).
3. False. The normal force on an object resting on an inclined plane is always perpendicular to the inclined plane,
which generally is not the direction of gravity.
4. W = Fg = mg = -500 N
5. Fg−x = mg sinθ = -250 N
6. Fg−y = mg cosθ = -433 N
7. FN = mg cosθ = +433 N
8.
FNet−x = 0 N
0 N = Fg−x +Ff
Ff = −Fg−x
Ff = mgsinθ = +250 N
9.
FNet−X = 500 N
−50 N = −250 N +Ff
Ff = +200 N
10.
FNet−X = −150 N
−150 N = −250 N +Ff
Ff = +100 N
62

5.3 Circular Motion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand that in circular motion there is always an acceleration (and hence a force) that
points to the center of the circle defined by the objects motion. This force changes the direction of the velocity
vector of the object but not magnitude (the object’s speed).
The International Space Station orbits the Earth.
1. The centripetal force on the International Space Station is due to
a. The force of gravity
b. The force of kinetic friction
c. The force of static friction
d. The tension force of a rope
2. The direction of the centripetal force on the International Space Station is
a. Downward
b. Upward
c. Clockwise
d. Toward the center of the circular orbit
3. The direction of the International Space Station’s acceleration is
a. Downward
b. Upward
c. Clockwise
d. Toward the center of the circular orbit
4. Explain why the International Space Station needed rockets to get into orbit, but doesn’t need rockets to keep
it in orbit.
5. Dispel the following misconception: "The astronauts on the International Space Station are floating because
there is no gravity in space."
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5.3. Circular Motion www.ck12.org
Lesson Objective: Understand how to calculate that speed using the period of motion and the distance of its
path (circumference of the circle it traces out).
Calculate the magnitude and direction of the centripetal acceleration of the following objects moving in a circle:
6. A 2000 kg truck drives along a circular round a bout with a radius of 20 m at a constant speed of 10 m/s.
7. A 0.08 kg marble moves in a circle with a radius of 0.5 m at a constant speed of 3 m/s.
8. A 64 kg skater travels around a skate rink with a radius of 25 m at a constant speed of 2.2 m/s.
Calculate the speed of the following objects moving in a circle:
9. A 1000 kg racecar drives along a circular track with a radius of 50 m with an acceleration of 4m/s2.
10. A 70 kg runner runs around a track with a radius of 36.8 m with an acceleration of 3 m/s2.
Answer Key
1. A
2. D
3. D
4. Answers will vary. Sample Answer: To get into orbit, the ISS needed a rocket to accelerate it to a high
sideways velocity that is tangent to its orbital path. Once the ISS reaches this velocity, it no longer needs the
rocket’s force. According to Newton’s 1st law, the ISS will remain at a constant speed. The ISS is in constant
free fall around the Earth.
5. Answers will vary. Sample Answer: There is gravity in space. The International Space Station is only 205
miles (220 km) from the Earth, so the force of gravity on the astronauts is almost the same as on the Earth.
The astronauts and the International Space Station are all falling at the same rate around the Earth, which
makes the astronauts appear to be floating.
6.
ac =
v2
r
ac =
100(m
s )2
20 m
= 5
m
s
2
towards the center o f the circle
7.
ac =
v2
r
ac =
9(m
s )2
0.5 m
= 18
m
s
2
64

8.
ac =
v2
r
ac =
9(m
s )2
0.5 m
= 18
m
s
2
9.
ac =
v2
r
4
m
s2
=
v2
50
v = 14 m/s
10.
ac =
v2
r
3
m
s2
=
v2
36.8
v = 10.5 m/s
65

5.4. Forces in Translational Equilibrium www.ck12.org
5.4 Forces in Translational Equilibrium
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to apply Newton’s Second Law under equilibrium conditions in two
dimensions.
A 10 kg picture is hanging in static equilibrium on a wall by three wires as depicted below.
Complete the following chart using your understanding of Newton’s Second Law under equilibrium conditions in
two dimensions.
TABLE 5.1:
Force Horizontal (x) Component Vertical (y) Component
Weight
Tension A
Tension B
Tension C
66

TABLE 5.1: (continued)
Force Horizontal (x) Component Vertical (y) Component
Net Force
Answer Key
67

www.ck12.org
CHAPTER
6 Work and Energy
Worksheets
Chapter Outline
6.1 WORK
6.2 ENERGY
6.3 ENERGY CONSERVATION
6.4 POWER
68

www.ck12.org Chapter 6. Work and Energy Worksheets
6.1 Work
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how work is defined in physics.
1. In your own words, described the concept of work in physics.
Read the following statements and determine whether or not they represent examples of work (in the scientific sense).
Circle YES or NO, and EXPLAIN the reasoning behind your choice.
2. Sonia applies a enough force to move her couch 15 m across the room.
YES / NO. Explain:
3. Jeffrey gets extremely tired after applying a force to a giant boulder that does not move.
YES / NO. Explain:
4. Joe applies enough force to lift a 100 lb barbell directly over his head.
YES / NO. Explain:
5. A woman is applying an upward normal force to hold her purse and walking rightward.
YES / NO. Explain:
6. Which of the following statements correctly describes the relationship between force, distance and work in a
simple machine?
a. Simple machines increase the amount of force needed to move an object by decreasing the distance over
which the force is applied. The work increases as well.
b. Simple machines increase the amount of force needed to move an object by decreasing the distance over
which the force is applied. The overall work stays the same.
c. Simple machines decrease the amount of force needed to move an object by increasing the distance over
which the force is applied. The amount of work decreases.
d. Simple machines decrease the amount of force needed to move an object by increasing the distance over
which the force is applied. The overall work stays the same.
Lesson Objective: Be able to solve problems involving work.
Use the prompt below for questions #7-10:
69

6.1. Work www.ck12.org
Three different families, each driving a 2000kg rental minivan, decide to drive to a ski resort for winter break. The
first family takes Route A, the second family takes Route B, and the third family takes Route C.
7. How much work does it take to get to the ski resort?
8. How much force does it take the family traveling on Route B to get to the ski resort?
9. How much force does it take the family traveling on Route C to the ski resort?
10. Did the family that took Route A use more, less, or the same amount of energy to get to the ski resort as the
family that took Route B? Explain.
Answer Key
1. Answers will vary. Sample Answer: In physics, work is done whenever a force is applied to move an object a
distance.
2. Yes. Sample Explanation: In physics, work is the done when a force is applied over a distance.
3. No. Sample Explanation: In physics, work is the product of force and distance. The boulder does not move,
so there is no distance. As a result, no work is done. **Misconception Alert: Just because Jeff is tired does
not mean he has done work in the scientific sense.
4. Yes. Sample Explanation: In physics, work is the done when a force is applied over a distance. Joe has applied
a force to move the barbell a distance.
5. No. Sample Explanation: In order for work to be done, the force cannot be perpendicular to the direction
of motion. In this case, the purse is moving rightward and the force is upward. Therefore, the force is
perpendicular to the motion and no work is being done.
6. D
7. W = fd = (20,000 N)(700 m) = 14,000,000 J
8. Work remains the same, 14,000,000 J
14,000,000 J = F(1,150 m)
F = 12,174 N
9. Work remains the same, 14,000,000 J
14,000,000 J = F(940 m)
F = 14894 N
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10. Same amount of energy because the same amount of work (both measured in Joules).
71

6.2. Energy www.ck12.org
6.2 Energy
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the relationship between work and energy.
You lift a 1 kg object from the floor to the top of a 1.5 m high table.
1. What is the force needed to lift the object to the table?
2. How much work must you do to lift the object to the table?
3. How much energy is needed to lift the object to the table?
4. Once the object is resting on the table, where does the energy go?
Lesson Objective: Be able to distinguish between kinetic and potential energy.
Use the following prompt for questions # 5-7:
A diver climbs a ladder to the top of a diving board. Once he reaches the top, he stands on top of the diving
board. Then, he jumps off the diving board into a pool.
5. Which of the following points describes when the diver does work?
a. When the diver climbs the ladder
b. When the diver stands on the diving board.
c. When the diver is falling into the pool
6. At which of the following points does the diver have the most potential energy?
7. At which of the following points does the diver have the most kinetic energy?
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Lesson Objective: Understand the role of friction as it pertains to work and energy.
Joe pushes a box rightward with a force of 3 N, causing it to slide 2m across the floor at a constant speed.
8. How much work did Joe do on the box?
9. How much work was done by friction on the box?
Lesson Objective: Be able to solve problems involving kinetic and potential energy and friction.
A 65 kg person climbs the ladder below.
10. At which point does this person have maximum potential energy?
a. Point A
b. Point B
c. Point C
Justify your answer by solving for the Potential Energy at points A-C below.
11. Potential Energy at Point A:
12. Potential Energy at Point B:
13. Potential Energy at Point C:
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6.2. Energy www.ck12.org
Answer Key
1. F = mg = (1 kg)(10 N/kg) = 10 N
2. W = Fd = (10 N)(1.5 m) = 15 J
3. 15 J (work is energy)
4. The energy is stored as Potential Energy due to the objects height above the Earth (PE=mgh).
5. A
6. B
7. C
8. W = Fd =(3 N)(2 m) = +6 J
9. W = (-3 N)(2 m) = -6 J
10. C
11. PE = mgh = (65)(10 N/kg)(0 m) = 0 J
12. PE = mgh = (65)(10 N/kg)(1 m) = 650 J
13. PE = mgh = (65)(10 N/kg)(2 m) = 1300 J
74

6.3 Energy Conservation
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the meaning of energy conservation.
The total mechanical energy of the roller coaster below is 1800 J. The mass of the cart is 100 kg and the velocity
at Point C is +6 m/s. Assume no energy is lost due to dissipative forces such as friction.
1. What is the total mechanical energy at Point A?
a. 1000 J
b. 1800 J
c. 2800 J
d. Not enough information to determine
2. What is the total mechanical energy at Point B?
a. 1000 J
b. 1800 J
c. 2800 J
3. What is the total mechanical energy at Point C?
a. 1000 J
b. 1800 J
c. 2800 J
4. When does the cart have maximum potential energy?
a. Point A
b. Point B
c. Point C
75

6.3. Energy Conservation www.ck12.org
5. When does the cart have maximum kinetic energy?
a. Point A
b. Point B
c. Point C
Lesson Objective: Be able to use energy conservation in solving problems.
Use your understanding of energy conservation to complete the following chart regarding the roller coaster below.
Assume no energy is lost due to dissipative forces such as friction.
TABLE 6.1: Roller coaster info
Point Speed of Cart Height of Cart Kinetic Energy Potential
Energy
Total Mechani-
cal Energy
A 0 m/s 20 m 0 J 16000 J
B 16 m
C 8 m
D 10 m
Answer Key
1. B
2. B
3. B
4. A
5. C
TABLE 6.2: Roller coaster solution
Point Speed of Cart Height of Cart Kinetic Energy Potential
Energy
Total Mechani-
cal Energy
A 0 m/s 20 m 0 J 16000 J 16000 J
B 8.95 m/s 16 m 3200 J 12800 J 16000 J
C 15.5 m/s 8 m 9600 J 6400 J 16000 J
D 14.14 m/s 10 m 8000 J 8000 J 16000 J
76

6.4 Power
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how power is defined in physics.
1. In physics, power depends on what two factors?
2. In your own words, describe the relationship between power and the amount of time it takes to do work.
Lisa expends 180 W of power by doing 1800 J of work in 10 s.
Determines what happens to her power output in the following situations:
3. She takes twice as long to do the same amount of work
4. It takes her half the time to do the same amount of work
5. Did your calculations in the problems above align with your answer to question #2?
Lesson Objective: Be able to solve problems involving power.
A piano with a mass of 130 kg is lifted 10m above the ground in 5 s by a crane.
6. What is the power used by the crane, measured in watts?
7. What is the power used by the crane, measured in kilowatts?
77

6.4. Power www.ck12.org
8. What is the power used by the crane, measured in horsepower?
A second piano with the same mass is lifted 10m above the ground in 15 s by a forklift.
9. Which does the most work, the crane or the forklift? Explain.
10. Which expends the most power, the crane or the forklift? Explain
Answer Key
1. The amount of work and the rate at which the work is done (P=W/t).
2. P = W/t, so power and the time it takes to do work are inversely proportional. As the time it takes to do a
certain amount of work increases, the power decreases.
3. The power is halved
P = W/t
1800 J/20 s = 90 W</pL>
4. The power is doubled
P = W/t
1800 J/5s = 360 W</pL>
5. Yes, as the time increased the power decreased by the same factor.
6. W = (1300 N)(10 m) = 13,000 J
T = 5 s
P = W/t = 2600 W
7. 1000 W = 1 kW
2600 W · 1 kW
1000 W = 2.6 kW
8. 1hp=746W
2600 W · 1 hp
746 W = 3.5 hp
9. They both do the same work because they lift the same mass to the same height (apply the same force over the
same distance).
10. The crane expends the most power because it does the work in the least amount of time (as time decreases,
power increases).
78

www.ck12.org Chapter 7. Momentum Worksheets
CHAPTER
7 Momentum Worksheets
Chapter Outline
7.1 MOMENTUM AND IMPULSE
7.2 CONSERVATION OF MOMENTUM IN ONE DIMENSION
7.3 CONSERVATION OF MOMENTUM IN TWO DIMENSIONS
7.4 COLLISIONS AND CONSERVATION PRINCIPLES
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7.1. Momentum and Impulse www.ck12.org
7.1 Momentum and Impulse
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Know how momentum is defined.
1. What two factors does momentum depend on?
2. Describe two ways in which a skateboarder could increase their momentum.
3. Is it possible for a 1 kg object to have the same momentum as a 100 kg object? Explain.
4. Circle the object with the greater momentum:
• A bus at rest
• A car traveling 65 mph on the freeway
Lesson Objective: Be able to solve problems using momentum.
Calculate the momentum of the following massive objects in motion for questions #6-8:
6. A 533 kg blimp moving east at +75 m/s.
7. A 900 kg rocket moving northwest at 7800 m/s.
8. A 105 kg hang glider moving west at -15 m/s.
9. Which has more momentum:
• A 36,000 kg semi truck moving -2 m/s leftward
• A 0.01 kg bullet traveling at -3000 m/s leftward
10. Explain the reason for your choice.
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Answer Key
1. Mass Velocity
2. Increase their mass (wear a backpack, etc); Increase their velocity (apply a force to cause an acceleration)
3. Even though the two objects have different masses, they can be traveling at certain velocities that will make
the product of their mass and velocity (momentum) the same. The 1 kg object could be traveling at a velocity
of 100 m/s and the 100 kg object could be traveling at a velocity of 1 m/s.
4. A car traveling 65 mph on the freeway
5. The car has more momentum. The bus has no momentum because it is as rest (v = 0 m/s)
6. p = mv =(533 kg)(+75 m/s) = 39,975 kg•m/s east
7. p = mv =(900 kg)(+75 m/s) = 39,975 kg•m/s northwest
8. p = mv =(105 kg)(-15 m/s) = -1,575 kg•m/s west
9. A 36,000 kg semi truck moving -2 m/s leftward
10. p = mv =(36,000 kg)(-2 m/s) = -72,000 kg•m/s leftward p = mv = (0.01 kg)(-3000 m/s) = -30 kg•m/s leftward
81

7.2. Conservation of Momentum in One Dimension www.ck12.org
7.2 Conservation of Momentum in One Dimen-
sion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Learn the meaning of impulse force and how to calculate both impulse and impulse force
in various situations.
While driving on a highway, a semi truck hits a fly.
Determine if the following statements are true or false by circling the correct answer. Then, explain the reason for
your choice.
1. The magnitude of contact force between the fly and the semi truck are the same.
True / False. Explain:
2. The direction of contact force between the fly and the semi truck are the same.
3. The time of the collision experienced by the fly and the semi truck are the same.
4. The magnitude of the impulse experienced by both the fly and semi truck is the same.
5. The direction of the impulse experienced by both the fly and semi truck is the same.
6. The magnitude of the change in momentum for the both the fly and semi truck is the same.
7. The direction of the change in momentum for the both the fly and semi truck is the same.
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8. The magnitude of the acceleration experienced by both the fly and semi truck is the same.
9. The direction of the acceleration experienced by both the fly and semi truck is the same.
10. The magnitude of the change in velocity for the fly and semi truck is the same.
Answer Key
1. True. According to Newton’s third law, the contact force between the fly and the semi truck are action-reaction
pairs. Therefore, they are equal in magnitude and opposite in direction.
2. False. According to Newton’s third law, the contact force between the fly and the semi truck are action-reaction
pairs. Therefore, they are equal in magnitude and opposite in direction.
3. True. The time of the collision is the same for both objects in the collision.
4. True. The equation for impulse is . If the magnitude of the contact force and the time of the collision are the
same for both the fly and the semi truck, then the magnitude of the impulse must be the same.
5. False. The equation for impulse is . Although the magnitude of the force and the time of the collision are the
same for both the fly and semi truck, the direction of the forces are opposite. Therefore, the direction of the
impulse for the fly and semi truck will also be opposite.
6. True. Impulse is a change in momentum ( ). Therefore, if the magnitude of the impulse is the same, then the
magnitude of the change in momentum will also be the same for both the fly and the semi truck.
7. False. Impulse is a change in momentum ( ). Therefore, if the direction of the impulse for the fly and the semi
truck are opposite, then the direction of the change in momentum will also be opposite.
8. False. According to Newton’s 2nd law, forces equal mass times the acceleration (F = ma). The magnitude of
the contact force between the fly and the semi truck are the same. The mass of the fly is much less than the
mass of the semi truck. As a result, the magnitude of the acceleration of the fly must be much greater than the
magnitude of the acceleration of the semi truck.
9. False. According to Newton’s 2nd law, the direction of the force must be in the same direction as the
acceleration (F = ma). The direction of the contact force between the fly and the semi truck are in opposite
direction. As a result, the direction of their accelerations will also be in opposite directions.
10. False. A change in velocity is the acceleration. The acceleration of the fly is much greater than the acceleration
of the semi truck (according to Newton’s 2nd law). As a result, the change in the fly’s velocity is much greater
than the semi truck’s change in velocity.
83

7.3. Conservation of Momentum in Two Dimensions www.ck12.org
7.3 Conservation of Momentum in Two Dimen-
sions
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand conservation of momentum.
1. In your own words, describe what it means for the total momentum of a system to be conserved.
2. Provide a real world example that illustrates the conservation of momentum.
3. Set up an equation, using only the variables for mass (m) and velocity (v), which represents the total momen-
tum of a cannon and a cannon ball before and after an explosion.
tum of a tennis ball and racket before and after the racket hits the ball.
tum before and after a fly is hit by a fly swatter (and sticks to it).
Lesson Objective: Be able to solve problems using the conservation of momentum.
In the Homecoming football game, a fullback (m=60kg) moves rightward at a velocity of +2 m/s and a linebacker
(mass = 80kg) moves leftward with a velocity of -3 m/s until they collide and move together.
6. What is the initial momentum of the fullback?
7. What is the initial momentum of the linebacker?
8. What is the initial total momentum of the system?
9. What is the final total momentum of the system?
84

10. What is the final speed of the fullback and linebacker and they move together after the collision?
Answer Key
1. Answers will vary. Sample Answer: The total momentum before two objects interact will be the same as the
total momentum after they are done interacting.
2. Answers will vary. Sample Answer: The game of pool illustrates the conservation of momentum. The initial
total momentum of the system is due to the white ball and is equal to the final total momentum of all the moving
billiard balls.
3. [mcannon · vi−cannon] + [mcannon ball · vi−cannonball] = [mcannon · vf−cannon] + [mcannon ball · (−vf−cannonball)]0 kg ·
m/s = [mcannon ·vf−cannon]+[mcannon ball ·(−vf−cannonball)]
4. [mtennis racket · vi−tennis racket] + [mtennis ball · (−vi−tennis ball)] = [mtennis racket · (−vf−tennis racket)] + [mtennis ball ∗
vf−tennis ball]
5. [mfly ·vi− fly]+[mfly swatter(−vi−fly swatter)] = [(mfly +mfly swatter)vf ]
6. p = mv = (60kg)(+2m/s) = +120kgm/s rightward
7. p = mv = (80kg)(−3m/s) = −240kgm/s le ftward
8. pi−fullback + pi−linebacker = (+120 kg∗m/s−240 kg∗m/s) = −120 kg∗m/s le ftward
9. -120 kg*m/s
10. −120 kg∗m/s = (60kg+80kg)vf vf = −0.9 m/s le ftward
85

7.4. Collisions and Conservation Principles www.ck12.org
7.4 Collisions and Conservation Principles
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the difference between elastic and inelastic collisions.
Categorize each of the following collisions in questions #1-5 as elastic or inelastic by circling the correct answer.
1. (Elastic / Inelastic) A white cue ball hits the black 8-ball in a game of pool. They bounce off each other, but
both move in the same direction.
2. (Elastic / Inelastic) Brittany catches a beach ball.
3. (Elastic / Inelastic) A tennis ball hits a racket and both move in the opposite direction after the collision.
4. (Elastic / Inelastic) A fullback tackles a linebacker and they move together in the air.
5. (Elastic / Inelastic) A dog catches a ball in his mouth.
6. Describe how you distinguished between elastic and inelastic collisions in the section above.
Lesson Objective: Be able to solve problems using both energy and momentum conservation.
A skateboarder (mass = 75 kg) is standing at rest on a skateboard. His friend throws him a football (mass = 0.45
kg) with a velocity of +6 m/s rightward. Assume the ground is frictionless.
7. What type of collision is this, elastic or inelastic? Explain.
8. What is the velocity of the skateboarder (and the football) after he catches the ball?
A 0.145 kg baseball is moving through the air. At point A, the baseball is 2 m high and moving with a velocity
of +15 m/s rightward. At point B, the baseball is 3 m high and moving with an unknown velocity.
9. Use the principle of conservation of energy to determine the velocity of the baseball at point B.
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10. Determine the momentum of the baseball at point B.
Answer Key
1. Elastic
2. Inelastic
3. Elastic
4. Inelastic
5. Inelastic
6. Answers will vary. Sample Answer: In elastic collisions, the objects bounce off each other. In inelastic
collisions, the objects stick together.
7. Inelastic. The skateboarder catches the football, so they stick together.
8. (0.45 kg)(6 m/s)=(75 kg+0.45 kg)vf vf = + 0.036 m/s rightward
9. Total Energy Point A = Total Energy Point B [PEA + KEA]= [PEB + KEB] mAghA + 1/2mAvA
2=mBghB +
1/2mBvB2 (0.145 kg)(10 N/kg)(2 m) + (1/2)(0.145 kg)(15 m/s)2=(0.145 kg)(10 N/kg)(3 m) + (1/2)(0.145
kg)(vB m/s)2 19.21 J = 4.35 J +0.0725vB
2 vB = +14.32 m/s rightward
10. p = mv (0.145 kg)(14.32 m/s) = +2.08 kg•m/s rightward
87

www.ck12.org
CHAPTER
8 Statics Worksheets
Chapter Outline
8.1 ANGULAR MOMENTUM
8.2 TORQUE
8.3 TWO CONDITIONS OF EQUILIBRIUM
8.4 APPLICATIONS OF EQUILIBRIUM CONDITIONS
88

www.ck12.org Chapter 8. Statics Worksheets
8.1 Angular Momentum
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand what angular momentum is and how to use it in solving problems.
In your own words, describe the following concepts in questions #1-3:
1. Rotational Inertia:
2. Angular Velocity:
3. Conservation of Angular Momentum:
4. Describe the effect of moving a mass closer to its axis of rotation.
5. Provide a real world example that illustrates the effect of moving a mass closer to its axis of rotating.
6. What is the angular momentum of a gymnast at rest with a rotational inertia of 60 kg•m2?
a. 0 kg•m2/s
b. 10 kg•m2/s
c. 180 kg•m2/s
d. 1800 kg•m2/s
7. What is the angular momentum of a gymnast that has an angular velocity of 3 rad/s and a rotational inertia of
60 kg•m2?
a. 0 kg•m2/s
b. 10 kg•m2/s
c. 180 kg•m2/s
d. 1800 kg•m2/s
8. If the rotational inertia of a rotating object is decreased by a factor of 4, what is the resulting angular velocity
according to the conservation of angular momentum?
a. 2ω
b. 4ω
c. 6ω
d. 8ω
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8.1. Angular Momentum www.ck12.org
9. Lisa is an ice skater. During a rotation, her initial angular velocity is 4 rev/s. She moves her arms in order
to decrease her rotational inertia by 50%. Assuming the angular momentum of the system is conserved,
determine Lisa’s resulting angular velocity.
10. What is the major difference between linear momentum and angular momentum?
Answer Key
1. Answers will vary. Sample Answer: A rotating object’s tendency to keep rotating.
2. Answers will vary. Sample Answer: How quickly an object is rotating.
3. Answers will vary. Sample Answer: Angular momentum of a system will remain the same. As a result, as the
rotational inertia of a rotating object decreases, the angular velocity will increase, and the overall angular
momentum will not change.
4. Answers will vary. Sample Answer: As a result of moving a mass closer to its axis of rotation, its rotational
inertia will decrease. As a result of the conservation of angular momentum, its angular velocity will increase
and the overall angular momentum of the system will remain the same.
5. Answers will vary. Sample Answer: An ice-skater who is spinning will begin with their arms out and bring
them in, moving their center of mass closer to the axis of rotation. This will decrease the rotational inertia
and increase the angular velocity, but the overall angular momentum will remain the same.
6. A
7. C
8. B
9. If the rotational inertia decreases by 50%, then the angular velocity must increase by 50%. Therefore, Lisa’s
resulting angular velocity will be 8 rev/s.
10. In linear momentum, the inertia of an object cannot change. In angular momentum, the rotational inertia of an
object can change.
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8.2 Torque
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand what torque is and how to use it in solving problems.
1. In your own words, define torque.
2. What are the units of torque?
a. kg•m2/s
b. kg•m/s2
c. N
d. N•m
3. In your own words, describe the requirements to produce a torque?
4. Explain why the following statement is false, "A torque is a force."
5. Explain why a wrench with a long handle has a better mechanical advantage than a wrench with a short handle.
6. Explain the physics behind why football coaches instruct players to stay as low as possible.
7. The door to your physics classroom has a width of 0.7 m and requires a torque of 12 N•m to open. If the
doorknob is position 0.05 m from the left edge of the door, what is the minimum force that must be applied to
open the door?
8. Determine the magnitude of the perpendicular force that must be applied to a see-saw to cause a torque of 75
N•m, 2.5 meters away from the center fulcrum.
A bookshelf with a mass of 3 kg extends 0.33 m from a wall and remains stationary.
9. Calculate the magnitude of the torque due to the force of gravity on the bookshelf.
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8.2. Torque www.ck12.org
10. Explain why the bookshelf not rotating.
Answer Key
1. Answers will vary. Sample Answer: A torque produces rotation. It is a perpendicular force applied to a lever
arm to get an object to spin.
2. D
3. In order for a torque to be produced, there must be (1) a lever arm and (2) a perpendicular force applied to the
lever arm a certain distance away from the center of mass
4. Answers will vary. Sample Answer: A torque is not simply a force; it is a force applied perpendicular to a
lever arm to get an object to rotate. A net force causes an object to accelerate, whereas a net torque causes
an object to spin.
5. Answers will vary. Sample Answer: You can decrease the force required to turn an object by increasing the
length of the lever arm. A wrench with a longer handle will require less force than a wrench with a short
handle to do the same amount of work.
6. Answers will vary. Sample Answer: When player with a low center of mass comes into contact with another
player with a high center of mass, the player with the high center of mass is more likely to rotate or spin. This
is due to the concept of torque, τ=rFsinθ
7.
τ = rF sinθ
12N ·m = (0.7−0.05 m)(F)(sin90◦
)
F = 18.5 N
8.
τ = rF sinθ
75N ·m = (2.5 m)(F)(sin90◦
)
F = 30 N
9.
Fg = (3 kg)(10 N/kg) = 30 N
τ = rF sinθ
τ = (0.33 m)(30 N)(sin90◦
)
τ = 9.9 N ·m
10. Answers will vary. Sample Answer: Whatever is fixing the bookshelf to the wall (a bolt, etc) is also producing
a torque of equal magnitude to torque due to gravity but in the opposite direction. Therefore, the net torque
on the bookshelf is zero and it is in rotational equilibrium (as well as translational equilibrium and static
equilibrium).
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8.3 Two Conditions of Equilibrium
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the necessity for two conditions of equilibrium to ensure static equilibrium.
Describe the requirements for an object to achieve the following:
1. Rotational equilibrium
2. Translational equilibrium
3. Static equilibrium
4. Which of the following is in rotational equilibrium?
a. A wrench experiencing a net torque of 9 N•m
b. A wrench rotating with an angular acceleration of 9 rad/s2
c. A wrench experiencing both a clockwise torque of -9 N•m and a counterclockwise torque of +9 N•m
d. A wrench experiencing a net force of zero Newtons
5. Which of the following is in translational equilibrium?
a. A football experiencing a net force of +9 N
b. A football experiencing a downward force due to gravity of -4.3 N
c. A football accelerating at a rate of 9 m/s2
d. A football at rest on the field right before kick off.
6. Which of the following objects is in static equilibrium?
a. A wrench rotating with an angular acceleration of 9 rad/s2
b. A wrench experiencing both a clockwise torque of -9 N•m and a counterclockwise torque of +9 N•m
c. A football accelerating at a rate of 9 m/s2
d. A football at rest on the field right before kick off.
Answer Key
1. The net torque on an object must be zero.
2. The net force on an object must be zero.
3. Both the net force and the net torque on an object must be zero; it is therefore stable and at rest.
4. C
93

8.3. Two Conditions of Equilibrium www.ck12.org
5. D
6. D
94

8.4 Applications of Equilibrium Conditions
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Use the conditions of equilibrium to solve problems.
Jack and Jill sit on a long seesaw that is in rotational equilibrium. Jack has a mass of 35 kg and sits 3 m from the
center axis. Jill has a mass of 20 kg.
1. What is the force due to gravity on Jack?
2. What is the force due to gravity on Jill?
3. What is the magnitude of torque that Jack exerts on the seesaw?
4. What is the net torque on the seesaw?
5. How far away from the center axis is Jill sitting?
Answer Key
1.
Fg = mg
Fg = (35 kg)(10 N/kg) = −350 N downward
2.
Fg = mg
Fg = (20 kg)(10 N/kg) = −350 N downward
3.
τ = rF sinθ
τ = (3 m)(350 N) = 1050 N ·m
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8.4. Applications of Equilibrium Conditions www.ck12.org
4. If the seesaw is in rotational equilibrium, the net torque must equal zero.
5.
τjack +τjill = 0 N ·m
1050 N ·m+τjill = 0 N ·m
1050 N ·m+(?)(−200 N) = 0 N ·m
−200r = −1050 N ·m
r = 5.25 m
96

www.ck12.org Chapter 9. Newton’s Universal Law of Gravity Worksheets
CHAPTER
9 Newton’s Universal Law of
Gravity Worksheets
Chapter Outline
9.1 KEPLER’S LAWS
9.2 NEWTON’S UNIVERSAL LAW OF GRAVITY
9.3 CIRCULAR ORBITS
97

9.1. Kepler’s Laws www.ck12.org
9.1 Kepler’s Laws
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand Kepler’s Laws.
1. Create a sketch the shape of the Earth’s orbit around the sun.
2. What is an astronomical unit?
For questions #3-8, match each of the following laws with their correct explanation:
A. Kepler’s First Law
B. Kepler’s Second Law
C. Kepler’s Third Law
D. Newton’s First Law
E. Newton’s Second Law
F. Newton’s Third Law
3. _____For every action, there is an equal and opposite reaction.
4. _____A planet will move at a faster speed when positioned closer to the sun.
5. _____The orbit of each planet about the sun is an ellipse with the sun at one of the foci.
6. _____An object at rest will stay at rest, and an object in motion will remain in motion, unless acted upon by
an unbalanced net force.
7. _____FNet=ma
8. _____The square of the time for one orbital period of a planet about the sun is proportional to the cube of the
average distance between the sun and the planet.
Lesson Objective: Use Kepler’s Third Law to solve problems.
9. Express Kepler’s Third Law of Motion in your own words.
10. Express Kepler’s Third Law of Motion as an equation.
11. Use Kepler’s Third Law of Motion to solve for the constant of proportionality (k) if the period of the Earth
around the sun is one year and the distance of the Earth to the sun is one AU.
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12. Use Kepler’s Third Law of Motion to solve for the period of Pluto around the sun, in years, if the distance of
Pluto to the sun is 39.5 AU.
13. Use Kepler’s Third Law of Motion to determine the distance of Mars to the sun, in AU, if the period of Mars
around the sun is 1.87 years.
Answer Key
1. The sketch should look like an ellipse
2. An astronomical unit is the average distance between the sun and the Earth
3. F
4. B
5. A
6. D
7. E
8. C
9. Answers will vary. [Sample Answer: The square of the time for one orbital period of a planet about the sun is
proportional to the cube of the average distance between the sun and the planet]
10. T2=kr3
11. T2=kr3
(1)2=k(1)3
k=1
12. T2=kr3
T2=(39.5)3
T =
√
61629
T=248 years
13. T2=kr3
(1.87)2=(r)3
r =
3
√
3.497
r=1.52 AU
99

9.2. Newton’s Universal Law of Gravity www.ck12.org
9.2 Newton’s Universal Law of Gravity
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand Newton’s Universal Law of Gravity.
In your own words, describe each the following three terms:
1. Universal:
2. Law:
3. Gravity
4. Use your answers to questions #1-3 to re-write Newton’s Universal Law of Gravity in your own words.
5. Explain why Newton’s Universal Law of Gravity is categorized as an inverse-square law.
Label the following statements in #6-10 as true or false by circling the correct answer.
6. Of the four fundamental forces in nature, gravity is the weakest force.
a. True
b. False
7. The moon is in free fall around the Earth.
a. True
b. False
8. Mars is in free fall around the sun.
a. True
b. False
9. The force acting on an apple as it falls from a tree is different from the force acting on Venus as it orbits the
sun.
a. True
b. False
10. The Earth is pulling down on me with a force due to gravity and I am pulling up on the Earth with a force due
to gravity of equal magnitude.
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a. True
b. False
Lesson Objective: Use Newton’s Universal Law to solve problems.
11. Based on your understanding of Newton’s Universal Law of Gravity, can a massive object ever be weightless?
Refer to the equation for Newton’s Universal Law of Gravity (F = Gm1m2
r2 ) to answer questions #12-15:
12. If the distance between two objects is doubled, the force of gravity will
a. Double
b. Quadruple
c. Decrease by a factor of 4
d. Decrease by a factor of 16
13. If the distance between two objects is quadrupled, the force of gravity will
a. Double
b. Quadruple
14. If the mass of an object is doubled, the force of gravity will
a. Double
b. Quadruple
15. If the mass of both objects are doubled, the force of gravity will
a. Double
b. Quadruple
Answer Key
1. Answers will vary. Sample Answer: Applies to everything in the universe; a commonality between everything
in the universe.
2. Answers will vary. Sample Answer: A general rule based on the conclusions of repeated experiments.
3. Answers will vary. Sample Answer: The force of an attraction between massive objects.
4. Answers will vary. Sample Answer: The Universal Law of Gravity is a general rule stating that every massive
object in the universe exerts a force of attraction on all other massive objects in the universe.
5. F = Gm1m2
r2 The farther away one massive object is from another, the smaller the force of gravity is between
them. If the distance is doubled, the force of gravity between two massive objects decreases by a factor of
four.
6. A
7. A
8. A
9. B
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9.2. Newton’s Universal Law of Gravity www.ck12.org
10. A
11. Answers will vary. Sample Answer: No, because Newton’s Universal Law of Gravity states that every massive
object in the universe experiences a force due to gravity from every other massive object in the universe. In
physics, weight is equal to the force due to gravity. Therefore, a massive object can never be weightless.
Objects experience “apparent weightlessness” when they do not have a normal force countering the force due
to gravity. These objects are in free fall.
12. C
13. D
14. A
15. B
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9.3 Circular Orbits
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Use Newton’s Universal Law of Gravity and Kepler’s Third Law to solve problems.
1. Describe the major difference between the orbits of planets and the orbits of satellites.
2. When solving problems involving circular orbits, you must consider which of the following?
a. Centripetal acceleration
b. Universal gravity
c. Both A B
3. What is the distance from the center of the Earth of a satellite orbiting at a distance equal to the Earth’s radius
(Re)?
a. 1
2 Re
b. Re
c. 2 Re
d. 3 Re
4. Write an equation that could be used to calculate the force due to gravity acting on a satellite orbiting at a
distance equal to the Earth’s radius (Re).
5. Calculate the acceleration of a satellite orbiting at a distance equal to the Earth’s radius (Re).
6. Calculate the velocity of a satellite orbiting at a distance equal to the Earth’s radius (Re).
Answer Key
1. The shape of a planetary orbit is an ellipse and the shape of a satellite orbit is a circle.
2. C
3. C
4. F = Gm1m2
(2Re)2
5. a = 1
(2)2
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9.3. Circular Orbits www.ck12.org
a = 1
(2)2 (10 m/s2) = 2.5 m/s2
6. a = v2
r ;v =
√
ar
v =
q
(2.5 m/s2)(6.37∗106 m)
v = 3991 m/s
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www.ck12.org Chapter 10. Periodic Motion Worksheets
CHAPTER
10
Periodic Motion Worksheets
Chapter Outline
10.1 SIMPLE HARMONIC MOTION
10.2 MASS ON A SPRING
10.3 SIMPLE PENDULUM
10.4 WAVES AND WAVE PROPERTIES
105

10.1. Simple Harmonic Motion www.ck12.org
10.1 Simple Harmonic Motion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand periodic motion.
1. Develop a list of requirements for periodic motion.
2. Use your list of requirements above to identify all of the objects that exhibit periodic motion. Circle your
answer choices below.
a. The pendulum in a grandfather clock
b. A basketball player jumping in the air
c. An arrow flying toward a target
d. A tetherball rotating around a pole
e. The Earth rotating around the sun
f. A child on a swing
g. A vibrating guitar string
h. A car on the freeway
i. A rider on a merry-go-round
j. A mass on a spring
Lesson Objective: Understand simple harmonic motion.
3. Describe the connection between periodic motion and simple harmonic motion (SHM).
4. Describe the connection between uniform circular motion and simple harmonic motion (SHM).
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5. What are the requirements for simple harmonic motion (SHM)?
6. Explain why a child on a swing exemplifies simple harmonic motion.
7. Sketch the general shape of a position-time (x-t) graph of an object in simple harmonic motion.
Answer Key
1. Answers will vary. Sample List: (1) The object is moving (2) The object repeats its motion in a pattern (3)
The object’s repetitive motion pattern is completed in equal time intervals.
2. A,D,E,F,G,I, J
3. Answers will vary. Sample Answer: Simple harmonic motion is a type of periodic motion in which an object
moves back and forth through a point of equilibrium due to a restoring force directly proportional to the
object’s displacement.
4. Answers will vary. Sample Answer: The conditions for uniform circular motion are the same as the conditions
for SHM. Also, when an object in uniform circular motion is projected in one dimension, the object exhibits
SHM.
5. (1) There must be a restoring force, or a force returning the object to its original position, that is directly
proportional to the displacement. (2) The object moves around a point of equilibrium.
6. A child on a swing meets the two conditions for SHM. (1) The restoring force of gravity is acting on the child
and (2) the child moves back and forth around a point of equilibrium.
7.
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10.2. Mass on a Spring www.ck12.org
10.2 Mass on a Spring
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Solve problems dealing with Simple Harmonic Motion.
1. Circle all the variables below that affect the period (T) of a spring-mass system.
a. Force on the spring (Fspring)
b. Spring constant (k)
c. Distance a spring is stretched (x)
d. Mass (m)
e. Force due to gravity (Fgravity)
f. Gravitational constant (g)
2. Circle all the following statements that correctly describe the restoring force in a mass-spring system.
a. The restoring force causes the mass-spring system to move toward the point of equilibrium
b. The restoring force cause the mass-spring system to move away from the point of equilibrium
c. The direction of the restoring force is always opposite of the displacement of the mass-spring system
d. The direction of the restoring force is always the same as the displacement of the mass-spring system
e. The magnitude of the restoring force is directly proportional to the displacement of the mass-spring
system
f. The magnitude of the restoring force is inversely proportional to the displacement of the mass-spring
system
A 3 kg mass is hung on a spring that stretches 15 cm.
3. What is the spring constant (k) of the mass-spring system?
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4. What is the period (T) of the mass-spring system?
5. What is the frequency (f) of this mass-spring system?
6. What is the amplitude of this mass-spring system?
7. How many times does this mass-spring system pass through the point of equilibrium if it vibrates for 10
seconds?
Answer Key
1. B D
2. A,C, E
3. Use Hooke’s Law to determine the spring constant: Fs=kx.
Since the spring is hung, the force on the spring (Fs) is equal to the force of gravity (Fg).
Fg = mg = (3 kg)(10 N/kg) = 30 N
30 N = k(0.15 m)
k = 200 N/m
4.
T = 2π
r
m
k
= 2π
s
3 kg
200 N/m
= 0.8 s
5.
f =
1
T
=
1
0.8
= 1.25 Hz
6. The amplitude (A) is the maximum distance from equilibrium and will be 0.15 m for this mass-spring system.
7. The mass will pass through the point of equilibrium two times each cycle. Its period is 0.8 s, so it takes 0.8
s for this spring-mass system to complete one cycle. If it is allowed to vibrate for 10 s, it will complete 12.5
cycles (10 s/0.8 s = 12.5 cycles). As a result, it will pass through the point of equilibrium 25 times in 10 s
(12.5 cycles x 2 times through the point of equilibrium =25 times passing through the point of equilibrium).
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10.3. Simple Pendulum www.ck12.org
10.3 Simple Pendulum
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand a simple pendulum.
Use the illustration of the pendulum below to answer questions #1-5:
1. Using words only, describe the period of the pendulum above.
2. Calculate the period of the pendulum.
3. Using words only, describe the frequency of the pendulum.
4. Calculate the frequency of the pendulum.
5. Sketch a position-time (x-t) graph of the pendulum as it moves back and forth from point A to point B.
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Lesson Objective: Solve problems involving a simple pendulum.
If a period of a pendulum with a 2m string is 2.8 seconds on Earth, calculate the period of the pendulum in the
following situations:
6. The mass of the pendulum bob is doubled
7. The length of the string is halved
8. The amplitude of the pendulum increases
9. An astronaut takes the pendulum to the moon where the gravitational constant, g, is 1.6N/kg
10. A spaceship takes the pendulum to Saturn, where the gravitational constant, g, is 11.2 N/kg.
Answer Key
1. The period of the pendulum above is from Point A to Point B and back to Point A again.
2.
T = 2π
s
L
g
= 2π
s
0.7 m
10 N/kg
= 1.7 s
3. The frequency of the pendulum is the reciprocal of the period (f=1/T)
4. f=1/t ; f = 0.6 Hz
111

10.3. Simple Pendulum www.ck12.org
5.
6. The period of a pendulum is independent of the mass, so it will remain 2.8 s.
7.
T = 2π
s
L
g
= 2π
s
1 m
10 N/kg
= 1.99 s
8. The period of a pendulum is independent of the amplitude, so it will remain 2.8 s.
9.
T = 2π
s
L
g
= 2π
s
2 m
1.6 N/kg
= 7.02 s
10.
T = 2π
s
L
g
= 2π
s
2 m
11.2 N/kg
= 2.64 s
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10.4 Waves and Wave Properties
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Be able to distinguish between types of waves.
1. What does a wave transport?
2. Explain how to distinguish between a longitudinal wave and a transverse wave.
3. Explain why a beach ball in the ocean will bob vertically up and down as a wave travels horizontally to the
shore.
4. Explain why a sound wave is classified as a longitudinal wave.
Use the following information to answer questions #5-6
A coiled spring, such as a slinky, can produce both transverse and longitudinal waves.
5. Describe how to move a slinky in order to produce a longitudinal wave.
6. Describe how to move a slinky in order to produce a transverse wave.
Lesson Objective: Be able to recognize the behavior of waves.
Classify each of the following examples of wave phenomena in questions #7-10 as a result of reflection, refraction,
or diffraction. Then, explain the reason for your choice.
7. Light passing through a small crack in the door illuminates an entire room
• Reflection
• Refraction
• Diffraction
Explain:
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10.4. Waves and Wave Properties www.ck12.org
8. A microscope bends light to magnify objects
• Reflection
• Refraction
• Diffraction
Explain:
9. Your voice echoes in an empty room
• Reflection
• Refraction
• Diffraction
Explain:
10. A telescope bends light in order to view objects very far away
• Reflection
• Refraction
• Diffraction
Explain:
Answer Key
1. Energy
2. A longitudinal wave causes vibrations parallel to the direction the wave is travelling. A transverse wave causes
vibrations perpendicular to the direction the wave is traveling.
3. An ocean wave is an example of a transverse wave.
4. A sound wave causes air molecules to vibrate back and forth, parallel to the direction the wave is traveling.
5. You need to move the slinky in a direction parallel to the direction of the wave energy to create a longitudinal
wave on a slinky. Therefore, you must move the slinky horizontally back and forth as the wave propagates
horizontally back and forth.
6. You need to move the slinky in a direction perpendicular to the direction of the wave energy to create a
transverse wave on a slinky. Therefore, you must move the slinky vertically up and down as the wave
propagates horizontally back and forth.
7. Diffraction. Explanations will vary. Sample explanation: Diffraction is the ability of light waves to spread
out. This explains how light traveling from a small crack in the door can spread out and illuminate a large
room.
8. Refraction. Explanations will vary. Sample explanation: When a wave bends, it exhibits refraction. In this
case, light bends to make an object appear larger.
9. Reflection. Explanations will vary. Sample explanation: Whenever a wave bounces, it is described as
reflecting. In this case, sound waves bounce off the walls in an empty room.
10. Refraction. Explanations will vary. Sample explanation: When a wave bends, it exhibits refraction. In this
case, light bends to make an object appear closer.
114

www.ck12.org Chapter 11. Vibrations and Sound Worksheets
CHAPTER
11 Vibrations and Sound
Worksheets
Chapter Outline
11.1 TRANSMISSION OF SOUND
11.2 WAVE SPEED
11.3 RESONANCE WITH SOUND WAVES
11.4 DOPPLER EFFECT
115

11.1. Transmission of Sound www.ck12.org
11.1 Transmission of Sound
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Describe how mechanical waves are transmitted.
1. Describe the conditions necessary to create a sound wave.
2. How are mechanical waves transmitted?
3. Why are sound waves classified as mechanical waves?
4. In your own words, define the term “medium”.
5. Predict what would happen to the vibration caused by your vocal cords if you screamed in outer space.
Lesson Objective: Explain what is meant by the superposition of waves and interference.
For questions #6-8, define the following terms in your own words:
6. Superposition
7. Constructive Interference
8. Destructive Interference
9. Explain how two sound waves can interfere to cancel each other out.
10. Explain how two sound waves can interfere to create a louder sound.
11. Explain the relationship between wave interference and beats.
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Use the following prompt to answer question #12:
Two sound waves have different amplitudes but the same wavelength and period. The first wave has an amplitude
of 5 m and the second wave has an amplitude of 2 m.
12. Which of the following statements is correct?
a. The maximum amplitude created as a result of their superposition is 3 m.
b. The minimum amplitude of created as a result of their superposition is 3 m.
c. The two waves will only experience constructive interference.
d. The two waves will only experience destructive interference.
Answer Key
1. Answers will vary. Sample answer: (1) There is a medium, or interacting particles, that the sound wave moves
through (2) There is an original source causing the initial vibration (3) The sound wave is transported from
one place to another as a result of particle interactions (the energy is transferred but each particle experiences
no net displacement).
2. Answers will vary. Sample answer: An original source causes a vibration (such as a speaker), which induces
vibrations in the particles nearby (such as air molecules. These particle interactions allow the wave energy
to be transmitted but each individual particle experiences no net displacement.
3. They require a medium to move through (unlike light waves that can move through a vacuum).
4. A medium is the group of particles in which a wave moves through. An example of a medium is water, in
which sonar sound waves move through.
5. Nothing –there would be silence because sound is a mechanical wave and requires a medium to move through.
Therefore, a scream in the vacuum of outer space would produce no sound (spooky!).
6. When two wave amplitudes are added together
7. When two waves are in phase and their superposition results in a larger amplitude (louder sound).
8. When two waves are out of phase and their superposition results in a smaller amplitude (quieter sound).
9. When two sound waves are completely out of phase, their superposition will result in complete destructive
interference or an amplitude of zero.
10. When two sound waves are in phase, their superposition will result in constructive interference and their
amplitude will get larger. The amplitude of a sound wave is related to its perceived loudness, so as the
amplitude increase the loudness increases.
11. When two waves interfere with similar frequencies, they create beats as a result of periodic constructive and
destructive interference.
12. B
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11.2. Wave Speed www.ck12.org
11.2 Wave Speed
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Solve problems involving wavelength, wave speed, and frequency.
Use the image of Wave A below to answer questions #1-5:
1. What is the period of Wave A?
a. 1 s
b. 4 s
c. 5 s
d. 7 s
2. What is the frequency of Wave A?
a. 0 Hz
b. 0.1 Hz
c. 0.2 Hz
d. 0.4 Hz
3. What is the amplitude of Wave A?
a. 0 m
b. 8 m
c. 12 m
d. 16 m
4. If the frequency of Wave A increased, what would happen to the wavelength?
a. Increase
b. Decrease
c. Stay the same
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5. If the frequency of Wave A increased, what would happen to the wave speed?
a. Increase
b. Decrease
c. Stay the same
Describe the affect on the following properties of a sound wave as it travels from a violin string, through the air, to
the ear of the violinist by circling the correct choice. Then, explain the reason for your choice.
6. Wave Speed
Changes
Remains the Same
Explain:
7. Frequency
Changes
Remains the Same
Explain:
8. Wavelength
Changes
Remains the Same
Explain:
9. Calculate the wavelength of sound waves that bats can hear if they occur at frequencies around 80,000 Hz.
10. Calculate the wavelength of sound waves that humans can hear if they occur at a maximum frequency of
20,000 Hz.
Answer Key
1. B
2. C
3. C
4. B
5. C
6. Changes; Sample Explanation: When a sound wave travels from one medium to another, it changes speed.
7. Remains the same; Sample Explanation: When a sound wave travels from one medium to another, the
frequency remains the same.
8. Changes; Sample Explanation: When a sound wave travels from one medium to another, the wavelength
changes (it is directly proportional to the wave speed).
9. v=fλ
343 m/s = (80,000 Hz)(λ)
119

11.2. Wave Speed www.ck12.org
λ=4*10−3 m
10. v=fλ
343 m/s = (20,000 Hz)(λ)
λ=2*10−2 m
120

11.3 Resonance with Sound Waves
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the conditions for resonance.
1. Describe the condition(s) necessary for resonance to occur.
2. Describe an example of resonance in detail, demonstrating your understanding of the concept.
Lesson Objective: Solve problems with strings and pipes using the condition for resonance.
A 0.3 m violin string vibrates in the third harmonic at 3430 Hz.
3. Create a sketch of the standing wave on the violin string at the third harmonic.
4. Calculate the speed of the wave on the violin string above.
5. Compare the velocity of the wave on the violin string (your answer to question #2) to the velocity of the sound
wave it creates in the air. If the two velocities differ, explain why.
A sound wave travels through a 2 m organ pipe, open at both ends, with a speed of 343 m/s.
6. Calculate the frequency and provide a sketch of the standing wave created at the 1st Harmonic in the space
below:
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11.3. Resonance with Sound Waves www.ck12.org
7. Calculate the frequency and provide a sketch of the standing wave created at the 2nd Harmonic in the space
below:
8. Calculate the frequency and provide a sketch of the standing wave created at the 3rd Harmonic in the space
below:
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Use the image of a standing wave produced in a pipe closed at one end to answer questions #9-10:
9. How many nodes are present in the standing wave illustrated above?
a. Zero
b. One
c. Two
d. Three
10. What is the harmonic of the standing wave illustrated above?
a. First
b. Second
c. Third
d. Fourth
Answer Key
1. Answer will vary. Sample Answer: The forced vibration frequency matches the natural frequency, causing the
amplitude of vibration to dramatically increase.
2. Answers will vary. Sample Answer: Pushing a child on a swing is a great example of using resonance to
increase the amplitude of an object in simple harmonic motion. When a parent’s “push frequency” matches
their child’s “swing frequency”, the amplitude of the swinging child will greatly increase. This is due to
the phenomenon of resonance, when the forced vibration frequency of one object is the same as the natural
frequency of another object, causing a dramatic increase in the second object’s amplitude.
3.
4. v=fλ
V=(3430 Hz)(0.2m)=686 m/s
5. Answers will vary. The speed of the wave on the violin string is faster than the speed of sound in air. The
velocity of the wave on the violin string is 686 m/s, which is double the speed of sound in air traveling at 343
m/s. This is due to the material the violin string is made of, which allows the wave energy to travel faster
through it than the molecules in the air. The speed of a wave depends on the medium. When the wave travels
from the violin string to the air, the frequency remains the same and the wave speed and wavelength change.
6.
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11.3. Resonance with Sound Waves www.ck12.org
• The wavelength of this wave is 2m x 2 = 4m
• The velocity of this wave is equal to the speed of sound in air (343 m/s)
• v=fλ
• 343 m/s=(f)(4 m)
• f=85.75 Hz
7.
• The second harmonic will occur at a frequency two times the first harmonic (fn=nf1)
• 85.75 Hz * 2 = 171.5 Hz
8.
124

• The third harmonic will occur at a frequency three times the first harmonic (fn=nf1)
• 85.75 Hz * 3 = 257.25 Hz
9. B
10. A
125

11.4. Doppler Effect www.ck12.org
11.4 Doppler Effect
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the Doppler effect.
1. In your own words, explain why a sound becomes higher in pitch as it approaches you.
Demonstrate your understanding of how the Doppler effect influences the following properties of sound waves as a
result of a sound source traveling away from an observer by answering questions #2-7 below:
2. Wavelength
a. Increases
b. Decreases
c. Remains constant
3. Frequency
a. Increases
b. Decreases
c. Remains constant
4. Wave Speed
a. Increases
b. Decreases
c. Remains constant
5. Amplitude
a. Increases
b. Decreases
c. Remains constant
6. The perceived pitch decreases as a result of the change in
a. Wavelength
b. Wave speed
c. Frequency
d. Amplitude
7. The perceived loudness decreases as a result of the change in
a. Wavelength
b. Wave speed
c. Frequency
d. Amplitude
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8. An ambulance is driving with a velocity of 11 m/s and its siren blaring at 670 Hz. Calculate the frequency you
hear as it approaches you in the space below.
Answer Key
1. According to the Doppler effect, if the source of sound is moving towards you, the waves are being compressed
and the wavelengths are decreasing. As the wavelengths decrease, the frequencies increase because the speed
of sound in air remains constant. The frequencies of the sound waves are related to the pitch. So, as the
frequencies increase, the overall pitch will increase as well.
2. A
3. B
4. C
5. A
6. C
7. D
8. f′ = f v+vr
v+vs
670 Hz( 343 m/s
343 m/s−11 m/s ) = 692.2 Hz
127

www.ck12.org
CHAPTER
12 Fluid Mechanics
Worksheets
Chapter Outline
12.1 PRESSURE IN FLUIDS
12.2 MEASURING PRESSURE
12.3 PASCAL’S LAW
12.4 ARCHIMEDES’ LAW
12.5 BERNOULLI’S LAW
128

www.ck12.org Chapter 12. Fluid Mechanics Worksheets
12.1 Pressure in Fluids
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand density and be able to solve problems with density.
1. In your own words, explain the difference between weight and density.
2. Provide an example of two objects with the same weight and different densities.
A wood block made of pine has a mass of 3.7 g and a volume of 10 cm3.
3. Calculate the density of the wood block in kg/m3.
4. Calculate the specific gravity of the wood block compared to water (1000 kg/m3).
5. Using your calculations above, do you believe the wood block will sink or float when placed in a pool of
water? Explain.
Lesson Objective: Understand pressure and be able to solve problems with pressure.
6. In your own words, explain the difference between force and pressure.
7. Provide an example of two objects with the same force and different pressures.
Describe how the following variables affect the pressure of a fluid at rest in the space provided:
8. Volume
129

12.1. Pressure in Fluids www.ck12.org
9. Shape of the Container
10. Density
11. Depth
12. The size of the container
13. Calculate the amount of force exerted by the atmosphere on the roof of your house (area = 95 m2) if the
pressure is 101,000 Pa.
Answer Key
1. Answers will vary. Sample Answer: Weight is the force of gravity on an object due to its mass. It can be
calculated by multiplying the mass of an object by the gravitational constant “g” on Earth (10 N/kg). The
more mass an object has, the more the Earth’s gravity will pull on it, causing an increase in its weight. Density
is the measure of how much mass is present in a given volume (mass per unit volume). The more mass in a
certain volume, the denser the object will be.
2. Answers will vary. Sample Answer: Box A has a volume of 0.5 m3 and Box B has a volume of 1 m3. Both
boxes have a mass of 15 kg. The weight of both Box A and Box B are the same (150 N), but the densities
differ. The density of Box A is 30 kg/m3 and the density of Box B is 15 kg/m3. This is because Box A has
more mass per unit volume.
3.
ρ =
m
v
ρ =
3.7 g
10 cm3
= 0.37
g
cm3
0.37 g
1cm3
×
1 kg
1000 g
×
(100 cm3
1m3
= 370 kg/m3
4.
sg =
density
1000 kg/m3
sg =
370 kg
m3
1000 kg
m3
= 0.37
5. The wood block will float because its density is less than the density of water, as shown by its specific gravity
being less than 1.
6. Answers will vary. Sample answer: Force is a push or pull. Pressure is the amount of force exerted over a
specific area.
7. Answers will vary. Sample answer: Person A and Person B are both 60kg. When person A stands on both
his feet (area = 0.09m2), he exerts a normal force of 600 N downward and produces a pressure of 6667 N/m2.
When person B stands on just one foot (area = 0.045m2), he also exerts a downward normal force of 600N but
produces a pressure of 13,333 N/m2.
130

8. Volume has no affect on the pressure of a fluid at rest.
9. The shape of a container has no affect on the pressure of a fluid at rest.
10. As the density of a fluid increases, the pressure increases.
11. As the depth of a fluid increases, the pressure increases.
12. The size of a container has no affect on the pressure of a fluid at rest.
13. P = F
A
F/95m2=101,000 Pa
F = 9,595,000 N
131

12.2. Measuring Pressure www.ck12.org
12.2 Measuring Pressure
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how atmospheric pressure is measured.
1. Is the following statement true or false, “Air molecules have a weight”.
a. True
b. False
2. Describe atmospheric pressure in your own words.
3. Explain why the roof of your house does not collapse under atmospheric pressure?
Briefly explain how atmospheric pressure is related to each of the following:
4. A drinking straw
5. A suction cup
6. A vacuum cleaner
7. What instrument do we use to measure the pressure of the atmosphere?
8. The atmospheric pressure in the mountains is the atmospheric pressure at sea level.
a. Greater than
b. Less than
c. Equal to
Lesson Objective: Understand how gauge pressure is defined.
9. What is gauge pressure?
132

10. What is the total pressure of a tire with a gauge pressure of 151.7kPa?
a. 101.3 kPa
b. 151.7 kPa
c. 253 kPa
d. 303.4 kPa
Answer Key
1. A
2. Answers will vary. Sample Answer: The pressure created by the force of gravity acting on air molecules in
the Earth’s atmosphere over a certain area.
3. Answers will vary. Sample Answer: The atmospheric pressure on both sides of the roof are equal and opposite,
making the net pressure on the roof zero.
4. Answers will vary. Sample Answer: By sucking, you reduce the air pressure in the straw. The atmospheric
pressure pushes down on the surface of the drink, causing it to go up into the straw. A straw works by using
the atmospheric pressure to PUSH liquid into the straw.
5. Answers will vary. Sample Answer: A suction cup reduces the air pressure on one side of the cup, so the
atmospheric pressure pushes on the other side of the cup, causing it to stick. Again, the atmospheric pressure
is PUSHING on the suction cup.
6. Answers will vary. Sample Answer: A vacuum cleaner reduces the air pressure inside the vacuum and relies
on atmospheric pressure to push the dirt up into the device. The dirt is not sucked up, but rather PUSHED up
into the vacuum.
7. Barometer
8. B
9. Answers will vary. Sample answer: Any pressure added to a system in addition to atmospheric pressure.
10. C
133

12.3. Pascal’s Law www.ck12.org
12.3 Pascal’s Law
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand and be able to solve problems using Pascal’s Law.
1. Explain the connection between Pascal’s Law and hydraulic machines.
2. Hydraulic lifts
a. obey the law of conservation of energy
b. produce more output energy than input energy
c. produce more output work than input work
d. do not provide a mechanical advantage
3. Draw a sketch of a hydraulic lift and label each of the parts.
Use the following prompt for questions #4-5
A hydraulic lift has a large piston with an area of 2.5 m2and a small piston with area of 1 m2.
4. What force must be applied by the large piston to lift a 1500 kg vehicle upward at a constant speed?
5. What force must be applied to the small piston to lift a 1500 kg vehicle upward at a constant speed?
Answer Key
1. Answers will vary. Sample Answer: Pascal’s law states that the pressure (P=F/A) will remain constant
everywhere in a liquid. Hydraulics work by applying a small input force over a small area and generating
a large output force over a large area.
2. A
3. Sketches will vary. All sketches should include a small piston filled with fluid connected to a large piston.
Pressure on the fluid in the smaller piston is transferred directly to pressure on the large piston.
4. To lift a 1500 kg vehicle at a constant speed, the upward force must be equal to the downward force of gravity
(or the vehicle’s weight).
F = mg = (1500 kg)(10 N/kg) = 15,000 N.
134

5. F1/A1=F2/A2
F1 = 15,000 N; A1 = 2.5m2
F2 = ?; A2 = 1m2
15,000 N/2.5 m2 = x/1m2
F2= 6000 N
135

12.4. Archimedes’ Law www.ck12.org
12.4 Archimedes’ Law
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand buoyancy and how it applies to Archimedes’ Law.
1. In your own words, describe displacement as it relates to fluid mechanics.
2. In your own words, describe the buoyant force.
3. Describe how does Archimedes’ Law combines displacement and the buoyant force.
For questions #4-6, consider the following statements regarding a rubber ducky floating in a tub of water. Label each
statement as true of false and include an explanation for your choice.
4. There are two forces acting on the rubber ducky.
a. True
b. False
Explain:
5. The magnitude of the buoyant force is equal to the weight of the rubber ducky.
a. True
b. False
Explain:
6. According to Archimedes’ Law, the weight of the rubber ducky determines if it will float or not.
a. True
b. False
Explain:
Lesson Objective: Be able to solve problems using Archimedes’ Law.
136

An aluminum cube with a volume of 1 m3has a density of 2700 kg/m3and is submerged in water with a density
of 1000 kg/m3.
7. Calculate the weight of the aluminum cube.
8. Calculate the buoyant force on the aluminum cube.
9. Calculate the weight of the water displaced by the aluminum cube.
10. Will the aluminum cube sink or float? Provide an explanation for your choice.
Answer Key
1. Answers will vary. Sample Answer: In fluid mechanics, displacement occurs when an object is placed in a
fluid and causes the fluid to move out of the way.
2. Answers will vary. Sample Answer: The buoyant force is the upward force from a fluid on an object ( ).
According to Archimedes’ Law, the buoyant force is equal to the weight of the fluid that is displaced by the
submerged object.
3. Answers will vary. Sample Answer: According to Archimedes’ Law, the buoyant force is equal to the weight
of the fluid that is displaced by the submerged object.
4. True. Sample Explanation: There is a downward gravitational force and an upward buoyant force acting on
the rubber ducky.
5. True. Sample Explanation: The rubber ducky is floating, so the downward force of gravity (weight) must be
balanced by the upward buoyant force.
6. False. Sample Explanation: Archimedes Law states that the buoyant force is equal to the weight of the fluid
the object displaces. Therefore, the weight of the displaced fluid determines if the ducky will float.
7. Solve for the mass of the cube using the equation for density (ρ = m
v );
2720 kg
m3 = x
1 m3 = 2720 kg
Then, use this mass to solve for the weight (force due to gravity); Fgravity = mg = (2729 kg)(10 N/kg) = 27,290
N
8. F_b = ρVg
Fb = (1000 kg/m3)(1 m3)(10 N/kg)=10,000 N
9. 10,000 N. According to Archimedes’ Law, the weight of the water displaced by the aluminum cube will be
equal to the buoyant force.
10. Answers will vary. Sample Answers: The aluminum cube will sink because the gravitational force (weight)
is greater than the buoyant force. As a result, there is a net downward force and, according to Newton’s 2nd
Law, the aluminum cube will experience a downward acceleration (it will sink). Other reasons include: The
aluminum cube does not displace its weight in water, and therefore will sink. The density of the aluminum
cube is greater than the density of water, and therefore it will sink.
137

12.5. Bernoulli’s Law www.ck12.org
12.5 Bernoulli’s Law
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand Bernoulli’s principle and be able to discuss its implications.
Use Bernoulli’s principle to answer the following questions:
1. When the speed of a fluid is high, the pressure is
a. Low
b. High
2. When the speed of a fluid is low, the pressure
a. Low
b. High
3. As air moves faster, the pressure
a. Decreases
b. Increases
4. As air moves slower, the pressure
a. Decreases
b. Increases
5. In baseball, a pitched curve ball causes air to spin faster on top of the ball and slower on the bottom of the ball,
resulting in the ball traveling along a curved path. According to Bernoulli’s principle, describe the pressure
on the top of the ball compared to the bottom of the ball.
Answer Key
1. A
2. B
3. A
4. B
5. Answers will vary. Sample Answer: According to Bernoulli’s principle, the faster the air moves, the lower the
pressure. Therefore, there will be less pressure on top of the ball than on the bottom of the ball.
138

www.ck12.org Chapter 13. Heat Worksheets
CHAPTER
13 Heat Worksheets
Chapter Outline
13.1 TEMPERATURE
13.2 KINETIC THEORY OF TEMPERATURE
13.3 HEAT
13.4 HEAT TRANSFER
13.5 SPECIFIC HEAT
139

13.1. Temperature www.ck12.org
13.1 Temperature
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain what is meant by temperature.
1. Circle all of the following statements that correctly complete the following sentence:
Temperature is ...
a. the measurement that describes how hot or cold an object is
b. only used to determine the amount of heat in a liquid
c. related to the motion of the atoms in an object
d. the energy transferred between two objects
e. related to the average kinetic energy of the atoms in an object
f. the measure of how much heat is required to boil water
g. commonly measured with a thermometer
h. measured in Fahrenheit
i. measured in Celsius
j. measured in Kelvin
k. measured in calories
l. measured in Joules
Lesson Objective: Use the centigrade (Celsius) and Kelvin temperature scales.
2. Circle all of the following temperatures in which water will freeze:
a. 373 K
b. 212°F
c. 20°C
d. 32°F
e. 293 K
f. 0°C
g. 68°F
h. 273 K
i. 100°C
3. Circle all of the following temperatures in which water will boil:
a. 373 K
b. 212°F
c. 20°C
d. 293K
e. 68°F
f. 32°F
g. 0°C
140

h. 273K
i. 100°C
Answer Key
1. A, C, E, G, H, I, J
2. D, F, H
3. A, B, I
141

13.2. Kinetic Theory of Temperature www.ck12.org
13.2 Kinetic Theory of Temperature
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Describe the relationship between temperature and kinetic energy.’
Describe the atomic movement in each of the following objects using words, pictures, or a combination of both:
1. A solid wood block
2. Water in a glass
3. Helium in a balloon
4. In your own words, describe the relationship between temperature and kinetic energy.
5. The internal energy (total energy) of a substance is
a. dependent only on the temperature
b. independent of the number of individual atoms
c. directly proportional to both the temperature and the number of individual atoms
d. the measure of the average kinetic energy of all the atoms
6. Which of the following objects has the highest average kinetic energy?
a. An ice cube
b. A pool of cool water
c. A cup of warm water
d. A cup of boiling water
7. Which of the following objects has the highest internal energy?
a. An ice cube
b. An large pool of water at room temperature
c. A cup of warm water
d. A cup of boiling water
Answer Key
1. Answers may vary. Sample answer: The atoms of this solid wood block vibrate back and forth in place.
142

2. Answers may vary. Sample answer: The atoms of the water (liquid) in a glass are free to move around each
other.
3. Answers may vary. Sample answer: The atoms of the Helium (gas) in this balloon can move freely in any
direction.
4. Answers will vary. Sample Answers: Temperature is the measure of the average kinetic energy of the atoms
in an object. As temperature increase, the average kinetic energy of the atoms in an object increases.
5. C
6. D
7. B
143

13.3. Heat www.ck12.org
13.3 Heat
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain the relationship between heat and energy transfer.
1. Heat is the transfer of
a. Temperature
b. Energy
c. Mass
d. Force
2. What causes heat to transfer from one object to another?
3. Describe the direction of heat flow between two objects.
4. In your own words, describe the difference between heat, temperature, and internal (thermal) energy.
Determine if the following statements are true or false. Then, explain the reason for your choice.
5. A hot object contains a lot of heat.
True
False
Explain:
6. Heat and temperature are two ways to describe the same thing.
True
False
Explain:
Lesson Objective: Describe how the calorie is a measure of energy.
7. What does one calorie measure?
144

8. How many Joules of energy are in one calorie?
9. What is the difference between a calorie and a food calorie?
10. How many Joules of energy are in a food calorie?
11. Convert 400 food Calories into Joules.
Answer Key
1. B
2. A difference in temperature between two objects.
3. Heat flows from an object with a higher temperature to an object with a lower temperature.
4. Answers will vary. Sample Answer: Heat is the transfer of energy. Temperature is the measure of the average
kinetic energy of the atoms in an object. Internal energy is directly proportional to both the temperature of an
object and the amount of atoms that make up an object.
5. False. A hot object does not contain heat; it contains internal energy. Heat is the energy transferred by a hot
object to a cold object. An object cannot contain heat.
6. False. Heat is the energy transferred between two objects with different temperatures. Temperature is the
measure of the average kinetic energy of the atoms in an object.
7. A calorie measures energy. One calorie is the amount of energy needed to raise the temperature of one gram
of water by one degree Celsius.
8. 4.186 J
9. 1000 calories = 1 food calorie.
10. 4186 J
11. 400 Calories× 4186 J
1 Calorie = 1,674,000 J
145

13.4. Heat Transfer www.ck12.org
13.4 Heat Transfer
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Describe how energy is transported through the processes of conduction, convection, and
radiation.
1. How is heat transferred through the process of conduction?
2. Provide an example of heat transfer through conduction.
3. How is heat transferred through the process radiation?
4. Provide an example of heat transfer through radiation.
5. How is heat transferred through the process of convection?
6. Provide an example of heat transfer through convection.
Answer Key
1. Heat is transferred by conduction when two objects with different temperatures come into contact. The hotter
object transfers heat to the cooler object.
2. Answers will vary. Sample Answer: Accidently touching a hot BBQ will burn your hand through conduction.
3. Heat is transferred by radiation through the movement of electromagnetic waves. Radiation does not rely on
the movement of atoms to transfer heat.
4. Answers will vary. Sample Answer: Radiation is how the sun’s heat energy travels through space.
5. Heat is transferred by convection through the movement of fluids. Hot fluids rise and cool fluids fall.
6. Answers will vary. Sample Answer: Water in the ocean gets colder as you swim deeper.
146

13.5 Specific Heat
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Solve problems involving specific heat.
1. What is specific heat?
2. Describe the relationship between the specific heat value and the energy needed to produce a change in
temperature.
Use the following prompt to answer questions #3-5
The specific heat of aluminum is 0.982 J/g°C. The specific heat of wood is 1.760 J/g°C.
3. Compare the amount of heat needed to raise the temperature of aluminum to that of wood.
4. If a piece of aluminum and a piece of wood were each exposed to one hour of sunlight, compare the amount
of energy absorbed by each material.
5. If a piece of aluminum and a piece of wood were each exposed to one hour of sunlight, which one would
experience an increase in temperature first?
6. Calculate the amount of joules required to raise the temperature of 17 g of wood from 20°C to 45°C using the
equation .
7. Calculate the amount of joules required to raise the temperature of 17 g of aluminum from 20°C to 45°C using
the equation .
147

13.5. Specific Heat www.ck12.org
Answer Key
1. Specific heat is the quantity of heat needed to raise the temperature of one gram of a substance by one degree
Celsius.
2. As the specific heat value increases, the amount of energy required to produce a temperature change increases.
3. About half as much heat energy is needed to raise the temperature of aluminum compared to wood.
4. The amount of energy absorbed by each material will be the same.
5. The aluminum’s temperature would increase first because it has a lower specific heat.
6. (17 g)(1.76 J/g°C)(25°C)=748 J
7. (17 g)(0.982 J/g°C)(25°C)=417 J
148

www.ck12.org Chapter 14. Thermodynamics Worksheets
CHAPTER
14 Thermodynamics
Worksheets
Chapter Outline
14.1 THE IDEAL GAS LAW
14.2 FIRST LAW OF THERMODYNAMICS
14.3 SECOND LAW OF THERMODYNAMICS
149

14.1. The Ideal Gas Law www.ck12.org
14.1 The Ideal Gas Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain the Ideal Gas Law.
1. What is an ideal gas?
2. Do ideal gases exist?
3. Under what conditions do gases act most ideal?
4. Under what conditions are gases not ideal?
5. What happens to the boiling point of water (100°C, 373K) in the mountains (at high altitudes)? Explain your
answer with reference to the Ideal Gas Law.
Lesson Objective: Solve problems using the Ideal Gas Law.
Use the following prompt to answer questions #6-8:
An ideal gas takes up a volume of 20 liters, has a pressure of 1.3 atm, and a temperature of 301 K.
6. How many moles of the gas are present?
7. Avogadro’s number defines one mole of a substance as having 6.022*1023 atoms. How many individual atoms
of the gas are present?
8. If the temperature of the gas increases to 349 K and the pressure decreases to 1 atm, what is the new volume
of the gas?
150

Answer Key
1. Answers will vary. Sample Answer: A conceptual gas whose atoms experience perfectly elastic collisions.
2. Answers will vary. Sample Answer: No, they are theoretical. However, real gases such as Nitrogen, Oxygen,
and Hydrogen will act as an ideal gas under certain conditions.
3. Most real gases will act as an ideal gas under higher temperature and lower pressure.
4. The ideal gas law fails at low temperature and high pressure.
5. Answers will vary. Sample answer: The boiling point of water at high altitudes decreases. According to the
Ideal Gas Law, PV=nRT. Pressure and temperature are directly proportional. At high altitudes, there is lower
atmospheric pressure. As a result, if the pressure drops, then the temperature must also drop.
6. PV=nRT
(1.30 atm)(20.0 L)=(n)(0.0821 L*atm/mol*K)(301 K)
n=1.05 mols
7. 1.05 mol × 6.022×1023 atoms
1 mol = 6.33×1023 atoms
8. P1V1
T1
= P2V2
T2
(1.3 atm)(20 L)
(301 K) = (1 atm)(V2)
349 K
V = 30.15 L
151

14.2. First Law of Thermodynamics www.ck12.org
14.2 First Law of Thermodynamics
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Describe the First Law of Thermodynamics.
1. The first law of thermodynamics is based on
a. The Conservation of Energy
b. Newton’s Third Law
c. Kepler’s First Law
d. The Conservation of Momentum
2. A thermodynamic process that takes place at constant pressure is called a
a. Isobaric process
b. Isochoric process
c. Isothermal process
d. Adiabatic process
3. A system in which only energy may enter or leave is a(n)
a. Isolated system
b. Closed system
c. Open system
4. Is the following statement true or false: “A given amount of work done on a system could raise the temperature
of the system”.
a. True
b. False
5. The internal energy of a system will decrease when
a. Heat flows into the system
b. Work is done on the system
c. The system does work on the environment
6. Explain why the variable Q is positive when heat flows into a system.
7. Explain why the variable W is negative when work is done by the system on the environment.
8. What is the purpose of a heat reservoir?
152

Lesson Objective: Solve problems using the First Law of Thermodynamics.
9. Calculate the change in the internal energy of a system that does 500 J of work as a heat reservoir transfers
700 J of energy into the system.
10. Calculate the change in the internal energy of a system that transfers 300 J of heat to the environment.
Answer Key
1. A
2. A
3. B
4. A
5. C
6. When heat flows into a system, the internal energy of the system increases. Therefore, energy is added to the
system and Q must be positive.
7. When work is done by the system, the internal energy of the system decreases because energy is lost by the
system. Therefore, the W must be negative.
8. A heat reservoir can be used to accept and deliver heat in order to maintain a system at constant temperature.
9. ∆U=+Q-W
∆U=700 J-500 J=200 J
10. ∆U=-W
∆U=-300 J
153

14.3. Second Law of Thermodynamics www.ck12.org
14.3 Second Law of Thermodynamics
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the second law of thermodynamics.
Label the following statements as true or false. Then, explain the reason for your choice.
1. Heat will always flow from hot to cold.
True
False
• Explain:
2. All natural processes are reversible.
True
False
• Explain:
Lesson Objective: Understand how to calculate the efficiency of a heat engine.
3. What is the function of a heat engine?
4. Which of the following are examples of a heat engine?
a. Refrigerator
b. Oxygen tank
c. Microwave
d. Toaster
Match each of the following processes of an internal combustion engine with its proper description in questions
#5-9.
a. Intake
b. Expansion
c. Ignition
d. Compression
e. Exhaust
154

5. Gasoline and air are mixed together in a cylinder that expands against a piston.
6. A crankshaft moves the piston upward compressing the mixture.
7. At the instant of maximum compression, a spark plug releases an electric spark into the mixture, igniting the
gasoline-air mixture and rapidly increasing the temperature in the cylinder.
8. The hot mixture QH expands rapidly.
9. The exhaust gases QL are ejected at a lower temperature as the piston and the process repeats.
10. Calculate the efficiency of a heat engine whose ignition transfers 7.25*103 J into the system and exhaust
transfers 4.32*103 J out of the system.
Lesson Objective: Understand how a Carnot engine operates.
11. What is a Carnot engine?
12. A Carnot engine relies on which of the following thermodynamic processes?
a. An Isochoric process
b. An Isothermal process
c. An Adiabatic process
d. Both B C
Lesson Objective: Understand that entropy is a measure of disorder.
13. Describe the Second Law of Thermodynamics in terms of entropy.
Answer Key
1. True. Answers will vary. Sample Answer: Heat is the transfer of energy from objects with a high temperature
to objects with a low temperature.
2. False. Answers will vary. Sample Answer: All natural processes are irreversible because the universe tends
to go from a more ordered state to a less ordered state.
3. Answers will vary. Sample Answer: Heat engines are used to convert heat into work.
4. A
5. A
6. D
7. C
8. B
9. E
10. e = (1− QL
QH
×100)
e = (1− 4.32×103
7.25×103 )×100
e = 40%
11. Answers will vary. Sample Answer: It is a hypothetical heat engine that operates on a reversible cycle at
maximum efficiency.
12. D
13. Answers will vary. Sample Answer: The total entropy of a system will always increase
155

www.ck12.org
CHAPTER
15Electrostatics Worksheets
Chapter Outline
15.1 STATIC ELECTRICITY
15.2 COULOMB’S LAW
15.3 ELECTROSTATIC FIELDS
156

www.ck12.org Chapter 15. Electrostatics Worksheets
15.1 Static Electricity
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how an imbalance of electric charge is produced.
1. Describe how an imbalance of charge can be produced through contact.
2. Describe how an imbalance of charge can be produced without contact.
Lesson Objective: Understand that there are two different kinds of electric charge.
3. Describe the differences between protons and electrons.
4. Describe the similarities between protons and electrons.
Lesson Objective: Understand that electric charge is conserved.
5. A person with a rubber soled shoe walks on carpet. As a result, the carpet becomes negatively charged and
the person becomes positively charged. Describe how this demonstrates the conservation of electric charge.
6. In the scenario described above, the person becomes positively charged as a result of
a. Gaining protons
b. Loosing electrons
c. Induction
d. The creation of electric charge
Lesson Objective: Understand that electric charges hold atoms together.
Describe the electrostatic force between each of the following charged particles by circling the correct answer choice.
Then, explain the reason for your choice.
7. Two protons
a. Repulsive
b. Attractive
157

15.1. Static Electricity www.ck12.org
Explain:
8. Two electrons
a. Repulsive
b. Attractive
Explain:
9. A proton and an electron
a. Repulsive
b. Attractive
Explain:
Lesson Objective: Understand the difference between conductors and insulators.
10. Describe one material that is a good conductor. Explain the reason for your choice.
11. Describe one material that is a good insulator. Explain the reason for your choice.
Answer Key
1. Friction or Conduction
2. Induction
3. Answers will vary. Sample answer: Protons are positively charged and electrons are negatively charged.
Protons are much more massive than electrons. Protons reside in the nucleus and electrons are in motion
around the nucleus. Electrons can be transferred from one atom to another, but protons always remain in the
nucleus.
4. Answers will vary. Sample answer: They both reside in an atom. The both have the same magnitude of charge.
In a neutral atom, there is the same number of protons as electrons.
5. Answers will vary. Sample answer: Electrons are neither created nor destroyed, they are simply transferred
from the person to the carpet. As a result, the person becomes positively charged (because they have lost
electrons) and the carpet becomes negatively charged (because it has gained electrons).
6. B
7. Repulsive. Sample answer: According to the law of charges, opposite charges attract and like charges repel.
Protons are positively charged. So, if two protons are interacting, they will repel each other with a repulsive
electrostatic force.
8. Repulsive. Sample answer: According to the law of charges, opposite charges attract and like charges repel.
Electrons are negatively charged. So, if two electrons are interacting, they will repel each other with a
repulsive electrostatic force.
158

9. Attractive. Sample Answer: According to the law of charges, opposite charges attract and like charges repel.
Protons are positively charged and electrons are negatively charged. So, if a proton and an electron are
interacting, they will experience an attractive electrostatic force.
10. Answers will vary. Sample answer: Metallic objects are good conductors because they allow electrons to
move freely.
11. Answers will vary. Sample answer: Rubber objects are good insulators because they do not allow electrons
to move about freely.
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15.2. Coulomb’s Law www.ck12.org
15.2 Coulomb’s Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand Coulomb’s Law.
According to Coulomb’s law, describe the effect on the electrostatic force between two charged particles in the
following scenarios:
1. The product of their charges is doubled
2. The product of their charges is decreased by a third
3. The separation of their distance is tripled
4. The separation of their distance is reduced by a factor of four
Lesson Objective: Understand how to solve problems using Coulomb’s Law.
5. Calculate the magnitude of the electrostatic force between a + 8.0µC charged particle and a + 9.0µC charged
particle separated by 0.5 cm.
Answer Key
1. Answers will vary. Sample answer: According to Coulomb’s law, the electrostatic force is directly propor-
tional to the product of two charges. As a result, in this scenario, the electrostatic force will double.
2. Answers will vary. Sample answer: According to Coulomb’s law, the electrostatic force is directly propor-
tional to the product of two charges. As a result, in this scenario, the electrostatic force will be reduced by
1/3.
3. Answers will vary. Sample answer: According to Coulomb’s law, the electrostatic force is inversely propor-
tional to the square of the distance between two charged particles. As a result, in this scenario, the electrostatic
force will be reduced by 1/9.
160

4. Answers will vary. Sample answer: According to Coulomb’s law, the electrostatic force is inversely propor-
tional to the square of the distance between two charged particles. As a result, in this scenario, the electrostatic
force will increase by a factor of 16.
5. First, convert µC to Coulombs and centimeters to meters.
8.0 µC = 8.0x10−6C
9.0 µC = 9.0x10−6C
0.5 cm = 5.0x10−3m
Then, use Coulomb’s law to solve:
F = k
q1q2
r2
F = (8.99×109 N ·m2
C2
)(
(8.0×10−6C)(9.0×10−6C)
(5.0×10−3m)2
F = 25891 N
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15.3. Electrostatic Fields www.ck12.org
15.3 Electrostatic Fields
Lesson 15.3 Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand what an electric field is.
1. Compare and contrast the gravitational field (g) and the electric field (E).
2. How is the strength of an electric field measured?
3. What are the units of an electric field?
a. Newtons (N)
b. Coulombs (C)
c. Newtons/Coulomb (N/C)
d. Newtons/Kilogram (N/kg)
4. The electric field lines from a positive charge
a. Point away from the charge
b. Point toward the charge
c. Run parallel to the charge
d. Do not exist
5. The density of electric field lines increases as the amount of
a. charge increases
b. charge decreases
c. mass increases
d. mass decreases
Lesson Objective: Understand how to solve electrostatic field problems.
Label the following statements regarding electric fields in questions #6-10 as true or false. Then, explain the reason
for your choice.
6. Electric field lines point toward a positive charge.
a. True
b. False
Explain:
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7. Electric field lines point in the direction a small, negative test charge would travel.
a. True
b. False
Explain:
8. Electric field lines can never cross.
a. True
b. False
Explain:
9. The denser the electric field lines, the greater the magnitude of the charge.
a. True
b. False
Explain:
10. A charge of +4C should have less electric field lines surrounding it compared to a +2C charge.
a. True
b. False
Explain:
11. A +3.0 mC charge is placed in an electric field at a point where the magnitude of the electric field is 4.23 x
105N/C. Calculate the magnitude of the electrostatic force acting on the charge.
12. Draw the electric field lines surrounding the charged particles below.
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15.3. Electrostatic Fields www.ck12.org
Answer Key
1. Answers will vary. Sample answer: The gravitational field surrounds a mass and the electric field surrounds
a charged particle. Both fields exert forces at a distance. Gravitational fields exert a gravitational force on
other massive objects. Electric fields exert an electrostatic force on other charged particles. Both fields are
vector quantities, with both magnitude and direction.
2. Answers will vary. Sample answer: The strength of an electric field is measured by calculating the force
exerted on a small, positive, test charge using the equation E=F/q.
3. C
4. A
5. A
6. False. Electric field lines point away from a positive charge. The field lines always point in the direction of
the force that would act on a small, positive, test charge.
7. False. Electric field lines point in the direction a small, positive test charge would travel (away from a positive
charge and toward a negative charge).
8. True. Electric field lines can never cross.
9. True. A +2 C charge should have double the amount of field lines as a +1 C charge.
10. False. A charge of +4 C should more electric field lines (actually double) than a +2 C charge. The greater the
amount of charge, the denser the electric field lines.
11. First, convert +3.0 mC to Coulombs: 3.0 x 10−3C
F = qE
F = (3.0 x 10−3C)(4.23 x 105N/C)=1269 N
12.
164

www.ck12.org Chapter 16. Electric Potential Worksheets
CHAPTER
16 Electric Potential
Worksheets
Chapter Outline
16.1 REVIEWING GRAVITATIONAL POTENTIAL ENERGY
16.2 ELECTRIC POTENTIAL
16.3 CAPACITANCE
16.4 DIELECTRICS
16.5 ELECTRICAL ENERGY STORAGE
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16.1. Reviewing Gravitational Potential Energy www.ck12.org
16.1 Reviewing Gravitational Potential Energy
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Review and understand gravitational potential energy.
1. Describe how you could increase the gravitational potential energy of an empty box on the ground.
You lift a 10 kg box from the floor to the top of a 1.5 m shelf.
2. What is the force needed to lift the object to the table?
3. How much work must you do to lift the box to the top of the shelf?
4. How much energy is needed to lift the box to the top of the shelf?
5. Once the box is resting on the table, where does the energy go?
Answer Key
1. Answers will vary. Sample answer: You could lift the box a height from the ground and fill the box with
massive objects. PEg=mgh; by increasing the height and mass, the gravitational potential energy of an object
will increase.
2. F=mg=(10kg)(10N/kg)=100N
3. W=Fd=(100N)(1.5m)=150J
4. Work = Energy = 150J
5. It is stored as gravitational potential energy (150J).
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16.2 Electric Potential
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to solve problems using electric potential energy.
1. List and describe all the variables that the electric potential energy depends on.
2. Describe the change in electric potential energy of an electron that moves from the negative plate of a parallel
plate conductor to the positive plate.
3. Calculate the electric potential energy of a particle with a net charge of -2 nC and an electric potential
difference of 2.27 V.
Lesson Objective: Understand how to solve problems using voltage differences.
4. What does voltage measure? What are the units of voltage?
5. Describe voltage in terms of the work done by the electric field in a parallel plate conductor.
6. Which of the following statements correctly describes the analogy between electric potential and gravitational
potential?
a. A height above the Earth provides gravitational potential just as a voltage provides electric potential.
b. A height above the Earth provides gravitational potential just as a charge provides electric potential.
c. A massive object provides gravitational potential just as a voltage provides electric potential.
d. A gravitational force provides gravitational potential just as a voltage provides electric potential.
7. Explain the difference between electric potential and electric potential energy.
8. Calculate the electric potential at 4 cm in an electric field with a strength of 50 N/C.
Lesson Objective: Understand how to solve problems in a uniform electric field.
9. The units for an electric field are
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16.2. Electric Potential www.ck12.org
a. N/C
b. V/m
c. Both A B
10. Determine the electric field in a 12V car battery that is 11cm long.
11. Explain the relationship between the electric field and the electric potential energy of a charged particle.
12. Calculate the change in voltage due to an electric field doing 50 J of work on a 0.5 C charge.
Answer Key
1. Answers will vary. Sample answer: The electric potential energy is dependent on the amount of charge (q),
the charge’s location in an electric field (x), and the strength of the electric field (E). In other words, it relates
to the amount of charge (q) and the voltage (V) or the difference in electric potential.
PEe = qEx
U = qV
2. Answers will vary. Sample answer: The electric potential energy decreases because it turns into kinetic
energy. Another explanation is that the work the electric field does on the negative charge is equal to negative
potential energy (or a decrease in electric potential energy).
3. U = qV = (–2 x 10˘ 9 C)(2.27 V) = –4.54x10−9 J
4. Answers will vary. Sample answer: Voltage measures the electric potential difference in volts (V).
5. Answers will vary. Sample answer: The voltage is equal to the amount of work the electric field does on each
charge, moving it between from the positive plate to the negative plate. V = W/q
6. A
7. Answers will vary. Sample answer: The electric potential (voltage) is the electric potential energy per unit
charge (J/C); V = PEe/q
8. V = Ed = (50 N/C)(0.04 m) = 2 V
9. C
10. V = Ed
12 V = (E)(0.11 m)
E = 12 V/0.11 m = 109 V/m
11. Answers will vary. Sample answer: Electric potential energy can be stored by doing work on a charge against
the electric field. A charged object has electric potential energy based on its location in an electric field.
12. V = W/q = 50 J/0.6 C = 100 V
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16.3 Capacitance
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand capacitance.
1. What is capacitance?
2. What is a parallel plate capacitor?
3. Explain the relationship between capacitance and a parallel plate capacitor.
4. List all the possible ways to increase the capacitance of a parallel plate capacitor.
5. The units of capacitance are
a. Coulombs/Volts
b. Farads
c. Both A B
6. Explain why the following statement is false, “A parallel plate capacitor always has an overall positive charge.”
7. Describe the electric field between the two plates in a parallel plate capacitor.
Lesson Objective: Understand how to solve problems involving capacitance.
8. Calculate the electric potential difference between the plates of a parallel plate capacitor with a capacitance of
0.5 mF and 0.5 mC of charge.
9. Determine the area of the plates in a parallel plate capacitor that are 1mm apart and have a capacitance of 0.2
µF.
10. Determine the amount voltage required to apply 3 µC of charge to a capacitor with a capacitance of 150 pF.
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16.3. Capacitance www.ck12.org
Answer Key
1. Answers will vary. Sample answer: The ability to store charge, Q.
2. Answers will vary. Sample answer: Two identical, parallel, conducting plates separated by a distance that
store electric potential energy.
3. Answers will vary. Sample answer: A parallel plate capacitor relies on the capacitance of its two conducting
plates in order to store electric potential energy. An ideal capacitor has high capacitance.
4. Answers will vary. Sample answer: Increase the area of the plates and/or decrease the distance between the
plates.
5. C
6. Answers will vary. Sample answer: A parallel plate capacitor is always neutral (no charge).
7. Answers will vary. Sample answer: A uniform electric field travels from the positive plate to the negative plate
in a parallel plate capacitor as a result of the electric potential generated by the voltage source.
8. Q = CV; V = Q/C = (5 x 10−4F)/(5 x 10−4C) = 1 V
9.
C = ε0
A
d
2.0×10−7
F =
(8.85×10−12 C2
N·m2 )(A)
(1.0×10−3 m
A = 22.6m2
10. Q = CV
(3 x 10−6C) = (1.50 x 10−7 F)(V)
V = 20 V
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16.4 Dielectrics
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand what a dielectric is and how it affects the capacitance of a capacitor.
1. What is a dielectric?
2. How does a dielectric affect the capacitance of a capacitor?
3. Describe the electric field created inside the dielectric.
Lesson Objective: Solve problems involving capacitors with dielectrics.
In physics class, you build a simple parallel plate capacitor using 1 mm square metal plates 2 mm apart.
4. Calculate the capacitance of your capacitor.
5. Calculate the amount of charged stored on this capacitor when you connect it to a 1.5 V battery.
6. If you added a rubber dielectric between the metal plates (k = 2.8), what would be the new capacitance?
7. How much more charge would be able to be stored due to the rubber dielectric (k = 2.8)?
Answer Key
1. Answers will vary. Sample answer: An easily polarized, insulating material that is inserted between the plates
of a parallel plate capacitor.
2. Answers will vary. Sample answer: It increases the capacitance of a capacitor by enabling it to store more
charge.
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16.4. Dielectrics www.ck12.org
3. Answers will vary. Sample answer: an electric field is created inside the dielectric that opposes the electric
field between the two plates of a parallel plate conductor. As a result, the overall electric field of a capacitor
with a dielectric decreases.
4.
C = ε0
A
d
C = (8.85×10−12 C2
N ·m2
)
(1.0×10−3m)2
2.0×10−3m
C = 4.43×10−15
F
5.
Q = CV
Q = (4.43×10−15
F)(1.5 V)
Q = 6.64×10−15
C
6. C = (2.8)(4.43 x 10−15 F) = 1.24 x 10−14 F
7. Q = (2.8)(6.64 x 10−15 C) = 1.9 x 10−14 C
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16.5 Electrical Energy Storage
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how energy is stored in a capacitor.
1. How is energy stored in a capacitor?
2. Do capacitors obey the law of conservation of energy? Explain.
3. List one way to increase the electric potential energy of a charged object in an electric field.
For questions #4-6, determine if each statement is true or false. Then, explain the reason for your choice.
4. A battery does work on the charges in a capacitor.
True
False
Explain:
5. A battery provides the charges in a capacitor.
True
False
Explain:
6. A battery no longer works when it runs out of charge.
True
False
Explain:
Lesson Objective: Solve problems involving energy stored in capacitors.
7. Calculate the electric potential difference between the two plates of a capacitor with 5 microfarads of capaci-
tance that is storing 10J of electric potential energy.
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16.5. Electrical Energy Storage www.ck12.org
8. Determine the amount of electric potential energy stored by a capacitor that carries 1 picocoulombs of charge
after being charged by a 12V battery.
Answer Key
1. Answers will vary. Sample answer: Work is done (by a battery or other voltage source) to move charges from
one plate to another against the electric field. As a result of the work done by a voltage source, the electrons
are all removed from one plate (the positive plate) and pushed to the other plate (the negative plate). The
energy from the work is now stored as electric potential energy do to this placement of charges.
2. Answers will vary. Sample answer: Yes, because energy is neither created nor destroyed –it is merely
transferred from the work done by a voltage source into electric potential energy stored in the capacitor.
3. Answers will vary. Sample answer: A battery can be used to do work on the charge and move it against the
electric field.
4. True. Sample explanation: The work done by a battery on the charges of a capacitor is transformed into
electric potential energy.
5. False. Sample explanation: A battery provides the energy to move a charge from a low potential to a high
potential, establishing an electric potential difference or a voltage.
6. False. Sample explanation: A battery no longer works when it runs out of energy. The chemical reaction that
produces energy has gone to completion in a dead battery.
7.
PEcap =
1
2
CV2
10 J =
1
2
(5.0×10−6
F)(V2
)
V = 0.005 V
8.
PEcap =
1
2
QVf
PEcap =
1
2
(1.0×10−12
C)(12 V) = 6.0×10−12
J
174

www.ck12.org Chapter 17. Circuits Worksheets
CHAPTER
17 Circuits Worksheets
Chapter Outline
17.1 ELECTRIC CURRENT
17.2 OHM’S LAW
17.3 RESISTIVITY
17.4 RESISTORS IN SERIES AND PARALLEL
17.5 MEASURING CURRENT AND VOLTAGE
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17.1. Electric Current www.ck12.org
17.1 Electric Current
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how electric current is defined.
1. Explain what it means to describe current as a rate quantity.
2. What causes a high current?
3. How does current compare at different points along a simple circuit?
4. What are the necessary conditions for current to flow in a circuit?
5. Where do the charges come from that move through an electrical circuit?
6. The units for current are
a. Coulombs/second
b. Amperes
c. Volts
d. Both A B
Lesson Objective: Solve problems involving electric current.
7. Calculate the current produced by 3 C of charge passing a point along a circuit in 30 seconds.
8. Calculate the amount of charge that passes by a cross section of a wire in 1.5 minutes if the current along the
wire is 0.3 amperes.
Answer Key
1. Answers will vary. Sample answer: A rate quantity is the measure of something over time. Current is the
measure of the quantity of electrical charge (Q) moving past a specific point in a circuit over time (I=Q/t).
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2. Answers will vary. Sample answer: A high is caused by a lot of charges passing through a point of a wire on
a circuit. The more charges that are present, the higher the current.
3. Answers will vary. Sample answer: The current at all points along a simple circuit is the same.
4. Answers will vary. Sample answer: In order for current to flow, there must be an energy source doing work
to create an electric potential difference (ex: a battery providing a voltage) and a closed loop of conducting
materials for charges to flow (ex: wire).
5. Answers will vary. Sample answer: They come from the wire or other conducting material used to build the
loop of the circuit. *They DO NOT come from the battery or outlet.
6. D
7.
I =
∆Q
∆t
I =
3 C
30 s
I = 0.1 A
8.
I =
∆Q
∆t
0.3 A =
q
90 s
q = 27 C
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17.2. Ohm’s Law www.ck12.org
17.2 Ohm’s Law
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how conventional current is defined.
1. Define conventional current.
2. What is the direction of conventional current?
3. What electrical charges actually move in a current? How does this differ from the definition and direction of
conventional current?
Lesson Objective: Understand electrical resistance.
4. What is electrical resistance?
5. How are resistors used in electrical devices?
6. Provide an example of an electrical resistor.
Lesson Objective: Understand how to solve problems using Ohm’s law.
7. According to Ohm’s law, what happens to the current flowing through a circuit if the resistance is held constant
and the voltage doubles?
8. According to Ohm’s law, what happens to the current flowing through a circuit if the resistance is doubled and
the voltage remains the same?
9. According to Ohm’s law, how could you maintain a constant current if the resistance in a circuit is tripled?
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10. What is the current that flows through a toaster, with an electrical resistance of 20 ohms, plugged into a wall
outlet that provides 120 volts?
Answer Key
1. Conventional current is the flow of positive charge.
2. The direction of conventional current is the direction that positive charge would flow (away from other positive
charges and towards negative charges)
3. Electrons are the charges that actually move in a current. However, conventional current is defined as the
direction positive charge would flow.
4. Answers will vary. Sample answer: Electrical resistance hinders the flow of charge (current) in a circuit.
5. Answers will vary. Sample answer: Resistors are used to control the current or transform electric potential
energy into other forms of energy.
6. Answers will vary. Sample answer: light bulb
7. According to Ohm’s law, voltage and current are directly proportional. So, the current will double as well.
8. According to Ohm’s law, when the voltage is held constant, resistance and current are inversely proportional.
So, the current will be cut in half.
9. According to Ohm’s law, the voltage must also be tripled to maintain a constant current when the resistance is
tripled.
10. V = IR
120 V = (I)(20 Ω ) = 6 A
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17.3. Resistivity www.ck12.org
17.3 Resistivity
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to solve problems involving resistivity.
1. Describe the relationship between resistivity and conductivity.
2. What does the gauge of a wire describe? Why is it important?
3. As the gauge of a wire increases, its resistivity
a. Increase
b. Decreases
c. Stays the same
4. Compare and contrast the diameter, and resulting resistivity, of a 10-gauge wire with an 18-gauge wire.
5. Which is more conductive, a 12-gauge wire or a 24 gauge wire? Why?
6. Which of the following wires allows the greatest current to flow through it?
a. A 10 cm piece of 10-gauge wire
b. A 10 cm piece 12-gauge wire
c. A 10 cm piece of 18-guage wire
d. A 10 cm piece of 22-gauge wire
8. Why do you think it is necessary for electricians to have access to wires with different gauges?
9. What is the relationship between the length of a wire and its resistivity?
10. Units of resistivity are
a. Ohms (Ω)
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b. Ohms meter (Ω * m)
c. Volts (V)
d. Amperes (A)
11. Describe an experiment that you could conduct to determine the resistivity of two wires made of different
materials.
12. Calculate the resistance of a copper wire (rcopper = 1.7 x 10−8) with a length of 20cm and a cross-sectional
area of 4 mm2.
Lesson Objective: Understand how to read the resistor code.
Describe the information that can be derived from the following bands on a four-band resistor for questions #13-16:
13. The First Band:
14. The Second Band:
15. The Third Band:
16. The Fourth Band:
Use the following chart to determine the resistance in ohms of the four-band resistors in questions #17-20:
17. A resistor with a band color sequence of Brown, Red, Brown, Gold has a resistance of
a. 16
b. 3.9 x 102
c. 9.1 x 105
d. 120
18. A resistor with a band color sequence of Brown, Blue, Black, Gold
a. 16
b. 3.9 x 102
c. 9.1 x 105
d. 120
19. A resistor with a band color sequence of Orange, White, Red, Silver
a. 16
b. 3.9 x 102
c. 9.1 x 105
d. 120
20. A resistor with a band color sequence of White, Brown, Yellow, None
a. 16
b. 3.9 x 102
c. 9.1 x 105
d. 120
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17.3. Resistivity www.ck12.org
Answer Key
1. Answers will vary. Sample answer: They are inversely proportional; as the resistivity of a material increases,
its conductivity decreases.
2. Answers will vary. Sample answer: The gauge of a wire describes its thickness, or diameter. It is important
because the resistivity of a wire depends on its cross sectional area (and its length).
3. B
4. Answers will vary. Sample answer: A 10-gauge wire has a greater diameter than an 18-gauge wire and, as a
result, as a lower resistivity.
5. Answers will vary. Sample answer: A 12-gauge wire because it has a much wider diameter, and therefore less
resistance, then a 24-gauge wire. The lower the resistivity of a wire, the greater its conductivity.
6. A
7. Answers will vary. Sample answer: All of the wires have the same length, but different diameters. A 10-gauge
wire is the thickest (has the greatest diameter) and therefore will allow the greatest current to flow through it
(has the least resistance).
8. Answers will vary. Sample answer: As the wire gauge increases in number, it decreases in thickness and
allows less current to flow through it. Therefore, the wire gauge allows an electrician to control the current in
a circuit.
9. Answers will vary; Sample answer: They are directly proportional; as the length of a wire increases, its
resistivity increases.
10. B
11. Answers will vary. Sample answer: Obtain wires with the exact same cross-sectional area and length, but
made of different materials. Apply the same voltage to each wire and measure the current. Use Ohm’s law
(V=IR) to determine the resistance in each wire. Now, you would have all variables to calculate the resistivity
(ρ) using the equation R = ρL
A.
12.
R = ρ
L
A
ρcopper = 1.7×10−8
;L = 0.02 m;A = 0.004 m2
R = (1.7×10−8
)(
0.02 m
0.004m2
R = 8.5×10−8
Ω
13. The first band codes for the first number of the resistance.
14. The second band codes for the second number of the resistance.
15. The third band codes for the multiplier of the resistance.
16. The fourth band codes for the tolerance or measure of accuracy (a percentage).
17. D
18. A
19. B
20. C
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17.4 Resistors in Series and Parallel
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Be able to distinguish between a series and parallel circuit.
For questions #1-8, refer to the diagrams of circuits A, B, & C below. Each circuit has identical batteries (9 V) and
resistors (100 Ω).
1. Which circuit has two resistors connected in series?
a. Circuit A
b. Circuit B
c. Circuit C
2. Which circuit has two resistors connected in parallel?
a. Circuit A
b. Circuit B
c. Circuit C
3. Which of the following statements correctly describes the path of an electron in Circuit B?
a. All electrons pass through only one resistor
b. All electrons pass through both resistors
c. The electrons will not pass through either resistor
4. Which of the following statements correctly describes the path of an electron in circuit C?
a. All electrons pass through only one resistor
b. All electrons pass through both resistors
c. The electrons will not pass through either resistor
5. Which circuit has the total lowest current running through it?
a. Circuit A
b. Circuit B
c. Circuit C
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17.4. Resistors in Series and Parallel www.ck12.org
6. Explain the reason for your choice in question #5 above.
7. In which circuit(s) is the voltage drop across every resistor 9 V?
a. Circuit A
b. Circuit B
c. Circuit C
d. Circuit A C
9. If the resistors were light bulbs, predict what would happen if one of the bulbs burned out in circuit B.
10. If the resistors were light bulbs, predict what would happen if one of the bulbs burned out in circuit C.
11. If the resistors were light bulbs, predict what would happen to each bulb’s brightness if another bulb was added
in series to circuit B.
12. If another 9V battery was added to each circuit, which circuit would experience an increase in current?
a. Circuit A
b. Circuit B
c. Circuit C
d. All of the above
Lesson Objective: Solve problems involving circuits with resistors.
For questions #13-20, refer to the diagrams of circuits X & Y below. Each circuit has identical batteries (1.5V) and
resistors (10 Ω).
13. What is the equivalent resistance of circuit X?
14. What is the equivalent resistance of circuit Y?
15. What is the total current running through circuit X?
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16. What is the total current running through circuit Y?
17. What is the voltage drop across each resistor in circuit X?
18. What is the voltage drop across each resistor in circuit Y?
19. What is the current through each resistor in circuit X?
20. What is the current through each resistor in circuit Y?
Answer Key
1. B
2. C
3. B
4. A
5. B
6. Answers will vary. Sample answer: Circuit B has two resistors in series. Therefore, the current has to go
through a greater equivalent resistance and the overall current will decrease.
7. D
8. Answers will vary. Sample answer: The resistors in circuit B are in series, so the electrons go through two
resistors and loose some voltage across the first resistor. In circuits A C, each electron only goes through one
resistor, so the voltage drop across every resistor is the full 9 V.
9. Answers will vary. Sample answer: If one of the bulbs burned out in circuit B, it would become an open circuit
(because the resistors are connected in series) and current would stop flowing. As a result, the second bulb
would also go out.
10. Answers will vary. Sample answer: If one of the bulbs burned out in circuit C, the current would only be able
to flow across the second resistor (because the resistors are in parallel). As a result, the second bulb would
still be able to work.
11. Answers will vary. Sample answer: If another bulb was added in series to circuit B, all the bulbs would dim
(decrease in brightness) because the overall current would decrease as a result of the increase in equivalent
resistance.
12. D
13. Req−X =[(10 Ω x10 Ω)/(10 Ω+10 Ω)]=[100 Ω/20 Ω]=5 Ω
14. Rseries−equivalent = R1 + R2 + ...
Req−Y = 10 Ω+10 Ω=20 Ω
15. V = IR = 1.5 V = (I)(5 Ω) = 0.3 A
16. V = IR = 1.5 V = (I)(20 Ω) = 0.075 A
17. The voltage drop across each resistor in a parallel circuit is the same for each resistor, or 1.5V.
18. The current running through each resistor in a series circuit is the same as the total current (question #16)
V = (0.075 A)(10 Ω) =0.75 V through each resistor
19. 1.5 V = (I)(10 Ω) = 0.15 A
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17.4. Resistors in Series and Parallel www.ck12.org
20. The current running through each resistor in a series circuit is the same as the total current (question #16).
V = IR = 1.5 V = (I)(20 Ω) = 0.075 A
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17.5 Measuring Current and Voltage
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how an ammeter is used.
Use the diagram of circuit X below to answer questions #1-2:
1. Where should an ammeter be placed in this circuit?
a. Point A
b. Point B
c. Point A and Point B
2. What would the ammeter read?
Lesson Objective: Understand how a voltmeter is used.
Use the diagram of circuit Y below to answer questions #3-5:
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17.5. Measuring Current and Voltage www.ck12.org
3. What should voltmeter 1 read?
a. 0 V
b. 0.5 V
c. 0.75 V
d. 1.5 V
4. What should voltmeter 2 read?
a. 0 V
b. 0.5 V
c. 0.75 V
d. 1.5 V
5. Another 100 Ω resistor is added parallel to this circuit with a voltmeter (called voltmeter 3) connected across
it. What should voltmeter 3 read?
a. 0 V
b. 0.5 V
c. 0.75 V
d. 1.5 V
Answer Key
1. B
2. First, calculate the equivalent resistance of this circuit in series.
Req−X = 50Ω+50Ω = 100Ω
Then, calculate the total current running through this circuit in series.
V = IReq
9 V = (I)(100 Ω)I = 0.09 A
3. D
4. A
5. D
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www.ck12.org Chapter 18. Magnetism Worksheets
CHAPTER
18 Magnetism Worksheets
Chapter Outline
18.1 MAGNETIC FIELDS
18.2 THE MAGNETIC FORCE ACTING ON A CURRENT-CARRYING WIRE
18.3 MAGNETIC FORCE ON MOVING ELECTRIC CHARGES
18.4 A PRACTICAL APPLICATION OF MAGNETIC FIELDS
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18.1. Magnetic Fields www.ck12.org
18.1 Magnetic Fields
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Know how to determine the direction of a permanent magnetic field.
1. Draw the magnetic field lines around the permanent bar magnet made of iron in the space below:
Lesson Objective: Know that a current-carrying wire creates a magnetic field.
Determine if the statements #2-5 below are true or false. Then, explain the reason for your choice in the space below.
2. Only straight wires generate magnetic fields.
True
False
Explain:
3. The magnetic fields surrounding the loops of wire in a coil cancel out to make the overall magnetic field
through the coil very weak.
True
False
Explain:
4. A magnetic field always surrounds a straight wire, even if there is no current running through it.
True
False
Explain:
5. The direction of the magnetic field is based on the direction of the current running through a wire.
True
False
Explain:
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Lesson Objective: Know how to determine the direction of the magnetic field produced by a current-carrying
wire.
6. When using the first Right-Hand Rule to determine the direction of magnetic field around a current-carrying
wire, the thumb should point in the same direction as
a. The current
b. The magnetic field
c. The magnetic force
d. The magnetic domain
7. When using the first Right-Hand Rule to determine the direction of magnetic field around a current-carrying
wire, the fingers should point in the same direction as
a. The current
Use the image of the loop of current-carrying wire to answer questions #8-10 below:
8. At what point does the magnetic field point out of the page?
a. Point A
b. Point B
c. Point C
d. Point D
9. At what point is the magnetic field the strongest?
a. Point A
b. Point B
c. Point C
d. Point D
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18.1. Magnetic Fields www.ck12.org
Answer Key
1.
2. False. Sample explanation: Any wire with a current through it produces a magnetic field. Moving charges
(current) create a magnetic field.
3. False. Sample explanation: The magnetic fields surrounding the loops of wire in a coil add together to make
the overall magnetic field very strong.
4. False. Sample explanation: A magnetic field surrounds any wire with a current through it. Moving charges
(current) create a magnetic field.
5. True. Sample explanation: The first Right-Hand Rule helps to determine the direction of the magnetic field
based on the direction of the current running through the wire.
6. A
7. B
8. A
9. A
10. Answers will vary. Sample explanation: In a loop, all the magnetic fields add together and are strongest at
the center of the loop.
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18.2 The Magnetic Force acting on a Current-
Carrying Wire
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Know under which conditions a current-carrying wire experiences a force when placed in
a magnetic field.
1. Explain why the following statement is a misconception, "A current-carrying wire experiences a force when
placed near a magnet because the electrons in the wire are repelled by the electrons in the magnet."
Lesson Objective: Use the right-hand rule to determine the force on a current-carrying wire in a magnetic
field.
Complete the following sentence to answer questions #2-4 below:
When using the second Right-Hand Rule to determine the direction of the force on a current-carrying wire in a
magnetic field .....
2. The fingers should point in the same direction as
a. The current
3. You should curl your hand in the same direction as
a. The current
4. Your thumb should point in the same direction as
a. The current
Use the image of the two current-carrying wires placed side by side to answer questions #5-6:
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18.2. The Magnetic Force acting on a Current-Carrying Wire www.ck12.org
5. Does wire B exert a force on wire A?
Yes
No
Explain the reason for your choice:
If yes, determine the direction of the force from wire B on wire A.
6. Does wire A exert a force on wire B?
Yes
No
If yes, determine the direction of the force from wire B on wire A.
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Lesson Objective: Solve problems involving the force on a current-carrying wire in a magnetic field.
7. Wire X has a length 0.08 m and is carrying a 0.3 A current in the +x-direction. Magnetic field Y has a
magnitude of 2.50 T in the +y-direction. Determine the magnitude and direction of the force exerted by
magnetic field Y on the current-carrying wire X.
Answer Key
1. Answers will vary. Sample explanation: It is a misconception to think that the force comes from the electrons
repelling. Magnetic fields push moving charges. As a result, a current-carrying wire (which consists of moving
charges) experiences a force when placed near a magnetic (which is surrounded by a magnetic field).
2. A
3. B
4. C
5. Yes. Sample explanation: The moving charges (current) in wire B creates a magnetic field. This magnetic
field exerts a force on the moving charges (current) in wire A. The direction of the force from wire B on wire A
is rightward.
6. Yes. Sample explanation: According to Newton’s 3rd Law, if wire B exerts a force on wire A, then Wire A must
exert a force equal in magnitude and opposite in direction on wire B. The direction of the force from wire A
on wire B is leftward.
7. F = ILB sin θ
F = (0.3 A)(0.08 m)(2.5 T)sin 90° = 0.06 N, along the + z-axis (out of the page)
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18.3. Magnetic Force on Moving Electric Charges www.ck12.org
18.3 Magnetic Force on Moving Electric
Charges
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Know under which conditions a moving electric charge experiences a force when placed in
a magnetic field.
1. Describe the conditions in which a moving electric charge experiences a force when placed in a magnetic field.
Decide if each of the particles described in questions #2-5 will experience a force when placed in a magnetic field
by circling yes or no. Then, Explain the reason for your choice.
2. An electron at rest in a magnetic field.
Yes
No
3. A neutron moving perpendicular to the magnetic field.
Yes
No
4. A proton moving perpendicular to the magnetic field.
Yes
No
5. An electron moving parallel to the magnetic field.
Yes
No
Lesson Objective: Use the right-hand rule in order to determine the force on a moving electric charge in a
magnetic field.
Use the prompt below to answer questions #6-9. The magnetic field (B) is illustrated in blue and the velocity vector
of the moving electric charge (V) is illustrated in red.
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An electron moves leftward into a magnetic field that is traveling into the page (along the –z-axis).
6. When using the second Right-Hand Rule to determine the direction of the force on the moving electron above,
the velocity vector (V) is represented by the direction of your
a. Thumb
b. Fingers
c. Palm
the magnetic field (B) is represented by the direction of your
a. Thumb
b. Fingers
c. Hand curling
the force (F) is represented by the direction of your
a. Thumb
b. Fingers
c. Hand curling
9. According to the second Right-Hand Rule, what is the direction of the force (F) on the moving electron
depicted in the magnetic field above? Explain the reason for your choice.
Lesson Objective: Solve problems involving the force acting on a moving electric charge in a magnetic field.
10. Calculate the magnitude of the velocity of an electron moving perpendicular to a magnetic field of 2 T that
feels a force of 4×10−16 N.
Answer Key
1. Answers will vary. Sample answer: An electric charge (proton/electron) will experience a force when it moves
through a magnetic field at an angle.
2. No. Sample explanation: The electric charge must be moving to experience a force when placed in a magnetic
field.
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18.3. Magnetic Force on Moving Electric Charges www.ck12.org
3. No. Sample explanation: The particle must be charged in order to experience a force when placed in a
magnetic field.
4. Yes. Sample explanation: The electric charge is moving at an angle to the magnetic field and will experience
a magnetic force as a result.
5. No. Sample Explanation: The velocity vector of the moving electric charge must form an angle with the
magnetic field vector to experience a force form a magnetic field.
6. B
7. C
8. A
9. The direction of the force on the moving electron is upward. Sample explanation: When using the second
Right-Hand Rule, you should place fingers to the left, turn your hand so it curls into the page, and the thumb
will point downward. However, this is a NEGATIVELY charged particle, so the direction of the force will be
reversed.
10.
F = qvBsinθ
4.0×10−16
N = (1.6×10−19
C)(V)(2×10−6
T)
V =
(4.0×10−16N)
(1.6×10−19C)(2.0×10−6T)
V = 1.25×109
m/s
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18.4 A Practical Application of Magnetic Fields
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the basic operation of an electric motor.
1. Describe the transformation of energy in an electric motor.
2. Which of the following is an example of a simple electric motor
a. Washing machine
b. Air conditioner
c. DVD players
d. All of the above
For questions #3-5, explain the role of each of the parts of a simple electric motor in your own words.
3. The coil of wire
4. A battery
5. A bar magnet
Answer Key
1. Answers will vary. Sample answer: An electric motor is used to transform electric potential energy into
mechanical energy (kinetic energy of a rotating loop of wire).
2. D
3. Answers will vary. Sample answer: The wire is coiled in order to increase the magnetic field generated by the
current-carrying wire.
4. Answers will vary. Sample answer: Moving charges experience a force from a magnetic field. Therefore,
current is necessary for the wire to experience a force from the bar magnet’s magnetic field.
5. Answers will vary. Sample answer: A permanent magnet is used to generate the magnetic field that exerts a
force on the current-carrying wire in a simple motor.
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www.ck12.org
CHAPTER
19 Electromagnetism
Worksheets
Chapter Outline
19.1 ELECTROMAGNETIC INDUCTION
19.2 THE ELECTRIC GENERATOR
19.3 ELECTRICAL POWER TRANSFER
19.4 THE ELECTROMAGNETIC SPECTRUM
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www.ck12.org Chapter 19. Electromagnetism Worksheets
19.1 Electromagnetic Induction
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand magnetic flux.
1. Describe what magnetic flux measures in your own words.
2. The plane of a coil of wire should be placed _____ the magnetic field to produce a maximum magnetic flux.
a. Perpendicular to
b. Parallel to
c. Outside of
3. Explain the reason for your answer choice above.
4. Calculate the magnetic flux through a coil of wire with a cross-sectional area of 0.03 m2 placed at a 60° angle
to a 0.7 T magnetic field.
5. The SI units of measurement for magnetic flux are
a. Teslas*m2 (T*m2)
b. Newtons (N)
c. Webers (Wb)
d. Both A C
Lesson Objective: Understand Faraday’s law of induction.
For questions #6-8, apply your understanding of Faraday’s law of induction to determine if the statements are true
or false. Then, explain the reason for your choice.
6. The magnitude of the induced voltage in a coil of wire depends on how quickly the magnetic flux through the
coil of wire changes.
True
False
Explain:
7. There is only an induced voltage in a coil of wire if the magnetic flux through the coil of wire changes.
True
False
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19.1. Electromagnetic Induction www.ck12.org
Explain:
8. An induced voltage is the same thing as an induced current.
True
False
Explain:
Lesson Objective: Understand Lenz’s law.
9. According to Lenz’s law, any induced current will result in
a. An induced magnetic field
b. A magnetic flux that opposes the original changing flux
c. A magnetic flux that encourages the original changing flux
d. Both A B
10. Use the diagram below of a stationary coil of wire (illustrated in red) in an increasing magnetic field (illustrated
in blue) directed into the page (along the –z-axis) to answer question #10:
According to Lenz’s law, what is the direction of the induced current? Explain the reason for your choice.
Answer Key
1. Answers will vary. Sample answer: Magnetic flux is the average number of magnetic field lines passing
through a given area (usually the center of a coil of conducting wire). It is determined by multiplying the
average number of field lines going through a given area with the cross-sectional area and the cosine of the
angle between the field vector and area vector (Φ=BA cos θ). It basically provides physicists with a way to
measure the magnitude of the magnetic field passing through a coil of wire.
2. A
3. Answers will vary. Sample answer: When the plane of a coil of wire is placed perpendicular to a magnetic
field, the angle between the magnetic field vector (B) and the cross-sectional area vector (A) of the coil is zero.
As a result, the magnetic flux (Φ=BA cos θ) will be at its greatest.
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4. Φ=BA cos θ
Φ=(0.7 T)(0.03 m2)(cos 60°)=0.01 Wb
5. D
6. True. Sample explanation: According to Faraday’s law of induction, the induced voltage in a coil is equal
to the product of the number of loops in the coil and the rate of change in the magnetic flux through the coil.
Therefore, the induced voltage is dependent on how quickly the magnetic flux changes.
7. True. Sample Explanation: According to Faraday’s law of induction, the induced voltage in a coil is equal
to the product of the number of loops in the coil and the rate of change in the magnetic flux through the coil.
Therefore, a changing magnetic flux is necessary for an induced voltage.
8. False. Sample Explanation: An induced voltage provides a potential difference. This causes the electrons in
the coil of wire to begin moving, or an induced current.
9. D
10. Counter Clockwise. Sample explanation: According to Lenz’s law, the induced current must create a magnetic
field to oppose a change in flux. Therefore, the induced magnetic field must be pointed out of the page, which
requires a counter clockwise induced current.
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19.2. The Electric Generator www.ck12.org
19.2 The Electric Generator
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how a generator produces an electric current.
1. What materials are necessary for a generator to produce an electric current?
2. Describe the difference between a generator and a motor.
3. What is a turbine? How is it used in a generator?
4. What can be done to a turbine to increase the amount of electricity it produces?
a. Increase the amount of wires near the turbine
b. Increase the strength of the magnetic field near the turbine
c. Increase the speed at which the turbine moves
d. All of the above
5. Describe how a fossil fuel power plant generates electricity.
6. Describe how a nuclear plant generates electricity.
7. In a generator, a rotating magnetic produces a magnetic field that increases and decreases relative to a coil of
conducting wire. This produces a(n)
a. Resistor
b. Capacitor
c. Direct current
d. Alternating current
Answer Key
1. Answers will vary. Sample answer: The materials necessary for a generator to produce an electric current
are a coil of wire and a magnet. The coil of wire and the magnet must be moving relative to each other.
2. Answers will vary. Sample answer: A motor converts electrical energy into mechanical energy and a genera-
tor converts mechanical energy into electrical energy.
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3. Answers will vary. Sample answer: A turbine is a device used to rotate a large magnet relative to a coil in a
generator to produce an electric current.
4. D
5. Answers will vary. Sample answer: Coil (fossil fuel) is burned, turning water into steam. This steam is used to
turn a turbine and rotate a magnet near a coil of wire, producing an electric current through electromagnetic
induction.
6. Answers will vary. Sample answer: In a nuclear plant, uranium atoms split in a process of nuclear fission,
producing the heat necessary to turn water into steam. This steam is used to turn a turbine and rotate a magnet
near a coil of wire, producing an electric current through electromagnetic induction.
7. D
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19.3. Electrical Power Transfer www.ck12.org
19.3 Electrical Power Transfer
Worksheet
Name___________________ Class______________ Date________
’Lesson Objective: Understand how transformers operate.
1. What is the main function of a transformer?
2. What is the difference between the primary coil and the secondary coil of a transformer?
3. Describe the difference between a step-up transformer and a step-down transformer.
4. Describe the power input of the primary coil and the power output of the secondary coil in a transformer.
A transformer has 300 turns in its primary coil and 150 turns in its secondary coil.
5. Is this a step-up or step-down transformer? Explain the reason for your answer.
6. If 240 V is put across the primary coil, what is the resulting voltage output of the secondary coil?
7. If 1200 W of power is input to the primary coil, what is the power output of the secondary coil? Explain the
reason for your answer.
Answer Key
1. Answers will vary. Sample answer: Transformers are used to change potential differences (voltages). Most
commonly, transformers are used to reduce the large potential differences produced by power stations to the
lower voltages in our electrical outlets (~120 V).
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2. Answers will vary. Sample answer: The primary coil is connected to the power source and the secondary coil
is not.
3. Answers will vary. Sample answer: In a step-up transformer, the number of loops in the secondary coil
is greater than the number of loops in the primary coil (Ns>NP), resulting in a greater secondary voltage
(Vs>VP). In a step-down transformer, the number of loops in the secondary coil is less than the number of
loops in the primary coil (Ns<NP), resulting in a smaller secondary voltage (Vs<VP).
4. Answers will vary. ;;Sample answer: The power input to the primary coil is equal to the power output of the
secondary coil. P=IV, so the current and voltage are inversely proportional as a result of the power remaining
constant.
5. Answers will vary. Sample answer: This is a step-down transformer because the secondary coil has less
number of loops than the primary coil, decreasing the voltage.
6.
Vp
Np
= Vs
Ns
120 V
300 = Vs
150
Vs = 60 V
7. Answers will vary. Sample answer: 1200 W, due to the conservation of energy. The voltage of the secondary
coil has been stepped down, but the current steps up, resulting in the same amount of power.
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19.4. The Electromagnetic Spectrum www.ck12.org
19.4 The Electromagnetic Spectrum
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand what the electromagnetic spectrum is.
1. What generates electromagnetic waves?
2. Which of the following are types of electromagnetic waves?
a. Radio waves
b. Microwaves
c. Visible light
d. All of the above
3. Compare and contrast electromagnetic waves to sound waves? How are they similar and how are they
different?
4. In the electromagnetic spectrum, electromagnetic waves are categorized according to their
a. Wavelengths
b. Frequencies
c. Energy levels
d. All of the above
The list below categorizes all the electromagnetic waves along the electromagnetic spectrum.
• Radio Waves
• Microwaves
• Infrared
• Visible Light
• Ultraviolet Rays
• X Rays
• Gamma Rays
5. Which of the electromagnetic waves listed above has the highest energy?
6. Which of the electromagnetic waves listed above has the highest frequency?
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7. Which of the electromagnetic waves listed above has the shortest wavelength?
8. UV rays, x-rays, and gamma rays all considered to be dangerous to human beings because
a. Their wavelengths are so long, they can penetrate the nucleus of our cells and destroy our DNA
b. Their wavelengths are so short, they can penetrate the nucleus of our cells and destroy our DNA
c. They vibrate at the same frequency as the water and fat molecules in our bodies
9. What is light? How does it relate to the electromagnetic waves along the electromagnetic spectrum?
10. If the frequency of blue visible light is about 7.5*1014 Hz, calculate the wavelength of blue light.
Answer Key
1. Answers will vary. Sample answer: A vibrating electric charge, commonly referred to as radiation, produces
an electromagnetic wave.
2. D
3. Answers will vary. Sample answer: Both sound waves and electromagnetic waves are produced by vibrations.
The difference is that sound waves are produced by vibrating air molecules (or water molecules, etc) and EM
waves are produced by vibrating electric charges. Both sound waves and EM waves transfer energy. However,
sound waves require a medium to transfer energy and EM waves can transfer energy through a vacuum (empty
space).
4. D
5. Gamma Rays
6. Gamma Rays
7. Gamma Rays
8. B
9. Answers will vary. Sample answer: Light is an electromagnetic wave that transfers energy through the electric
and magnetic field. All the electromagnetic waves along the electromagnetic spectrum are light; visible light
is just a small range in the middle of the spectrum.
10. V=fλ ; velocity is the speed of light = 3.0*108 m/s
3.0*108 m/s =(7.5*1014Hz)(λ)
λ=4.0*10−7 m
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www.ck12.org
CHAPTER
20 Geometric Optics
Worksheets
Chapter Outline
20.1 LIGHT AS A RAY AND THE LAW OF REFLECTION
20.2 CONCAVE AND CONVEX MIRRORS
20.3 INDEX OF REFRACTION
20.4 THIN LENSES
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www.ck12.org Chapter 20. Geometric Optics Worksheets
20.1 Light as a Ray and the Law of Reflection
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Explain the ray model of light.
1. What is light and how does this differ from how light is perceived by our eyes?
2. What physical phenomena does the ray model of light help to explain?
Describe the following rays of light in your own words:
3. An incident ray
4. A reflected ray
5. A refracted ray
Lesson Objective: Describe the Law of Reflection.
6. Describe the steps involved in using the law of reflection to draw ray diagrams.
7. Follow the steps listed above to determine the angle of reflection and draw the reflecting ray off the mirror
below.
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20.1. Light as a Ray and the Law of Reflection www.ck12.org
Lesson Objective: Explain how images are formed from flat mirrors.
8. Describe the size of an object compared to the size of the image it forms in a flat mirror.
9. Describe the distance of an object in front of a flat mirror compared to the distance of the image it forms
behind the mirror
10. Explain why the following statement is false, “That image in the flat mirror is real.”
Answer Key
1. Answers will vary. Sample answer: Light is a transverse electromagnetic wave created by the vibrations of
electric charges. Although light is a wave, the motion of the electrons that produce light are so fast and the
wavelengths are so small that it is perceived by our eyes as a straight line, or ray.
2. Answers will vary. Sample answer: The ray model is used in geometrical optics to explain the reflection and
refraction of light.
3. Answers will vary. Sample answer: Incident rays are the incoming rays of light that strike a surface, such as
a mirror or glass lens.
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4. Answers will vary. Sample answer: The ray of light that is reflected by a surface is referred to as the reflected
ray.
5. Answers will vary. Sample answer: The ray of light that passes through a surface is referred to as the refracted
ray.
6. Answers will vary. Sample answer:
Step 1: Draw a normal line that is perpendicular (90° angle) to the reflecting surface.
Step 2: Measure the incident angle (θi) that the incident ray makes with the normal line using a protractor.
Step 3: According to the law of reflection, the angle of reflection (θr) will be equal to the angle of incidence
(θi). Measure the angle of reflection from the normal line and draw the reflecting ray using a protractor.
7.
8. The size of the image in a flat mirror will be equal to the actual size of the object.
9. The distance of the image behind a flat mirror will be equal to the distance of the object in front of the flat
mirror.
10. Answers will vary. Sample answer: The image in a flat mirror is always a virtual image. A flat mirror will
always create a virtual image because the reflecting rays will never actually meet in real space. As a result,
you use a dotted line to illustrate the reflected rays of light behind the mirror, where they only exist in our
minds.
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20.2. Concave and Convex Mirrors www.ck12.org
20.2 Concave and Convex Mirrors
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to draw ray diagrams for concave mirrors.
Use the image below, illustrating a standard set-up for a ray diagram of concave mirror, to answer questions #1-4:
1. Which of the following symbolizes the concave mirror in the image above?
a. A
b. B
c. C
d. D
2. Which of the following signifies the focal point (f) in the image above?
a. A
b. B
c. C
d. D
3. Which of the following signifies the center of curvature (c) in the image above?
a. A
b. B
c. C
d. D
4. Which of the following signifies the principal axis (p) in the image above?
a. A
b. B
c. C
d. D
5. Provide a general description of the image of an object placed closer to a concave mirror than its focal point
by circling the correct choices below:
Image orientation:
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UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
Relative size of the image:
BIGGER / SMALLER
Image location:
IN FRONT OF MIRROR / BEHIND MIRROR
6. Provide a general description of the image of an object placed beyond the focal point of a concave mirror by
circling the correct choices below:
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
7. Describe the three principle rays that can be drawn to construct ray diagrams for concave mirrors.
8. Use the three principle rays described above to construct a ray diagram for the image of a tree in the following
concave mirror.
215

9. Describe the image of the tree in question #8 by circling the correct answer choices below:
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
10. What could you do create a virtual image of the tree in the concave mirror?
Lesson Objective: Understand how to solve problems involving concave mirrors.
11. Complete the following chart regarding sign conventions for spherical mirrors:
Use the diagram below of a tree beyond the focal point of a concave mirror to answer questions
216

12. Use the mirror equation ( 1
do
+ 1
di
= 1
f ) to solve for the image distance (di) in the illustration above.
13. Use the magnification equation (m = hi
ho
= − di
do
) to solve for the magnification of the image (m) in the
illustration above.
14. Based in your calculations and the chart in question #11, describe the image of the tree in the concave mirror
by circling the correct answer choices below:
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
15. Does your mathematical answers and description above match the image formed by your ray diagram in
question #8?
Lesson Objective: Understand how to draw ray diagrams for convex mirrors.
217

16. Provide a general description of the image of an object placed anywhere in front of a convex mirror by
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
17. Describe the three principle rays that can be drawn to construct ray diagrams for convex mirrors.
18. Use the three principal rays described above to construct a ray diagram for the image of a tree in the following
convex mirror.
Lesson Objective: Understand how to solve problems involving convex mirrors.
Use the diagram below of a tree beyond the focal point of a convex mirror to answer questions #19-22:
218

19. Use the mirror equation ( 1
do
+ 1
di
= 1
ho
= − di
do
illustration above.
21. Based in your calculations and the chart in question #11, describe the image of the tree in the convex mirror
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
22. Do your mathematical answers and description above match the image formed by your ray diagram in question
#18?
Answer Key
1. C
2. B
219

3. A
4. D
5. Upright, virtual, bigger, behind the mirror
6. Inverted, real, smaller, in front of the mirror
Ray 1: A ray drawn parallel to the principal axis and then reflects off the mirror through the focal point, f.
Ray 2: A ray drawn through the focal point, f, and then reflects off the mirror parallel to the principal axis
Ray 3: A ray drawn through the center of curvature, c, and then reflects back through c.
∗∗The point where these three rays intersect is the location of the image.
8.
9. Inverted, real, smaller, in front of the mirror
10. Answers will vary. Sample answer: You could place the tree at a location closer to the concave mirror than
its focal point, creating an upright, virtual, larger, image located behind the mirror.
11.
12. Based on the given scale, d0 = 7 m and f = 1 m.
1
do
+
1
di
=
1
f
1
7m
+
1
di
=
1
1m
1
di
=
1
1 m
−
1
7m
1
di
+
(7−1)
(7)
= 0.9
di = 1.2 m
13.
m =
hi
ho
= −
di
do
m = −
1.2 m
7 m
= −0.2
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14. REAL Explanation: the distance of the image (di) is positive, so the rays of light converge in front of the
mirror and actually come together in real space.
INVERTED Explanation: the magnification (m) is negative, so the image is inverted.
SMALLER Explanation: the magnification (m) is less than one, so the image is smaller than the object.
15. Answers will vary. Sample answer: Yes, the image is real, inverted, smaller than the actual tree, and forms
about 1.2m from the mirror.
16. Upright, virtual, smaller, behind the mirror
Ray 1: A ray drawn parallel to the principal axis and then reflects off the mirror through the focal point, f.
Ray 2: A ray drawn through the focal point, f, and then reflects off the mirror parallel to the principal axis
Ray 3: A ray drawn through the center of curvature, c, and then reflects back through c.
18.
19. Based on the given scale, d0 = 4 m and f = -1 m.
1
do
+
1
di
=
1
f
1
4m
+
1
di
= −
1
1m
1
di
= −
1
1 m
−
1
4m
1
di
+
(4+1)
(4)
= −1.25
di = −0.8 m
20.
m =
hi
ho
= −
di
do
m = −
−0.8 m
4 m
= 0.2
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21. VIRTUAL Explanation: the distance of the image (di) is negative, so the rays of light converge behind the
mirror and only converge in our minds.
UPRIGHT Explanation: the magnification (m) is positive, so the image is upright.
22. Answers will vary. Sample answer: Yes, the image is virtual, upright, smaller than the actual tree, and forms
about 0.8 m behind the mirror.
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20.3 Index of Refraction
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how the index of refraction is defined.
1. What causes the refraction, or bending, of light?
2. What information can be derived from the index of refraction?
3. Explain why the index of refraction for any material will always be greater than one.
Lesson Objective: Solve problems involving the index of refraction.
4. Complete the following chart by applying your understanding of the index of refraction and the equation n =
c/v.
Lesson Objective: Understand Snell’s Law.
Use the image below to answer questions #5-9:
5. Which of the following is the normal line in the image above?
a. A
b. B
c. C
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20.3. Index of Refraction www.ck12.org
6. Which of the following is the angle of incidence (θi) in the image above?
a. θ1
b. θ2
c. θ3
d. Both A C
7. Which of the following is the angle of refraction (θr) in the image above?
a. θ2
b. θ3
c. θ4
d. Both A C
8. Which of the following statements is correct according to geometry?
a. θ1 = θ2
b. θ2 = θ3
c. θ3 = θ4
d. Both A C
9. Which of the following statements is correct according to Snell’s law?
a. θ1 >θ2
b. θ3 >θ4
c. Both A C
Lesson Objective: Solve problems involving Snell’s Law.
Use the image below to answer questions #10-11:
10. If θ is 22°, calculate the measurements of the following angles using Snell’s law:
θ1=
θ3=
θ4=
224

11. Do your mathematical answers match your answers to question #9 above?
Answer Key
1. Refraction is caused by the changes in the speed of light as it travels from one material to another.
2. Answers will vary. Sample answer: The index of refraction (n) is the ratio of the speed of light in a vacuum
to the speed of light in a given material (n=c/v). It indicates how much light will change speed as a result of
traveling from one material to another.
3. Answers will vary. Sample answer: The speed of light in a vacuum (3.0 x 108 m/s) is the universal speed limit,
or the maximum speed at which any matter in the universe can travel. The index of refraction is the ratio of
the speed of light in a vacuum to the speed of light in another material (which must be equal to or less than 3.0
x 108 m/s). As a result of nothing traveling faster than the speed of light in a vacuum, the index of refraction
(n=c/v) will always be equal to or greater than one.
4.
5. B
6. D
7. D
8. B
9. C
10. nair = 1.00; noil = 1.48; nwater = 1.33
Snell’s Law: n1 sin θ1 = n2 sin θ2
θ3 = 22° due to being alternate interior angles (geometry)
1.00 sin θ1 = 1.48 sin 22° θ1 = 33.4°
1.48 sin 22°= 1.33 sin θ4; θ1 = 24.8°
11. Yes; Sample answer: When a light ray travels from air to oil, it slows down and bends toward the normal
line. As a result, the angle of incidence (θ1 = 33.4°) is greater than the angle of refraction (θ222°). When a
light ray travels from oil to water, it speeds up and bends away from the normal line. As a result, the angle of
incidence (θ3 = 22°) is greater than the angle of refraction (θ2 = 24.8°).
225

20.4. Thin Lenses www.ck12.org
20.4 Thin Lenses
Lesson Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how to draw ray diagrams for convex (converging) lenses.
Use the image below, illustrating a standard set-up for a ray diagram of a convex lens, to answer questions #1-4:
1. Which of the following correctly describes the lens above?
a. It is a convex lens because it is thicker in the center than its edges
b. It is a convex lens because it is thinner in the center than its edges
c. It is a converging lens because it makes rays of light parallel to the principal axis converge at the focal
point
d. Both A C
2. Which of the following signifies the focal point (f) in the image above?
a. A
b. B
c. C
d. D
3. Which of the following signifies the ray of light in the image above?
a. A
b. B
c. C
d. D
4. Which of the following signifies the principal axis (p) in the image above?
a. A
b. B
c. C
d. D
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5. Provide a general description of the image of an object placed beyond the focal point of a convex lens by
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
SAME SIDE / OPPOSITE SIDE
6. Provide a general description of the image of an object placed closer to a convex lens than its focal point by
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
7. Describe the three principle rays that can be drawn to construct ray diagrams for convex lenses.
8. Use the three principle rays described above to construct a ray diagram for the image of a tree through the
following convex lens.
227

9. Describe the image of the tree by circling the correct answer choices below:
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
10. What could you do create a virtual image of the tree in the convex lens above?
Lesson Objective: Understand how to solve problems involving convex (converging) lenses.
11. Complete the following chart regarding sign conventions for thin lenses:
Use the diagram below of a tree beyond the focal point of a convex lens to answer questions #12-15:
228

12. Use the lens equation ( 1
do
+ 1
di
= 1
ho
= − di
do
illustration above.
14. Based in your calculations and the chart in question #11, describe the image of the tree in the concave mirror
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
15. Do your mathematical calculations and description above match the image formed by your ray diagram in
question #8?
Lesson Objective: Understand how to draw ray diagrams for concave (diverging) lenses.
Use the image below, illustrating a standard set-up for a ray diagram of a concave lens, to answer question #16:
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16. Which of the following correctly describes the lens above?
a. It is a concave lens because it is thinner in the center than its edges
b. It is a diverging lens because it makes rays of light parallel to the principal axis diverge
c. It is a diverging lens because the extension of the refracted ray converge at a focal point to the left of the
lens
d. All of the above
17. Provide a general description of the image of an object placed anywhere in front of a concave lens by circling
the correct choices below:
Image orientation:
UPRIGHT / INVERTED
Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
18. Describe the three principle rays that can be drawn to construct ray diagrams for concave lenses.
19. Use the three principle rays described above to construct a ray diagram for the image of a tree in the following
concave lens.
230

Lesson Objective: Understand how to solve problems involving concave (diverging) lenses.
Use the diagram below of a tree beyond the focal point of a concave lens to answer questions #20-23:
20. Use the lens equation ( 1
do
+ 1
di
= 1
ho
= − di
do
illustration above.
22. Based in your calculations and the chart above, describe the image of the tree in the concave mirror by circling
the correct answer choices below:
Image orientation:
UPRIGHT / INVERTED
231

Type of image:
REAL / VIRTUAL
BIGGER / SMALLER
Image location:
23. Do your mathematical calculations and description above match the image formed by your ray diagram in
question #19?
Answer Key
1. D
2. B
3. A
4. C
5. INVERTED, REAL, SMALLER, OPPOSITE SIDE
6. UPRIGHT, VIRTUAL, LARGER, SAME SIDE
Ray 1: A ray drawn parallel to the principal axis is refracted through the opposite focal point, f.
Ray 2: A ray drawn through the focal point, f, on the same side of the lens as the object refracts parallel to the
principal axis.
Ray 3: A ray drawn through the center the lens does not refract.
8.
232

10. Answers will vary. Sample answer: You could place the tree at a location closer to the convex lens than its
focal point, creating an upright, virtual, larger, image located on the same side of the lens as the object.
11.
12. Based on the given scale, do = 4 m and f = 1 m.
1
do
+
1
di
=
1
f
1
4m
+
1
di
=
1
1m
1
di
=
1
4 m
−
1
1m
1
di
+
(4−1)
(4)
= 0.75
di = +1.3 m
13.
m =
hi
ho
= −
di
do
m = −
1.3 m
4 m
= −0.33
14. REAL Explanation: the distance of the image (di) is positive, so the image is real and located on the opposite
side of the lens as the object.
INVERTED Explanation: the magnification (m) is negative, so the image is inverted.
15. Answers will vary. Sample answer: Yes, the image is real, inverted, smaller than the actual tree, and forms
about 1.3 m on the opposite side of the lens.
16. D
Ray 1: A ray drawn parallel to the principal axis is refracted through the opposite focal point, f.
Ray 2: A ray drawn through the focal point, f, on the same side of the lens as the object refracts parallel to the
principal axis.
Ray 3: A ray drawn through the center the lens does not refract.
19.
233

20. Based on the given scale, do = 4 m and f = -1 m(**for a concave/diverging lens, the focal point is negative).
1
do
+
1
di
=
1
f
1
4m
+
1
di
=
1
−1m
1
di
=
1
4 m
−
1
−1m
1
di
+
(4+1)
(−4)
= −1.25
di = −0.8 m
21.
m =
hi
ho
= −
di
do
m = −
−0.8 m
4 m
= 0.2
22. REAL Explanation: the distance of the image (di) is positive, so the image is real and located on the opposite
side of the lens as the object.
UPRIGHT Explanation: the magnification (m) is positive, so the image is upright.
23. Answers will vary. Sample answer: Yes, the image is virtual, upright, smaller than the actual tree, and forms
about 0.8 m on the same side of the lens.
234

www.ck12.org Chapter 21. CK-12 Physics IH-Chapter-Physical Optics Worksheets
CHAPTER
21 CK-12 Physics
IH-Chapter-Physical Optics Worksheets
Chapter Outline
21.1 DISPERSION
21.2 THE DOUBLE-SLIT EXPERIMENT
21.3 THIN FILMS
21.4 POLARIZATION
235

21.1. Dispersion www.ck12.org
21.1 Dispersion
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the causes dispersion through a glass prism.
1. How does physical optics differ from geometrical optics?
2. How is does the color of a light wave depend upon its frequency?
3. How does the speed of a light wave through a glass prism depend upon its frequency?
4. How does the index of refraction of a light wave through a glass prism depend upon its frequency?
5. Explain the dispersion of light through a glass prism with reference to color, speed, and index of refraction.
Answer Key
1. Answers will vary. Sample answer: Physical optics focuses on the behavior of light as a wave, rather than
a ray like in geometrical optics. Physical optics includes such phenomena as dispersion, interference, and
polarization.
2. Answers will vary. Sample answer: Our eyes are able to detect a small range of frequencies, which we refer
to as the visible spectrum. Specific colors have specific frequencies. Violet light has the highest frequency
(shortest wavelength) in the visible spectrum and red light the lowest frequency (longest wavelength).
3. Answers will vary. Sample answer: The speed of light in a medium (other than a vacuum) depends on its
frequency. The higher the frequency of a light wave (the shorter the wavelength) the slower the speed through
a glass prism. As a result, violet light will travel slower than red light through a glass prism.
4. Answers will vary. Sample answer: The index of refraction (n=c/v) depends on the speed of light in the
medium. The speed of violet light is less than red light through a glass prism and, as a result, violet light will
have a higher index of refraction (as v decreases, n increases). As a result, violet light bends the most as it
travels through a glass prism (and red light bends the least).
5. Answers will vary. Sample answer: The spreading out of white light into the colors of the visible spectrum
through a glass prism is called dispersion. Dispersion is a result of the various colors of light having different
frequencies. As the frequency of light increases, the speed of light through a glass prism decreases and the
236

index of refraction increases. As a result of these differences in light speed and refraction, white light disperses
into all the colors of the rainbow as it travels through a prism.
237

21.2. The Double-Slit Experiment www.ck12.org
21.2 The Double-Slit Experiment
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the Double-Slit Experiment.
1. Provide a simple sketch illustrating the Double-Slit Experiment.
2. Explain the significance of the Double-Slit Experiment.
3. What is monochromatic light and how is it used in the Double-Slit Experiment?
4. What is diffraction and how is it related to the Double-Slit Experiment?
Lesson Objective: Solve problems involving the Double-slit Experiment.
5. In a physics experiment, light was directed upon a screen with two slits spaced 0.002 mm apart. A bright
first order fringe appeared at an angle of 17.4°. Determine the color of the light used in this Double-Slit
Experiment.
Answer Key
1. Images will vary, but all images should include:
238

• A source of monochromatic light
• A screen with two slits
• The constructive and destructive interference of light waves as a result of passing through the two slits
• A series of light and dark bands as a result of the interference of light
Refer the following image of the set-up of a Double-Slit Experiment from CK12 Lesson 21.2: http://www.c
k12.org/flx/show/default/image/user%3AY2sxMnNjaWVuY2VAY2sxMi5vcmc./98045-1367368473-94-94-Ph
y-Int-Honors-22-03.png
2. Answers will vary. Sample answer: Thomas Young discovered that when monochromatic light was shown
through a screen with two small, closely spaced openings, it produced a pattern of light and dark bands. The
light bands resulted from the constructive interference of light waves and the dark bands resulted from the
destructive interference of light waves. Through his Double-Slit Experiment, Young provided the necessary
evidence to prove that light behaved as a wave.
3. Answers will vary. Sample answer: Monochromatic light is light of a single frequency (or color). Monochro-
matic light vibrates at the same frequency and, as a result, will produce light waves that are in phase and
create an interference pattern when shown through a screen with two slits.
4. Answers will vary. Sample answer: Diffraction describes the behavior of a wave as it spreads out through
an opening or bends around an obstacle. The diffraction of light waves through the two openings in the
Double-Slit Experiment resulted in the interference pattern of light and dark bands.
5. Bright fringe indicates constructive interference, therefore the equation d sinθ = mλ must be used.
d = 0.002 mm = 2.0 x 10−6m
θ=17.4°
m = 1
λ = wavelength
(2.0 x 10−6m)(sin 17.4°)=(1)(λ)
λ = 5.98 x 10−7m or 598 nm, which is yellow light.
239

21.3. Thin Films www.ck12.org
21.3 Thin Films
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand how thin films recreate constructive and destructive interference.
1. What is a thin film? Provide an example.
2. Although monochromatic light consists of one frequency and wavelength, two waves exit a thin film and
interfere. Explain how the monochromatic incident light produces these two waves.
3. What conditions are necessary for constructive thin film interference?
4. What conditions are necessary for destructive thin film interference?
5. What conditions are necessary for a phase change to occur in a thin film?
Answer Key
1. Answers will vary. Sample answer: A thin film describes a very small layer of material that reflects light in
such a way to create wave interference. Examples of a thin film include a soap bubble, a layer of oil on water,
or the protective coating on a CD or DVD.
2. Answers will vary. Sample answer: Monochromatic incident light is reflected off both the top and bottom of
the thin film. As a result, two waves of light exit the thin film and can interfere.
3. Answers will vary. Sample answer: The light waves must be very close together and in phase with each other.
4. Answers will vary. Sample answer: The light waves must be very close together and out of phase with each
other.
5. Answers will vary. Sample answer: A phase change will occur when monochromatic light reflects off the
surface of a medium with a greater index of refraction.
240

21.4 Polarization
Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand the meaning of polarization and its mechanism.
1. Is light a transverse or longitudinal wave? Explain the reason for your choice.
2. Which of the following best describes the light wave produced by a vertically vibrating electron?
a. Vertically polarized light
b. Horizontally polarized light
c. Non-polarized Light
d. Light is not produced by a vibrating electron
3. Explain why sunlight is non-polarized.
Lesson Objective: Understand polarization by transmission and reflection.
4. Describe how polarizers polarize light by transmission.
5. Describe the polarization of light by the reflection off non-metallic surfaces, such as the ocean.
Answer Key
1. Answers will vary. Sample answer: Light is a transverse wave because the medium (the electromagnetic field)
propagates perpendicularly to the direction the wave travels. A longitudinal wave (a sound wave) propagates
the medium (air) parallel to the direction the wave travels.
2. A
3. Answers will vary. Sample answer: Sunlight is produced by many electrons vibrating in random electrons.
Polarized light is created by either a single vibrating electron or a group of electrons with the same periodic
motion.
4. Answers will vary. Sample answer: Polarizers are transparent materials that are composed of long chains of
molecules that act as a filter for non-polarized light. Polarizers will only allow light waves through that are
aligned along the same plane (while blocking the non-aligned waves). This is described as polarization by
transmission.
5. Answers will vary. Sample answer: Light is polarized by the reflection off non-metallic surfaces along the
same plane as the surface. The light that reflects off the horizontal boundary of the ocean will become
horizontally polarized. This is often perceived by our eyes as a glare. Many sunglasses are made with vertical
polarizers in order to block the polarization of light by reflection.
241

www.ck12.org
CHAPTER
22 The Special Theory of
Relativity
Chapter Outline
22.1 THE SPECIAL THEORY OF RELATIVITY
242

www.ck12.org Chapter 22. The Special Theory of Relativity
22.1 The Special Theory of Relativity
Worksheet
Name___________________ Class______________ Date________
Galilean Relativity
1. Provide TWO examples of inertial frames of reference in the space below.
Sound waves travel at approximately 343 m/s in air. Use the principles of Galilean Relativity to determine the
relative velocity of the sound waves in each of the various inertial frames of reference below.
2. The sound waves observed by the pilot of a jet travelling at a constant 360 m/s, producing a sonic boom.
3. The sound waves observed by a driver of an ambulance traveling at 29 m/s (65 mph).
4. How does the observance of sound waves described in questions #2-3 differ from what was observed about
the speed of light?
Time Dilation and Length Contraction
5. Which of the following statements correctly follow the theory of special relativity?
a. Absolute time and space do not exist
b. Space and time are interdependent
c. Any change in time must result in a change in space
d. All of the above
6. Which of the following statements correctly exemplifies time dilation?
a. A clock moving relative to an observer will run more slowly than a clock at rest relative to the observer
b. A clock moving relative to an observer will run more quickly than a clock at rest relative to the observer
c. A clock at rest relative to an observer will run more slowly than a clock moving relative to the observer
d. A clock at rest relative to an observer will run more quickly than a clock moving relative to the observer
7. As time dilates, the length of an object _____ , in order to maintain the speed of light as constant.
a. Contracts
b. Expands
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22.1. The Special Theory of Relativity www.ck12.org
c. Remains the same
8. According to time dilation, clocks on the International Space Station (ISS) run slightly _____ than clocks on
Earth.
a. Faster
b. Slower
c. At the same rate
9. According to time dilation, upon returning from a mission aboard the International Space Station (ISS),
astronauts will be slightly _____ than if they had remained on Earth.
a. Younger
b. Older
c. Same age
10. According to the special theory of relativity, do astronauts aboard the ISS sense the dilatation of time? Explain
the reason for your answer.
Simultaneity
11. Describe a thought experiment illustrating the relativity of simultaneous events.
Mass-Energy Equivalence
12. What is rest energy?
13. According to mass-energy equivalence, when the mass of an object decreases
a. Energy is consumed
b. Energy is released
c. Matter is created
d. Matter is destroyed
14. Which equation can be used to calculate the rest energy of a stationary piece of matter?
a. KE=1/2 mv2
b. PE=mgh
c. E=mc2
d. PE=1/2 kx2
General Theory of Relativity
15. What is space-time and how does it fit into the general theory of relativity?
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www.ck12.org Chapter 22. The Special Theory of Relativity
Answer Key
Note to Teachers: The questions contained in Chapter 22 of the Physics Intermediate Workbook have been consol-
idated to include one worksheet for the entire chapter, as opposed to previous chapters that are composed of one
worksheet per individual lesson. The Chapter 22 worksheet has a set of practice problems for every lesson in the
chapter, rather than every objective. The conceptual questions included are meant to provide an efficient introduction
to the theory of special and general relativity appropriate for the high school level.
1. Answers will vary. All answers should describe a frame of reference with uniform motion (at constant velocity,
not acceleration).
Sample answer:
(1) On a train, traveling with a constant velocity (constant motion, no acceleration)
(2) Standing still on the sidewalk (constant velocity, v=0 m/s; no acceleration)
2. Answers will vary. Sample answer: From the pilot’s frame of reference, the sound waves will be traveling at
-17 m/s (343 m/s –360 m/s = -17 m/s).
3. Answers will vary. Sample answer: From the driver’s frame of reference, the sound waves will be traveling at
+314 m/s (343 m/s –29 m/s = 314 m/s).
4. Answers will vary. Sample answer: According to Galilean Relativity, the velocity vectors describing the
motion of the sound waves and the motion of the observer simply add together. This differs from light, which
always moves at the same speed (c=3.0 x 108 m/s) despite the motion of the light source or the observer.
5. D
6. A
7. A
8. B
9. A
10. Answers will vary. Sample answer: The first postulate of the special theory of relativity is that the laws of
physics are the same for all inertial frames of reference. As a result, astronauts aboard the ISS will not be able
to perceive the dilation of time compared to the Earth, because they will view the passing of time normally in
their frame of reference.
11. Answers will vary. Example: a description of the twin paradox or Einstein’s train-and-platform though
experiment. All examples should include observers in different inertial frames who measure unequal time
intervals when observing the same event. This highlights the relativity of time.
12. Einstein concluded that matter at rest (even if it did not have a height above the ground) had energy –which
he referred to at rest energy. Energy is stored in all matter as rest energy, similar to a potential energy.
13. B
14. C
15. Answers will vary. Sample answer: Space-time refers to the combination of the three dimensions of space
(the x-axis, the y-axis, and the z-axis) and the additional fourth dimension of time. In the general theory of
relativity, Einstein proposed that gravity was actually a result of a curvature in space-time produced by a mass
(rather than a force that acted at a distance).
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CHAPTER
23 CK-12 Physics
IH-Chapter-Quantum Physics
Worksheets
Chapter Outline
23.1 QUANTUM PHYSICS
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www.ck12.org Chapter 23. CK-12 Physics IH-Chapter-Quantum Physics Worksheets
23.1 Quantum Physics
Worksheet
Name___________________ Class______________ Date________ Answer each of the questions below to show
your achievement of the lesson objectives.
Blackbody Radiation and Planck’s Quantum Hypothesis
1. What is a quantum?
2. How did Planck’s mathematical equation lead to a quantum hypothesis?
3. Use Planck’s equation to calculate the energy of a photon of red light (λ = 633 nm).
4. What is a blackbody? Why is it important to the development of Planck’s quantum hypothesis?
5. Which of the following acts most similar to a blackbody?
a. The sun
b. A black hole
c. Both A B
Photons and the Photoelectric Effect
6. What is a photon?
7. Describe the photoelectric effect.
8. Experimental results show that violet light incident on a metallic surface ejected electrons and green light
incident on the same surface had no effect. Explain these results with reference to the photons and the
photoelectric effect.
Wave-Particle Duality
9. What is wave-particle duality?
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10. Describe an instance in which light behaves as a wave.
11. Describe an instance in which light behaves as a particle.
12. De Broglie suggested that
a. Particles with momentum have an associated wavelength
b. Moving matter exhibits wave-like behavior
c. The wavelength of matter can be calculated in the same way as the wavelength of light
d. All of the above
Answer Key
∗∗Note to Teachers: The questions contained in Chapter 23 of the Physics Intermediate Workbook have been
consolidated to include one worksheet for the entire chapter, as opposed to previous chapters that are composed of
one worksheet per individual lesson. The Chapter 23 worksheet has a set of practice problems for every lesson in the
chapter, rather than every objective. The conceptual questions included are meant to provide efficient introduction
quantum physics appropriate for the high school level.
1. Answers will vary. Sample answer: A quantum describes the smallest possible amount of something that can
be quantized (an elemental unit). Something can be quantized if it only comes in discrete amounts, not all
amounts.
2. Answers will vary. Sample answer: Planck provided a mathematical equation (E = nhf) to solve for the energy
of light based on its frequency. This equation implied that light must be quantized. Now we know that Planck’s
equation describes the energy of each photon in a beam of light.
3. First, solve for the frequency:
V = fλ
(3 x 108m/s) = (6.33 x 10−7m)(f)
f = 4.73 x 1014Hz
Then, use Planck’s equation E=hf to solve for the energy
E = (6.626 x 10−34 Js)(4.47 x 1014Hz)
E = 2.7 x 10−19J
4. Answers will vary. Sample answer: A blackbody is an idealized body that absorbs all incident light. According
to classical physics, a blackbody should emit all wavelengths of light continuously. However, Planck observed
that this was not the case –light was emitted in discrete amounts, proportional to the frequency of the radiation.
This led to his quantum hypothesis that energy was radiated at certain frequencies.
5. C
6. Answers will vary. Sample answer: A photon is a discrete amount of electromagnetic energy that composes a
quantum of light.
7. Answers will vary. Sample answer: The photoelectric effect describes the phenomenon of certain frequencies
of incident light on a metallic surface resulting in the ejection of electrons.
8. Answers will vary. Sample answer: The violet light had more energy per photon and was able to eject
electrons as a result.
9. Answers will vary. Sample answer: A theory that states light behaves like a wave but emits and absorbs
energy like a particle.
10. Answers will vary. Sample answer: Evidence of the wave-like behavior of light includes interference, refrac-
tion, diffraction, etc.
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11. Answers will vary. Sample answer: Evidence of the particle-like behavior of light includes photoelectric
effect, blackbody radiation, etc.
12. D
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CHAPTER
24 CK-12 Physics
IH-Chapter-Atomic Physics Worksheets
Chapter Outline
24.1 ATOMIC PHYSICS
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www.ck12.org Chapter 24. CK-12 Physics IH-Chapter-Atomic Physics Worksheets
24.1 Atomic Physics
Worksheet
Name___________________ Class______________ Date________
Modeling the Atom
Describe the following models of the atom, including the scientists associated with developing each model and the
supporting experimental evidence.
1. The plum pudding model
2. The nuclear model
3. The planetary model
4. The electron cloud model
The Bohr Atom
5. Describe the emission spectrum of hydrogen and its connection to the Bohr model of the atom.
6. What were some sources of error in Rutherford’s planetary model of the atom? How did Bohr plan to resolve
these inconsistencies?
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7. Describe the arrangement of electrons in Bohr’s atomic model.
8. Describe the quantization of energy in Bohr’s atomic model.
Uncertainty Principle
9. What is the fundamental constraint described by the Heisenberg uncertainty principle?
10. The uncertainty principle is only applicable to
a. Quantum Mechanics
b. Astronomy
c. Macroscopic world
d. All of the above
Answer Key
∗∗Note to Teachers: The questions contained in Chapter 24 of the Physics Intermediate Workbook have been
consolidated to include one worksheet for the entire chapter, as opposed to previous chapters that are composed of
one worksheet per individual lesson. The Chapter 24 worksheet has a set of practice problems for every lesson in the
atomic physics appropriate for the high school level.
1. Answers will vary. Sample answer: The plum pudding model of the atom was developed by J.J. Thompson,
after his discovery of the electron based on his research with cathode rays. Thompson hypothesized that
the negatively charged electrons were spread throughout the atom and surrounded by a positively charged
pudding-like substance, resulting in an overall neutral charge.
2. Answers will vary. Sample answer: Rutherford later disproved Thompson’s plum pudding model with his gold
foil experiment, in which he sent a beam of alpha particles toward a piece of gold foil and observed that the
majority of the particles passed through the foil and a few were deflected. As a result, Rutherford proposed
that the majority of the atom was empty space (explaining why most atoms traveled through the foil) and all of
the mass was concentrated in the center of the atom and had an overall positive charge, which he named the
nucleus (explaining why some of the particles were repelled by the positively charged gold foil). This is often
referred to as the nuclear model of the atom and has greatly contributed to the modern model of the atom,
which is accepted today.
3. Answers will vary. Sample answer: In his planetary model, Rutherford proposed the negatively charged
electrons orbited around the positively charged nucleus, similar to how the planets orbit the sun in our solar
system.
4. Answers will vary. Sample answer: This is the modern model of the atom, in which electrons exhibit wavelike
behavior. As a result, their exact location around the nucleus of an atom cannot be specified. Instead, their
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motion around the nucleus is illustrated by a cloud, in which the densest area signifies where the electrons are
most likely to be found.
5. Answers will vary. Sample answer: When hydrogen gas is heated, it emits light. When refracted through
a prism, this light produces distinct bright lines (rather dispersing into all the colors of the rainbow). This
is called the element’s emission spectrum and is unique to that element. The specific emission spectrum of
hydrogen led Bohr to believe that the atomic model must somehow be quantized.
6. Answers will vary. Sample answer: A moving electric charge should produce an electromagnetic wave.
However, a hydrogen atom radiated no light and only produced certain frequencies of light when energized.
Bohr felt that the electrons should somehow be quantized. He planned to join the planetary model of the atom
with Einstein’s quantum theory of light.
7. Answers will vary. Sample answer: Bohr maintained the planetary model of the electrons circling the nucleus
but proposed that the electrons were organized into step-like energy levels within an electron cloud.
8. Answers will vary. Sample answer: The electrons did not radiate energy when travelling in circular orbits, but
only when moving from one energy level to another. The energy absorbed or emitted by the electrons moving
from one energy level to another was quantized, and only came in discrete amounts.
9. Answers will vary. Sample answer: It is impossible to simultaneously know both the position and momentum
of subatomic particles, such as electrons.
10. A
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CHAPTER
25 Nuclear Physics
Chapter Outline
25.1 WORKSHEET
25.2 ANSWER KEY
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www.ck12.org Chapter 25. Nuclear Physics
25.1 Worksheet
Name___________________ Class______________ Date________
Lesson Objective: Understand magnetic flux.
The Nucleus
1. What are nucleons?
2. Describe the strong nuclear force and its connection to the stability of an atom’s nucleus.
Radioactive Half-life
3. Which of the following spontaneous reactions exemplifies alpha decay?
a. 137
56 Ba →137
56 Ba+γ
b. 232
90 Th →228
88 Ra+4
2 He
c. 14
6 C →14
7 N +0
−1 e− +ν
d. All of the above
4. Explain the reason for your answer choice in question #3 above.
5. Which of the following spontaneous reactions exemplifies beta decay?
a. 137
56 Ba →137
56 Ba+γ
b. 232
90 Th →228
88 Ra+4
2 He
c. 14
6 C →14
7 N +0
−1 e− +ν
d. All of the above
7. Which of the following spontaneous reactions exemplifies gamma decay?
a. 137
56 Ba →137
56 Ba+γ
b. 232
90 Th →228
88 Ra+4
2 He
c. 14
6 C →14
7 N +0
−1 e− +ν
d. All of the above
A sample of 300 grams of a radioactive isotope with half-life of 10 years decays for 50 years.
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25.1. Worksheet www.ck12.org
9. The time period for the decay is equivalent to
a. 0.25 half-lives
b. 1 half-life
c. 4 half-lives
d. 5 half-lives
10. Calculate how much of the original isotope will remain at the end of the 50 year period.
Nuclear Fission and Fusion
11. Nuclear fission is a process in which
a. The repelling electromagnetic force between protons overcomes the attractive strong nuclear force be-
tween nucleons
b. Heavy nuclei split to become lighter nuclei
c. Heavy nuclei loose mass and release energy
d. All of the above
12. Nuclear fusion is a process in which
a. Extremely high temperatures are required
b. Light nuclei collide at high speed
c. Light nuclei loose mass and release energy
d. All of the above
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www.ck12.org Chapter 25. Nuclear Physics
25.2 Answer Key
Note to Teachers: The questions contained in Chapter 25 of the Physics Intermediate Workbook have been consol-
idated to include one worksheet for the entire chapter, as opposed to previous chapters that are composed of one
worksheet per individual lesson. The Chapter 25 worksheet has a set of practice problems for every lesson in the
nuclear physics appropriate for the high school level.
1. Answers will vary. Sample answer: Nucleons are the subatomic particles contained in an atom’s nucleus.
They consist of positively charged protons and neutrally charge neutrons, held together by an attractive strong
nuclear force.
2. Answers will vary. Sample answer: The strong nuclear force is one of the four fundamental forces of nature
and is only found in the nucleus of an atom. The strong nuclear force is a short-range, attractive force that
exists between nucleons. This strong nuclear force between the protons and neutrons counters the repulsive
electrostatic force between the positively charged protons in the nucleus and helps to make the nucleus stable.
As the number of protons in an atom’s nucleus increases, the stability of the atom decreases.
3. B
4. Answers will vary. Sample answer: Alpha decay produces atoms with a nucleus made up of two protons and
two neutrons, identical to the nucleus of a helium atom, referred to as alpha particles. This is exemplified by
the radioactive decay of Thorium in answer B.
5. C
6. Answers will vary. Sample answer: Beta decay results in the ejection of electrons. This is exemplified by the
radioactive decay of Carbon in answer C.
7. A
8. Answers will vary. Sample answer: Gamma decay results in the production gamma rays, made up of photons
with a large amount of electromagnetic energy. This is exemplified by the radioactive decay of Barium in
answer A.
9. D
10. N = (1
2 )nN0
N = (1
2 )5(300 g)
11. D
12. D
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