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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
11. Explain the reason for your choice in question #10.
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
70

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?
72

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:
73

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
79

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.
80

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.
82

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

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