Unit 1

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Unit 1

  1. 1. Chapter 1 Measurements Units of Measurement
  2. 2. Measurement You are making a measurement when you ♦Check you weight ♦Read your watch ♦Take your temperature ♦Weigh a cantaloupe What kinds of measurements did you make today?
  3. 3. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard.
  4. 4. Some Tools for Measurement
  5. 5. Units of Measurements MKS: meters (m), Kilogram (kg), second (s) kilometer (km), hour (h) CGS: centimeter (cm), gram (g), second (s) FPS: foot (ft.), pound (lb.), second (s) miles (mi.), hour (h)
  6. 6. Learning Check From the previous slide, state the tool (s) you would use to measure A. temperature ____________________ B. volume ____________________ ____________________ C. time ____________________ D. weight ____________________
  7. 7. Solution From the previous slide, state the tool (s) you would use to measure A. temperature thermometer B. volume measuring cup, graduated cylinder C. time watch D. weight scale
  8. 8. Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature
  9. 9. Solution Some possible answers are A. length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature °F
  10. 10. Metric System (SI)  Is a decimal system based on 10  Used in most of the world  Used by scientists and hospitals
  11. 11. Units in the Metric System  length meter m  volume liter L  mass gram g  temperature Celsius °C
  12. 12. Stating a Measurement In every measurement there is a ♦Number followed by a ♦ Unit from measuring device
  13. 13. Learning Check What is the unit of measurement in each of the following examples? A. The patient’s temperature is 102°F. B. The sack holds 5 lbs of potatoes. C. It is 8 miles from your house to school. D. The bottle holds 2 L of orange soda.
  14. 14. Solution A. °F (degrees Fahrenheit) B. lbs (pounds) C. miles D. L (liters)
  15. 15. Learning Check Identify the measurement in metric units. A. John’s height is 1) 1.5 yards 2) 6 feet 3) 2 meters B. The volume of saline in the IV bottle is 1) 1 liters 2) 1 quart 3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams 3) 0.6 pounds
  16. 16. The Seven Base SI Units Quantity Unit Symbol Length meter m Mass kilogram kg Temperature kelvin K Time second s Amount of Substance mole mol Luminous Intensity candela cd Electric Current ampere a
  17. 17. SI Unit Prefixes - Part I Name Symbol Factor tera- T 1012 giga- G 109 mega- M 106 kilo- k 103 hecto- h 102 deka- da 101
  18. 18. SI Unit Prefixes- Part II Name Symbol Factor deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p 10-12 femto- f 10-15
  19. 19. Derived SI Units (examples) Quantity unit Symbol Volume cubic meter m3 Density kilograms per cubic meter kg/m3 Speed meter per second m/s Newton kg m/ s2 N Energy Joule (kg m2 /s2 ) J Pressure Pascal (kg/(ms2 ) Pa
  20. 20. SI Unit Prefixes for Length Name Symbol Analogy gigameter Gm 109 megameter Mm 106 kilometer km 103 decimeter dm 10-1 centimeter cm 10-2 millimeter mm 10-3 micrometer μm 10-6 nanometer nm 10-9 picometer pm 10-12
  21. 21. Scientific Notation M x 10n M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10
  22. 22. Factor-Label Method of Unit Conversion: Example Example: Convert 789m to km: 789m x 1km =0.789km= 7.89x10- 1 km 1000m
  23. 23. Limits of Measurement Accuracy and Precision
  24. 24. Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.
  25. 25. Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0cm? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm
  26. 26. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.
  27. 27. Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm Amy: 15.5cm, 15.0cm, 15.2cm, 15.3cm
  28. 28. Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.
  29. 29. Finding the Number of Sig Figs:  When the decimal is present, start counting from the left.  When the decimal is absent, start counting from the right.  Zeroes encountered before a non zero digit do not count.
  30. 30. Measuring Tools  Vernier caliper  Vernier caliper is a measuring device used to measure precise increments between two points.  Micrometer  Micrometer is a measuring device used for precisely measuring thickness, inner and outer diameter, depth of slots.  SWG  A gauge for measuring the diameter of wire, usually consisting of a long graduated plate with similar slots along its edge.
  31. 31. Vernier caliper  Function  To measure smaller distances  Can measure up to .001 inch or .01mm.  Features  Larger, lower jaws are designed to measure outer points e.g. diameter of a rod.  Top jaws are designed to measure inside points e.g. size of a hole.  A rod extends from the rear of the caliper and can be used to measure the depth.
  32. 32. Structure of Vernier caliper
  33. 33. Structure of the Vernier caliper  Main Scale  Main scale is graduated in cm and mm.  Vernier Scale  It slides on the main scale.  On Vernier scale 0.9cm is divided into 10 equal parts.  Jaws  Two inside jaws (Upper)  Two outside jaws (Lower)
  34. 34. Least Count  Least count (L.C) is the smallest reading we can measure with the instrument.  L.C = one main scale division – one vernier scale division L.C = 1mm – 0.09mm L.C = 0.1mm = 0.01cm  Least Count = Value of the smallest division on MS/ Total number of division on VS L.C = 1mm / 10 = 0.1 cm / 10 = 0.01cm
  35. 35. Reading of the Instrument  Reading of the instrument = MS div + (coinciding VS div x L.C)  = 3.2 + (3 x 0.01)  = 3.2 + 0.03  = 3.23 cm
  36. 36. Micrometer  Function  Micrometer allows the measurement of the size of the body i.e. thickness, depth, inner/outer diameter.  Features  Two jaws (one fixed, one movable)  Spring loaded twisting handle  Easy to use and more précised  Can measure up to .001cm
  37. 37. Structure of the Micrometer
  38. 38. Structure of Micrometer  Jaws  2 jaws (one fixed, one movable)  Circular Scale  Movable jaw is attached to a screw, scale on this screw is called Circular scale.  Either 50 or 100 divisions  Linear Scale  Horizontal Scale
  39. 39. Structure of Micrometer  Frame  The C-shaped body that holds the anvil and sleeve in constant relation to each other.  Anvil  The jaw which remains stationary.  Spindle  The jaw which moves towards the anvil.  Lock Nut  A lever, one can tighten to hold the spindle stationary.  Sleeve  The stationary round part with the linear scale on it. (Main Scale)  Thimble  Thimble rotates around the sleeve.  Ratchet Stop  Device on end of handle that limits applied pressure by slipping at a calibrated torque.
  40. 40. Pitch of Micrometer  When the head of the micrometer rotate through one rotation, called pitch of the micrometer.  The screw moves forward or backward 1mm on the linear scale.  Pitch of Micrometer = distance on linear scale / one rotation Pitch of Micrometer = 1/1 = 1mm
  41. 41. Reading of the Instrument  Reading of the instrument = MS div + (coinciding CS div x L.C)  = 8+ (12 x 0.01)  = 8 + 0.120mm  = 8.120 mm = 8120 µm
  42. 42. Scalars A scalar quantity is a quantity that has magnitude only and has no direction in space Examples of Scalar Quantities:  Length  Area  Volume  Time  Mass
  43. 43. Vectors A vector quantity is a quantity that has both magnitude and a direction in space Examples of Vector Quantities:  Displacement  Velocity  Acceleration  Force
  44. 44. Vector Diagrams Vector diagrams are shown using an arrow  The length of the arrow represents its magnitude  The direction of the arrow shows its direction
  45. 45. April 2, 2014 Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1.
  46. 46. Distance, Speed and Time April 2, 2014 Speed = distance (in metres) time (in seconds) D TS 1) Dave walks 200 metres in 40 seconds. What is his speed? 2) Laura covers 2km in 1,000 seconds. What is her speed? 3) How long would it take to run 100 metres if you run at 10m/s? 4) Steve travels at 50m/s for 20s. How far does he go? 5) Susan drives her car at 85mph (about 40m/s). How long does it take her to drive 20km?
  47. 47. April 2, 2014 Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1. Velocity is speed in a given direction and has the same units as speed.
  48. 48. Speed vs. Velocity April 2, 2014 Speed is simply how fast you are travelling… Velocity is “speed in a given direction”… This car is travelling at a speed of 20m/s This car is travelling at a velocity of 20m/s east
  49. 49. April 2, 2014 Speed is defined as the distance travelled per unit time and has the units of m/s or ms-1. Velocity is speed in a given direction and has the same units as speed.
  50. 50. To calculate speed we use the equation: Average speed = distance travelled/time taken = d/t Distance is measured in metres (m) and time is measured in seconds (s). The greater the distance travelled in a given time then the greater is the speed.
  51. 51. April 2, 2014 A useful way to illustrate how the distance throughout a journey varies with time is to plot a DISTANCE AGAINST TIME graph. This gives us a visual representation of how the journey progressed and allows us to see quickly how long each stage of the journey took compared with the other stages.
  52. 52. The steepness (gradient) will also give us the speed. The following graphs show how the shape of distance-time graphs may vary and how to interpret them
  53. 53. April 2, 2014 Distance Time0 0 A B C AB- constant speed BC - stationary Gradient = rise/run = speed Rise Run Distance - Time GraphsDistance - Time Graphs
  54. 54. April 2, 2014 DISTANCE is a SCALAR quantity and has size only but DISPLACEMENT is a VECTOR quantity and has size (or magnitude) and DIRECTION. 10 metres is a distance (size only) but 10 metres due south (size and direction) is a vector quantity. If we use DISPLACEMENT instead of distance then the graph will also give an indication of the direction taken with respect to its starting point.
  55. 55. April 2, 2014 Displacement Time0 0 AB - constant velocity (speed & direction) BC - stopped CD - Returning to its starting position at a constant velocity A B C D Distance - Time GraphsDistance - Time Graphs
  56. 56. Distance-time graphs April 2, 2014 40 30 20 10 0 20 40 60 80 100 4) Diagonal line downwards = 3) Steeper diagonal line =1) Diagonal line = 2) Horizontal line = Distance (metres) Time/s
  57. 57. April 2, 2014 40 30 20 10 0 20 40 60 80 100 1) What is the speed during the first 20 seconds? 2) How far is the object from the start after 60 seconds? 3) What is the speed during the last 40 seconds? 4) When was the object travelling the fastest? Distance (metres) Time/s
  58. 58. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. (a) Plot a distance-time graph. (b) What was the snail’s speed before lunch? (c) What was the snail’s speed after lunch?
  59. 59. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s)
  60. 60. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 4 8 12 16 800 160 240
  61. 61. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 4 8 12 16 0 80 160 240
  62. 62. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80 160 240
  63. 63. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80 160 240
  64. 64. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 (a) See graph (b) Speed before lunch = initial gradient = rise/run = 8/80 = 0.1m/s 4 8 12 16 80 160 240
  65. 65. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 4 8 12 16 0 80 160 240
  66. 66. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80 160 240
  67. 67. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 4 8 12 16 80 160 240
  68. 68. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 (a) See graph (b) Speed before lunch = initial gradient = rise/run = 8/80 = 0.1m/s 4 8 12 16 80 160 240
  69. 69. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples A snail slithers 8m in 80s then stops for lunch ( a lettuce leaf) for 40s. After lunch it continues the journey and it takes a further 120s to reach his final destination which is a further 8m away. Plot a distance-time graph. What was the snail’s speed before lunch? What was the snail’s speed after lunch? Distance (m) Time (s) 0 0 (a) See graph (b) Speed before lunch = initial gradient = rise/run = 8/80 = 0.1m/s (c) Speed after lunch = final gradient = rise/run = 8/120 = 0.067 m/s4 8 12 16 80 160 240
  70. 70. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Distance (m) Time (s) 0 200 400 600 800 200 40 60
  71. 71. April 2, 2014 Distance - Time Graphs: ExamplesDistance - Time Graphs: Examples Consider a car starting from rest and its speed is increasing continuously. Find the speed of the car at 40 seconds after the start of the journey. Distance (m) Time (s) 0 200 400 600 800 200 40 60
  72. 72. April 2, 2014 Acceleration is defined as the change in velocity in unit time and has the units m/s/s or m/s2 or ms-2 Acceleration is a vector quantity and so has size and direction. Velocity - Time GraphsVelocity - Time Graphs
  73. 73. To calculate acceleration we use the equation: Average acceleration = change in velocity/time taken = (final velocity – initial velocity)/time taken = (v – u)/t Velocity is measured in metres per second (m/s) and time is measured in seconds (s). The greater the change in velocity in a given time then the greater is the acceleration.
  74. 74. Acceleration April 2, 2014 V-U TA Acceleration = change in velocity (in m/s) (in m/s2 ) time taken (in s) 1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? 2) A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by? 3) A car accelerates from 10 to 20m/s with an acceleration of 2m/s2 . How long did this take? 4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration?
  75. 75. April 2, 2014 A useful way to illustrate how the velocity throughout a journey varies with time is to plot a VELOCITY AGAINST TIME graph. This gives us a visual representation of how the journey progressed and allows us to see quickly how long each stage of the journey took compared with the other stages. . Velocity - Time GraphsVelocity - Time Graphs
  76. 76. The steepness (gradient) will also give us the ACCELERATION. The area under a velocity-time graph gives us the distance travelled. The following graphs show how the shape of velocity- time graphs may vary and how to interpret them
  77. 77. April 2, 2014 Velocity Time0 0 A B C AB- constant acceleration BC - constant velocity Gradient = rise/run = acceleration (m/s2 ) Rise Run Velocity - Time GraphsVelocity - Time Graphs
  78. 78. April 2, 2014 Velocity Time0 0 A B C D E Constant Acceleration Constant Velocity At B,C & D there is instantaneous change in acceleration Area Under Graph = Total Distance Travelled Velocity - Time GraphsVelocity - Time Graphs
  79. 79. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (a) Constant Velocity Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10
  80. 80. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (a) Constant Velocity Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled = area under graph = area of rectangle = length x breadth = 8 x 8 = 64m
  81. 81. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10
  82. 82. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10
  83. 83. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled = area under graph = area of triangle = ½ base x height = ½ 8 x 8 = 32 m
  84. 84. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled= area under graph = area of triangle = ½ base x height = ½ 8 x 8 = 32 m Acceleration = gradient = rise/run = 8/8 = 1 ms-2
  85. 85. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10
  86. 86. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled= area under graph = ½ base x height = ½ 10 x 10 = 50m
  87. 87. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (c) Uniform Deceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled= area under graph = ½ base x height = ½ 10 x 10 = 50m Acceleration = gradient = rise/run = -10/10 = -1 ms-2 (Deceleration = +1 ms-2
  88. 88. April 2, 2014 A car starts from rest and accelerates uniformly to 20m/s in 10 seconds. It travels at this velocity for a further 30 seconds before decelerating uniformly to rest in 5 seconds. (a) draw a velocity - time graph of the car’s journey (b) calculate the car’s initial acceleration (c) calculate the car’s final deceleration (d) calculate the total distance travelled by the car (e) calculate the distance travelled by the car in the final 25 seconds Velocity - Time Graphs: ExampleVelocity - Time Graphs: Example
  89. 89. April 2, 2014 Velocity Time0 0 20 (m/s) (s) 10 40 45 Initial acceleration = initial gradient = rise/run = 20/10 = 2m/s2 Velocity - Time GraphsVelocity - Time Graphs
  90. 90. April 2, 2014 Velocity Time0 0 20 (m/s) (s) 10 40 45 final acceleration = final gradient = rise/run = -20/5 = -4m/s2 Velocity - Time GraphsVelocity - Time Graphs
  91. 91. April 2, 2014 Velocity Time0 0 20 (m/s) (s) 10 40 45 A B C Total distance travelled = total area under graph = area A + B + C = ½ x 10 x 20 + 30 x 20 + ½ x 5 x 20 = 100 + 600 + 50 = 750m Velocity - Time GraphsVelocity - Time Graphs
  92. 92. April 2, 2014 Velocity Time0 0 20 (m/s) (s) 10 40 45 C Distance travelled in final 25s = part area under graph = area D + C = 20 x 20 + ½ x 5 x 20 = 400 + 50 = 450m D 20 Velocity - Time GraphsVelocity - Time Graphs
  93. 93. April 2, 2014 Velocity - Time Graphs: ExamplesVelocity - Time Graphs: Examples (b) Uniform Acceleration Velocity (ms-1 ) Time (s) 10 8 6 4 2 0 0 2 4 6 8 10 Distance travelled= area under graph = area of triangle = ½ base x height = ½ 8 x 8 = 32 m Acceleration = gradient = rise/run = 8/8 = 1 ms-2
  94. 94. Velocity-time graphs April 2, 2014 80 60 40 20 0 10 20 30 40 50 Velocity m/s T/s 1) Upwards line = 2) Horizontal line = 3) Steeper line = 4) Downward line =
  95. 95. April 2, 2014 80 60 40 20 0 1) How fast was the object going after 10 seconds? 2) What is the acceleration from 20 to 30 seconds? 3) What was the deceleration from 30 to 50s? 4) How far did the object travel altogether? 10 20 30 40 50 Velocity m/s T/s
  96. 96. THE ACCELERATION OF FREE FALL
  97. 97. Questions:  Do heavier objects fall faster than lighter ones when starting from the same position?  Does air resistance matter?  If the free fall motion has a constant acceleration, what is this acceleration and how was it found?  How do we solve problems involving free fall?
  98. 98. Galileo (1564 – 1642) and the leaning tower of Pisa.
  99. 99. Air Resistance  The force of friction or drag acting on an object in a direction opposing its motion as it moves through air.
  100. 100. Hammer & Feather in the presence of air
  101. 101. Hammer & Feather in the absence of air
  102. 102.  If the free fall motion has a constant acceleration, what is this acceleration and how was it found?
  103. 103. If there were no air resistance both objects would fall with the same downward acceleration ;9.8 m/s2.this is called the acceleration of free fall
  104. 104.  The acceleration of free fall if represented by the symbol ‘g’.  Its value varies from one place on earth to another  Moving away from the earth and out into space ,g decreases  The value of g near the earth surafce is close to 10 m/s
  105. 105. How Fast?

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