2. Chapter: Motion and Momentum Table of Contents Section 3: MomentumMomentum Section 1: What is Motion? Section 2: AccelerationAcceleration 18

3. All matter in the universe is constantly in motion, from the revolution of Earth around the Sun to elections moving around the nucleus of an atom. Matter and Motion 1 1 What is Motion?

4. Something is in motion if it is changing position. Changing Position What is Motion? It could be a fast-moving airplane, a leaf swirling in the wind, or water tricking from a hose. When an object moves from one location to another, it is changing position. 1 1

5. The runners sprint from the start line to the finish line. Changing Position What is Motion? Their positions change, so they are in motion. 1 1

6. An object changes position if it moves relative to a reference point. Relative Motion What is Motion? Picture yourself competing in a 100-m dash. You begin just behind the start line. When you pass the finish line, you are 100 m from start line. 1 1

7. The position variable Position is a variable and it is always relative to an origin, or the place where the object’s starting point was zero.

8. If the start line is your reference point, then your position has changed by 100 m relative to the start line, and motion has occurred. Relative Motion What is Motion? 1 1

9. Forward and backward Position and distance are similar but not the same. Both use units of length. Distance can have only positive values.

10. Forward and backward Position uses positive and negative numbers. Positive numbers are for positions to the right (in front) of the origin. Negative numbers are for positions to the left (or behind) the origin.

11. 3.1 Forward and backward Many variables can be positive or negative. These include position, speed, and force. These variables are called vectors because they can have a value and a direction. We use the term velocity to mean speed with direction.

12. Displacement includes the distance between the starting and ending points and the direction in which you travel. Distance and Displacement What is Motion? This figure shows the difference between distance and displacement. 1 1

13. Speed is the distance traveled divided by the time taken to travel the distance. Speed What is Motion? Speed can be calculated from this equation: 1 1

14. In SI units, distance is measured in m and time is measured in s. Speed What is Motion? As a result, the SI unit of speed is the m/s— the SI distance unit divided by the SI time unit. 1 1

15. Average speed is found by dividing the total distance traveled by the time taken. Average Speed What is Motion? An object in motion can change speeds many times as it speeds up or slows down. 1 1

16. The speed of an object at one instant of time is the object's instantaneous speed. Average Speed What is Motion? If it takes you 0.5 h to walk 2 km to the library, your average speed would be as follows: 1 1

17. Average speed, instantaneous speed, and constant speed are illustrated here. Average Speed What is Motion? 1 1

18. You can represent the motion of an object with a distance-time graph. Graphing Motion What is Motion? For this type of graph, time is plotted on the horizontal axis, and distance is plotted on the vertical axis. 1 1 Click box to view movie.

20. Reading a graph A graph can give you an accurate answer even without doing the experiment. Students doing an experiment measured the speed of the car at 20, 40, 60, and 80 cm positions. They want to know the speed at 50 cm.

21. Look at the graph. Distance-Time Graphs and Speed What is Motion? 1 1 According to the graph, after 1 s student A traveled 1 m. Student B, however, traveled only 0.5 m in the first second.

22. So student A traveled faster than student B. Distance-Time Graphs and Speed What is Motion? 1 1 The line representing the motion of student A is steeper than the line for student B.

23. A steeper line on the distance-time graph represents a greater speed. Distance-Time Graphs and Speed What is Motion? 1 1 A horizontal line on the distance-time graph means that no change in position occurs.

24. Slope You can use position vs. time graphs to quickly compare the speeds of different objects. A steeper line on a position vs. time graph means a faster speed.

25. Slope The “steepness” of a line is called its slope. Visualize a triangle with the slope as the hypotenuse. The rise is equal to the height of the triangle. The run is equal to the length along the base of the triangle.

26. Speed vs. time graphs These graphs each show the same event. What differences do you notice?

27. Do these graphs display the same data?

28. If you are hiking in the woods, you want to know not only your speed, but also the direction in which you are moving. Velocity What is Motion? 1 1

29. The velocity of an object is the speed of the object and direction of its motion. Velocity What is Motion? 1 1 This is why a compass and a map are useful to hikers.

30. Velocity has the same units as speed, but it also includes the direction of motion. Velocity What is Motion? 1 1 The velocity of an object can change if the object's speed changes, its direction of motion changes, or they both change.

31. Section Check 1 1 Question 1 To determine whether something has changed position, you need a _______. A. compass B. global positioning system C. map D. reference point

32. Section Check 1 1 Answer The answer is D. If someone starts a car and drives it 100 meters from its parking spot, the parking spot can be used as a point of reference to show that the car moved.

33. Section Check 1 1 Question 2 Displacement includes your _______ and _______ as well as the _______ in which you have traveled.

34. Section Check 1 1 Answer It includes your starting point, ending point, and direction in which you have traveled. It is possible to have traveled a great distance and still have a displacement of zero if you traveled in an enormous circle and ended right where you began.

35. Section Check 1 1 Question 3 Speed equals distance divided by _______. A. force B. mass C. time D. velocity

36. Section Check 1 1 Answer The answer is C. The smaller the t value in s=d/t, the greater the speed.

37. Acceleration and Motion Acceleration is the change in velocity divided by the time it takes for the change to occur. Acceleration has a direction. If an object speeds up, the acceleration is in the direction that the object is moving. 2 2 Acceleration

38. Acceleration and direction Acceleration occurs whenever there is a change in speed, direction, or both.

39. Speed and acceleration Speed and acceleration are not the same thing. Acceleration is the change in speed divided by the change in time.

40. Speed and acceleration An acceleration in m/s/s is often written as m/s 2 (meters per second squared). It is better to think about acceleration in units of speed change per second (that is, meters per second per second).

41. Acceleration and Motion If an object slows down, the acceleration is opposite to the direction that the object is moving. If the direction of the acceleration is at an angle to the direction of motion, the direction of motion will turn toward the direction of the acceleration. If you speed up your acceleration is positive, if you slow down your acceleration is negative. 2 2 Acceleration

42. Speeding Up When an object that is already in motion speeds up, it also is accelerating. When the speed of an object increases, it is accelerating. 2 2 Acceleration The toy car is accelerating to the right. Its speed is increasing.

43. Slowing Down Acceleration occurs when an object slows down, as well as when it speeds up. The car is slowing down. 2 2 Acceleration During each time interval, the car travels a smaller distance, so its speed is decreasing.

44. Changing Direction Motion is not always along a straight line. If the acceleration is at an angle to the direction of motion, the object will turn. 2 2 Acceleration At the same time, it might speed up, slow down, or not change speed at all.

45. Changing Direction Motion is not always along a straight line. If the acceleration is at an angle to the direction of motion, the object will turn. 2 2 Acceleration At the same time, it might speed up, slow down, or not change speed at all. Click image to view movie.

46. Calculating Acceleration If an object is moving in a straight line, its acceleration can be calculated using this equation. 2 2 Acceleration In SI units, acceleration has units of meters per second squared (m/s 2 ).

47. Positive and Negative Acceleration 2 2 Acceleration So subtracting your initial speed from your final speed gives a positive number. As a result, your acceleration is positive when you are speeding up. When you speed up, your final speed always will be greater than your initial speed.

48. Positive and Negative Acceleration When your final speed is less than your initial speed, your acceleration is negative. 2 2 Acceleration Therefore, your acceleration is negative when you slow down.

49. Graphing Accelerated Motion The motion of an object that is accelerating can be shown with a graph. 2 2 Acceleration For this type of graph, speed is plotted on the vertical axis and time on the horizontal axis.

50. Graphing Accelerated Motion An object that is speeding up will have a line on a speed-time graph that slopes upward. 2 2 Acceleration An object that is slowing down will have a line on a speed-time graph that slopes downward. A horizontal line on the speed-time graph represents an acceleration of zero or constant speed.

51. Acceleration and motion graphs A speed vs. time graph is useful for showing how the speed of a moving object changes over time. If the line on the graph is horizontal, then the car is moving at a constant speed. There is no change in speed so there is no acceleration.

52. Acceleration and motion graphs Like velocity, acceleration can be positive or negative. Positive acceleration adds more speed each second. Speed is increasing at the same rate.

53. Acceleration and motion graphs Negative acceleration subtracts some speed each second, so things get slower. People sometimes use the word deceleration to describe slowing down. Speed is decreasing at the same rate.

54. Acceleration and motion graphs The position vs. time graph shows acceleration more clearly. This graph is a curve when there is acceleration.

55. 3.3 Free fall An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it. Objects in free fall on Earth accelerate downward.

56. 2 2 Section Check Question 1 A change in velocity divided by the time it takes for the change to occur equals the object’s _______.

57. Section Check 2 2 Answer The answer is acceleration. Remember that, like velocity, acceleration has a direction. A car that takes a turn has changed its acceleration, even if nothing else changes.

58. 2 2 Section Check Question 2 Imagine yourself driving a car down an empty stretch of road. How many ways could you change your acceleration?

59. Section Check 2 2 Answer You could step on the gas; you could also step on the brake; you could turn the wheel, or do any combination of these.

60. 2 2 Section Check Question 3 What is happening at point C in this speed-time graph?

61. 2 2 Section Check A. the object is speeding up B. the object is slowing down C. the object is at rest D. the object is gone

62. Section Check 2 2 Answer The answer is B. When the line falls, the object is slowing down.

63. Mass and Inertia The mass of an object is the amount of matter in the object. In SI units, the unit for mass is the kilogram. 3 3 Momentum The weight of an object is related to the object's mass.

64. Mass and Inertia Objects with more mass weigh more than objects with less mass. However, the size of an object is not the same as the mass of the object. 3 3 Momentum

65. Mass and Inertia The more mass an object has, the harder it is to start it moving, slow it down, speed it up, or turn it. This tendency of an object to resist a change in its motion is called inertia. 3 3 Momentum Objects with more mass have more inertia.

66. Momentum The momentum of an object is a measure of how hard it is to stop the object, and it depends on the object's mass and velocity. Momentum is usually symbolized by p. 3 3 Momentum

67. Mass is measured in kilograms and velocity has units of meters per second, so momentum has units of kilograms multiplied by meters per second (kg. m/s). Momentum has a direction that is the same as the direction of the velocity. 3 3 Momentum

68. Conservation of Momentum According to the law of conservation of momentum, the total momentum of objects that collide is the same before and after the collision. This is true for the collisions of billiard balls, as well as for collisions of atoms, cars, football players, or any other matter. 3 3 Momentum

69. Using Momentum Conservation There are many ways that collisions can occur. Sometimes, the objects that collide will bounce off of each other. 3 3 Momentum In other collisions, objects will stick to each other after the collisions. In both of these types of collisions, the law of conservation of momentum enables the speeds of the objects after the collisions to be calculated.

70. Sticking Together Imagine being on skates when someone throws a backpack to you. Before the student on skates and the backpack collide, she is not moving. 3 3 Momentum

71. Sticking Together 3 3 Momentum

72. Sticking Together Supposed a 2-kg backpack is tossed at a speed of 5 m/s. 3 3 Momentum Your mass is 48 kg, and initially you are at rest. Then the total initial momentum is

73. Sticking Together After the collision, the total momentum remains the same, and only one object is moving. 3 3 Momentum You can use the equation for momentum to find the final velocity.

74. Colliding and Bouncing Off Supposed two identical objects moving with the same speed collide head on and bounce off. 3 3 Momentum Before the collision, the momentum of each object is the same, but in opposite direction. So the total momentum before the collision is zero. Click image to view movie.

75. Colliding and Bouncing Off If momentum is conserved, the total momentum after the collision must be zero also. 3 3 Momentum This means that the two objects must move in opposite directions with the same speed after the collision.

76. 3 3 Section Check Question 1 An object’s momentum can be increased either by increasing its _______ or its _______.

77. 3 3 Section Check Answer The answer is mass or velocity. A thrown baseball is harder to stop than a thrown ping- pong ball. At the same time, a baseball thrown by a professional pitcher is harder to stop than the same baseball lobbed by a fan.

78. 3 3 Section Check Question 2 Explain the law of conservation of momentum. Answer This law says that the total momentum of objects in collision is always the same after the collision as it was before the collision.

79. 3 3 Section Check Question 3 Two objects of the same mass are moving directly toward each other at the same speed. What is the total momentum of the two objects? Answer The total momentum is zero. This will be the same after the collision as well.

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81. End of Chapter Summary File