Chapter 3: LINEAR MOTION

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Wesley King
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1 Chapter 3: LINEAR MOTION Here we'll consider only the simplest form of motion that along a straight-line path linear motion. Linear Motion (Motion in a straight line, such as falling straight downward) Speed and Velocity Acceleration Relationships among distance, velocity, and acceleration. Falling motion.

2 Vector & Scalars Scalar quantity- gives only magnitude vector- gives magnitude and direction.

3 Motion can be described by Sentence Mathematical Graph Motion Diagrams/ Pictures Images of a moving object that records its position after equal time intervals If the distance between is equal= constant If different distances= acceleration Operational definitions- describe motion (speeding up, slowing down, at rest & constant speed)

4 Particle Model Uses of dots instead of pictures to represent movement.

5 Shows a series of images of an A Motion diagram object that records its position after equal time intervals

6 Coordinate System based on where to put the measuring tape & when to start the stopwatch tells zero point of variable & direction the values of variable should increase origen- zero pt/beginning Position vector- gives direction & amount

7 Linear Motion Straight line Is relative to other objects or reference points Distance vs. displacement Point of origin /reference point Force Push or pull Causes acceleration Net Force is the combination and sum of all forces Net force ~ acceleration; directly proportional Double one Friction In opposite directions of movement You increase a force- you increase the friction

8 Motion Is Relative Everything moves. Even things that appear at rest move. They move relative to the sun and stars. You're moving at about 107,000 km/hr relative to the sun. And even faster relative to the center of our galaxy. When we discuss the motion of something, we describe motion relative to something else.

9 Motion Is Relative When walking down the aisle of a moving bus, your speed is relative to the floor of the bus which is likely quite different from your speed relative to the road. a racing car with a speed of 300 km/hr is relative to the track. Unless stated otherwise, when we discuss the speeds of things in our environment we mean relative to the surface of the Earth.

10 A change in position Need a reference point Motion Compare the motion of a person sitting on the bus to the bus Compare to a Boy riding his bike on a sidewalk Being observed by kid on another bus traveling at 20 km/hr Also observed by lady standing at corner What is the speed?

11 Position separation between that object & a reference point. Needs both distance & direction Symbol- d

13 Distance vs Displacement Distance Displacement The total length that is traveled by that object. Unit: metre (m) Type of Quantity: Scalar quantity the shortest distance of the object from point O in a specific direction. Unit: metre (m) Type of Quantity: Vector quantity

14 Distance traveled = 200 m Distance is a scalar quantity Displacement = 120 m, in the direction of Northeast Displacement is a vector quantity

15 What is happening?

16 Speed is the rate of change Type of quantity: Scalar quantity in distance.

17 Speed Speed is a measure of how fast something moves, measured by a unit of distance divided by a unit of time Any combination of distance and time units is legitimate for measuring speed; for motor vehicles (or long distances) the units kilometers per hour (km/h) or miles per hour (mi/h or mph) are commonly used. shorter distances, meters per second (m/s) are often useful units.

18 Approximate Speeds in Different Units

19 Instantaneous Speed Cars vary in speed on a trip You can tell the speed of the car at any instant by looking at its speedometer. The speed at any instant is the instantaneous speed.

20 Average Speed Average speed is defined as: the whole distance covered divided by the total time of travel it doesn't indicate the different speeds and variations that may have taken place during shorter time intervals.

21 Velocity is the rate of change in displacement Vector quantity m/s/s or m/s 2

23 Velocity changes when you speed up, slow down or change direction.

24 Velocity Speed = distance / time Velocity = The car on the circular track may have a constant speed, but its velocity is changing every instant. Why? distance/time + direction

25 Velocity Constant velocity and constant speed, however, can be very different Constant velocity means constant speed with no change in direction. A car that rounds a curve at a constant speed does not have a constant velocity its velocity changes as its direction changes

26 For objects traveling in a straight line, speed & velocity will be the same. Average velocity = total distance time interval v = d t

27 Calculating Speed Skater A skates at 4 m/s You skate for 100 m for 20 seconds. Who skates faster? V = d/t V = 100 m/20 s = 5 m/sec You are faster

29 Graphing Speed Independent variable = time Dependent variable = distance Velocity- vertical separation of 2 points time interval- horizontal separation ratio of displacement to time interval is average velocity

30 Instantaneous Velocity May use a position-time graph to determine the slope at different times. Is the tangent to a curve on a position-time graph

31 Calculating Time from Speed Sound travels at 330 m/s. If lightning hits 1 km from you, how long will it take the sound to reach you? V = d/t same as t = d/v T = 1 km/330 m/s = 1000m/330m/s =3.03 s

32 Plate tectonics Pieces of Earth s solid crust floats on a molten mantle. Causes plates continents are on to move

33 Measuring speeds of tectonic movements Because it is slow- we measure in units of year San Andreas Fault moves 2 cm/yr Australian plate moves 17 cm/yr

34 What speed units would you use for Running a race Drive between Denver and Laramie The speed of a slug

35 Changes in Velocity Velocity changes if speed or direction of motion change. 10 m/s, downward Velocity changes in both these cases. 25 m/s, downward 25 meters per second, 45 degrees upward 25 meters per second, 45 degrees downward 14-Feb-12 Physics 1 (Garcia) SJSU

36 The best way to imagine a situation with several physical quantities is by drawing a graph. To picture the behavior of the speed of an object, we plot the distance on the vertical axis and the time on the horizontal axis.

37 Here, the total distance travelled ( y) divided by the time taken ( x) is the gradient of the slope. This is also equal to the average speed of the object - remembering that In this case, the speed is constant as the slope of the distance-time graph is constant.

38 By re-arranging the equation we can plot slopes of either distance, or time, on a graph to find their values. For example, we can see how to find the distance from a speed-time graph by rearranging to get: We then plot a speed-time graph as shown below: The blue rectangle has an area equal to the speed multiplied by the time. We can see from the equation above, that this is equal to the distance travelled.

39 The speedometer of a car moving to the east reads 100 km/h. It passes another car that moves to the west at 100 km/h. Do both cars have the same speed? Do they have the same velocity?

40 During a certain period of time, the speedometer of a car reads a constant 60 km/h. Does this indicate a constant speed? A constant velocity?

41 We can change the velocity of something by changing its speed, by changing its direction, or by changing both its speed and its direction. Acceleration

42 Acceleration Define acceleration as, (ACCELERATION) = (Change in Velocity) (Time interval) Note: An object accelerates anytime its velocity changes. Examples include: Object speeds up. Object slows down (speed decreases). Object speed constant but direction changes (curved path) Best example of acceleration is objects in free fall 14-Feb-12 Physics 1 (Garcia) SJSU

43 Acceleration it is a rate of a rate Acceleration is not velocity, nor is it even a change in velocity. Acceleration is the rate at which velocity itself changes

44 Uniform or constant Acceleration Does not change velocity-time graph = straight line initial velocity- when the clock reading is zero

45 acceleration measured in m/s/s or m/s 2 Acc.= final veloc.-initial veloc. time needed to change veloc. A = vf-vi = Δv t t Make sure your final & initial acceleration are identified so that you can ID it is positive or negative (speeding up or slowing down)

46 Speed = distance /time Velocity = distance /time + direction You may have constant speed & velocity is going straight If you are changing direction they are not the same Constant velocity Instantaneous velocity Average velocity

47 Force Causes Acceleration Consider a hockey puck at rest on ice. Apply a force, and it starts to move it accelerates. When a force is no longer pushing the puck- it moves at constant velocity. Apply another force by striking the puck again, and again the motion changes. Applied force produces acceleration.

48 Crash Safety During a crash, your body continues to move at the same rate of speed. An abrupt stop at 50 m/hr would have you hitting the steering wheel/windshield at that speed. Things that slow the time of impact can save your life.

49 Crash Safety The force needed to slow a person from 50 km/h to zero in 0.1 sec is equal to 14 X the body weight. Seat belts allows your body to slow at the same rate as the seat Seatbelt Air bags?

50 3.4 Connecting Motion w Forces Force A push or a pull Can change the motion of objects Balanced forces- equal & opposite Unbalanced-

51 Force The sum of forces is called the net force. If the net force is not zero, the applied forces are unbalanced. If the net forces are zero, the applied forces are balanced and cancel each other out. The object is in equilibrium.

52 What is meant by unbalanced force? If the forces on an object are equal and opposite, they are said to be balanced, and the object experiences no change in motion. If they are not equal and opposite, then the forces are unbalanced and the motion of the object changes.

53 Some Examples from Real Life A soccer ball is sitting at rest. It takes an unbalanced force of a kick to change its motion. Two teams are playing tug of war. They are both exerting equal force on the rope in opposite directions. This balanced force results in no change of motion.

54 Acceleration Video Why things fall

55 Velocity acquired in free fall, from rest; v = gt (where g = 10 m/s 2 or 9.8 m/s 2 ) 1. Calculate the instantaneous speed of an apple that falls freely from a rest position and accelerates at 10 m/s2 for 1.5 seconds. 2. An object is dropped from rest and falls freely. After 7 seconds, calculate its instantaneous speed. 3. A skydiver steps from a high-flying helicopter. In the absence of air resistance, how fast would she be falling at the end of a 12- second jump? 4. On a distant planet, a freely falling object has an acceleration of 20 m/s2. Calculate the speed that an object dropped from rest on this planet acquires in 1.5 seconds

56 LAW OF UNIVERSAL GRAVITATION Every object attracts every other object with a force that is directly related to the mass of each object It is inversely proportional to the square of the distance between their centers.

58 The force on Timex's craft is only 1/4 of that on Tripod's because Timex is 2x as far from the earth's center.

59 How does the earth's pull on Dr. J's craft compare to that on Tripod's?

60 Law of Universal Gravitation The force of gravitational attraction between the earth & each spaceship can be found using the frmula abve where G is the universal constant of gravitation (6.67 x N-m 2 /kg 2 ).

61 gravitational forceweakest force attractive force that exists between all objects electromagnetic force- give materials their strength, ability to bend Forces strong nuclear forcestrongest- holds the particles in the nucleus together weak force- involved in radioactive decay

62 Gravity depends on The size of the mass The distance between objects Distance is more important than mass gravitational force of an object proportional to its mass measured in newtons

63 Weight The measure of the force of gravity on the object Depends on location The greater the mass, the greater the attraction (gravity) 9.8 m/s 2 on Earth

64 Falling Objects Falling objects fall with the same accelerationregardless of mass A larger mass has a greater inertia, requiring a greater force to change its velocity A smaller mass has less inertia, requiring less force to affect its velocity About falling things

65 Demo: String of Falling Balls Falling objects accelerate (speed increases). Listen for the sound as balls hit the ground. Time between clicks gets shorter & shorter (falling faster & faster). String does not pull; no tension while falling. 14-Feb-12 Physics 1 (Garcia) SJSU

66 Velocity in Free Fall (Down) How fast do objects go when they fall? Acceleration of gravity is 10 meters per second per second. With each second of fall, speed increases by 10 meters/second Release 1 second 2 seconds 3 seconds Zero meters per sec. 10 meters per sec. 20 meters per sec. 30 meters per sec. 4 seconds 14-Feb-12 Physics 1 (Garcia) SJSU 40 meters per sec.

67 Velocity in Free Fall (Up & Down) Moving upward, with each second the speed decreases by 10 meters/second. Going back down the motion exactly reverses itself. Zero meters per sec. 10 meters per sec. 20 meters per sec. 30 meters per sec. 14-Feb-12 Physics 1 (Garcia) SJSU 40 meters per sec.

68 Position in Free Fall How far do objects go when they fall? More complicated because speed is increasing. There s a pattern & Galileo figured it out. But it wasn t easy. Release 1 second 2 seconds 3 seconds 5 meters Higher than this ceiling 20 meters 45 meters Higher than King library 14-Feb-12 Physics 1 (Garcia) SJSU 4 seconds 80 meters

69 How about an object thrown straight upward? Once released, it continues to move upward for a while and then comes back down. At the highest point, when it is changing its direction of motion from upward to downward, its instantaneous speed is zero. Then it starts downward just as if it had been dropped from rest at that height.

70 How about an object thrown straight upward? the object slows as it rises. at the rate of 10 meters per second each second the same acceleration it experiences on the way down. the instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward The velocities are opposite, because they are in opposite directions. the downward velocities have a negative sign, indicating the downward direction

71 vertical motion The relationship between time up or down and vertical height is given by

72 How about an object thrown straight upward? Whether moving upward or downward, the acceleration is 10 m/s 2 the whole time. up positive, and down negative.

73 B/c the acceleration is the same whether the object is moving up or down, the figure could just as well represent the person at the bottom throwing the ball upward. What would be the speed of the ball when it reaches the top? Answer: 0 m/s

76 Time of Fall (seconds) Distance Fallen (meters) t ½ 10 t 2

77 Lab: Acceleration of Gravity Record position of falling object using spark timer and paper tape. 14-Feb-12

79 We're talking here of vertical motion. How about running jumps? Hang time depends only on the jumper's vertical speed at launch. While airborne, the jumper's horizontal speed remains constant while the vertical speed undergoes acceleration. Interesting physics!

80 Summary of Terms Speed How fast something moves. The distance traveled per unit of time. Velocity The speed of an object and specification of its direction of motion. Acceleration The rate at which velocity changes with time; the change in velocity may be in magnitude or direction or both. Free fall Motion under the influence of gravity only.

81 Summary of Formulas Speed = distance/time Average speed = total distance covered time interval Acceleration = change of velocity time interval Acceleration (linear) = change in speed time interval Freefall velocity from rest v = gt Distance fallen in freefall from rest

82 Acceleration of Gravity Video If force = mass X acceleration And weight is a force, Then weight = mass x acceleration Since the acceleration of gravity = 9.8 m/s 2 Weight = mass x 9.8 m/s 2 If an object is thrown down- gravity is no longer the only force!

83 Graphing Acceleration

84 Demo: Dropping the Ball How long does it take a ball to fall 3 meters? Using the formula, (Distance Fallen) = ½ (Acceleration)(Time)(Time) Can check that it takes 0.77 seconds since (3) = ½ (10)(0.77)(0.77) Beauty of science: Predict, then verify by dropping balls!

Demo: Reaction Time Distance (inches) Time (sec.) 1 0.07 2 0.10 3 0.12 4 0.14 5 0.16 6 0.17 7 0.

85 Demo: Reaction Time Distance (inches) Time (sec.) Catch Release 14-Feb-12 Physics 1 (Garcia) SJSU

86 EOC

87 Distance fallen in free fall, from rest; d = 1/2 gt 2 5. An apple drops from a tree and hits the ground in 1.5 seconds. Calculate how far it falls. 6. Calculate the vertical distance an object dropped from rest covers in 12 seconds of free fall. 7. On a distant planet a freely falling object has an acceleration of 20 m/s2. Calculate the vertical distance an object dropped from rest on this planet covers in 1.5 seconds.

88 ON WHICH OF THESE HILLS DOES THE BALL ROLL DOWN WITH INCREASING SPEED AND DECREASING ACCELERATION ALONG THE PATH?

89 Air resistance depends on Objects Speed Size Shape Density Compare the falling rate of Snow Sleet hail

90 Air Resistance is responsible for different accelerations a feather and a coin in the presence of air fall with different accelerations. But in a vacuum, the feather and coin fall with the same acceleration

91 air resistance If all objects fall with the same acceleration, why does a paper wadded up, fall faster than a flat one? Air resistance pushes in the opposite direction of movement Air resistance pushes up as gravity pulls down.

92 Air drag depends on the size and the speed of a falling object When acceleration terminates, we say that the object has reached its terminal speed. If we are concerned with direction, down for falling objects, we say the object has reached its terminal velocity

93 As a falling skydiver gains speed, air drag may finally build up until it equals the weight of the skydiver If and when this happens, the net force becomes zero and the skydiver no longer accelerates; she has reached her terminal velocity. For a skydiver, it is about 200 kilometers per hour. A skydiver may vary this speed by varying position. Minimum terminal velocity is attained when the parachute is opened.

Consider a man and woman parachuting together from the same altitude and the man is twice as heavy as the woman, but they are using the same-sized parachutes The woman will reach her terminal speed

94 Consider a man and woman parachuting together from the same altitude and the man is twice as heavy as the woman, but they are using the same-sized parachutes The woman will reach her terminal speed when the air drag against her parachute equals her weight. When this occurs, the air drag against the parachute of the man will not yet equal his weight He must fall faster than she does for the air drag to match his greater weight

95 When Acceleration Is Less Than g Nonfree Fall When weight mg is greater than air resistance R, the falling sack accelerates. At higher speeds, R increases. When R = mg, acceleration reaches zero, and the chute reaches its terminal velocity.

96 Non-Horizontally Launched Projectiles

97 Suppose a rescue airplane drops a relief package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane?

98 The Plane and The Package

When the air resistance balances the pull of gravity An object reaches terminal velocity when the drag force has the same magnitude as the accelerating force.

99 When the air resistance balances the pull of gravity An object reaches terminal velocity when the drag force has the same magnitude as the accelerating force. Why does a piece of paper fall more slowly under gravity than a piece of chalk if the acceleration due to gravity is the same for all objects? (Demonstrate this.) Terminal velocity

Skydiving is kind of like sticking your head out of the window of a car that is traveling at 100 miles per hour." Here's a closer look at the physics of skydiving.

100 Skydiving is kind of like sticking your head out of the window of a car that is traveling at 100 miles per hour." Here's a closer look at the physics of skydiving. Here he is in free fall without a parachute. At this point the force of gravity is greater than the drag on his body so he is accelerating. As he accelerates the amount of drag increases, because the faster an object moves through air, the greater the drag. Skydiving forces

101 reached terminal velocity Eventually drag is equal to the force of gravity. He is no longer accelerating, but rather moving at a constant speed. He has reached terminal velocity, going as fast as he will go. This is roughly 200 kilometers per hour ( 125 miles per hour). Making contact with the ground at that speed would be rather uncomfortable so Philippe opens his parachute.

When drag is more than gravity he slows down With the parachute spread out above him rather than folded up tightly on his back, Philippe plus his parachute present a much larger surface area to the

102 When drag is more than gravity he slows down With the parachute spread out above him rather than folded up tightly on his back, Philippe plus his parachute present a much larger surface area to the air they are moving through, greatly increasing drag. Since upward force is now greater than downward force, he suddenly begins to slow down. But as he moves slower and slower, drag decreases until...

103 Falling at reduced constant velocity...gravity and drag are once again equal and Philippe is again dropping at a constant velocity. But now that velocity is only about 22 kph (14 mph)... Then he lands

104 Terminal Velocity

105 Terminal Velocity

106 Free Fall Table 3.2 shows the instantaneous speed of a freely falling object at 1-second intervals

107 Free Fall During each second of fall, the object gains a speed of 10 meters per second. Free-fall acceleration is approximately equal to 10 m/s 2

108 freely falling objects use g because the acceleration is due to gravity g varies slightly in different locations, dependent on mass Where accuracy is important, the value of 9.8 m/s 2 should be used.

109 Free Fall When a falling object is free of all restraints no friction, air or otherwise, and falls under the influence of gravity alone, the object is in a state of free fall.

110 The instantaneous velocity of an object falling from rest can be expressed in shorthand notation as V = gt the instantaneous velocity or speed in meters per second is simply the acceleration g = 10 m/s 2 multiplied by the time t in seconds.

111 Acceleration it is a rate of a rate Acceleration is not velocity, nor is it even a change in velocity. Acceleration is the rate at which velocity itself changes

112 a falling rock is equipped with a speedometer. In each succeeding second of fall, you'd find the rock's speed increasing by the same amount: 10 m/s.

113 How about an object thrown straight upward? Once released, it continues to move upward for a while and then comes back down. At the highest point, when it is changing its direction of motion from upward to downward, its instantaneous speed is zero. Then it starts downward just as if it had been dropped from rest at that height.

114 How about an object thrown straight upward? the object slows as it rises. at the rate of 10 meters per second each second the same acceleration it experiences on the way down. the instantaneous speed at points of equal elevation in the path is the same whether the object is moving upward or downward The velocities are opposite, because they are in opposite directions. the downward velocities have a negative sign, indicating the downward direction

115 How about an object thrown straight upward? Whether moving upward or downward, the acceleration is 10 m/s 2 the whole time. up positive, and down negative.

116 Time of Fall (seconds) Distance Fallen (meters) t ½ 10 t 2

4.1 Motion Is Relative. An object is moving if its position relative to a fixed point is changing. You can describe the motion of an object by its

4.1 Motion Is Relative. An object is moving if its position relative to a fixed point is changing. You can describe the motion of an object by its 4.1 Motion Is Relative You can describe the motion of an object by its position, speed, direction, and acceleration. An object is moving if its position relative to a fixed point is changing. 4.1 Motion