1. CHAPTER 2 – MOTION

2. GOALS
1. Distinguish between instantaneous and average speeds.
2. Use the formula v = d/t to solve problems that involve distance, time, and speed.
3. Distinguish between scalar and vector quantities and give several examples of each.
4. Use the Pythagorean theorem to add two vector quantities of the same kind that act as right
angles to each other.
5. Define acceleration and find the acceleration of an object whose speed is changing.
Use the formula v = v + at to solve problems that involve speed, acceleration, and time.
1 7. Use the formula d = v t + ½ at to solve problems that involve distance, time, speed, and 2
acceleration.
8. Explain what is meant by the acceleration of gravity.
9. Describe the effect of air resistance on falling objects.
10. Separate the velocity of an object into vertical and horizontal components in order to
determine its motion.
11. Define force and indicate its relationship to the first law of motion.
12. Discuss the significance of the second law of motion, F = ma.
13. Distinguish between mass and weight and find the weight of an object of given mass.
14. Use the third law of motion to relate action and reaction forces.
15. Explain the significance of centripetal force in motion along a curved path.
16. Relate the centripetal force on an object moving in a circle to its mass, speed, and the radius
of the circle.
17. State Newton's law of gravity and describe how gravitational forces vary with distance.
18. Account for the ability of a satellite to orbit the earth without either falling to the ground or
flying off into space.
19. Define escape speed.

3. Motion Everything in the universe is in nonstop motion
The laws of motion that govern the behavior of atoms and stars apply just as well to the objects of everyday life
Motion is the ability of an object to move from one place to another
The first step in analyzing motion is to describe how fast or slow the motion is

4. Motion SPEED Rate at which something covers distance
Speed is distance divided by time
v = speed
d = distance
t = time

5. Speed Example 2.1
A car going 40 miles/hour in a 6 hour period travels how far?
v =
40 mi/hr
t =
6 hours
d = v x t
240 miles
This is an average speed.
The speedometer of a car
shows an instantaneous
speed.

6. Vector Quantities Vectors have direction as well as magnitude
They tell us “which way” as well as “how much”
velocity (v) and force (F) are examples
An arrowed line that represents the magnitude and direction of a quantity is called a vector

7. Vector Quantities have Direction And Magnitude
Vector v is 40 km/s to the right
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Figure 2-4

8. Vectors can be Added
Figure 2-5
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9. Adding Vectors
Besides manually measuring the length of “C” as in the previous slide, vectors can be added using the Pythagorean theorem when you have a right angle triangle
More accurate than using a scale drawing
a2 + b2 = c2

10. Using the Pythagorean theorem
Example 2.3 – use the Pythagorean theorem to find the displacement of a car that goes north for 5 km and then east for 3 km, as in Fig. 2-5

11. Scalar Quantities Need only a number and a unit; Not direction
mass (m)
speed (v)

12. Vector and Scalar Quantities
Vector quantities are printed in boldface type
Scalar quantities are printed in italic type.

13. Acceleration A change in velocity or direction (Curved Path)
Acceleration, in general, is a vector quantity
For our purposes, we will be calculating straight line motion, where acceleration is the rate of change of speed (a scalar quantity)
SI units are m/s2
It is customary to write (m/s)/s as just m/s2 since

14. Acceleration
a=acceleration
v2=final speed
v1=initial speed
t=time

15. Acceleration Example 2.4 Figure 2-8
The speed of a car changes from 15 m/s to 25 m/s in 20 s when its gas
pedal is pressed hard. Find its acceleration.
Figure 2-8
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16. Acceleration Example 2.4
= 0.5m/s2

17. Free Fall
Galileo Galilei ( ) – Italian physicist who discovered that the higher a stone is when dropped, the greater its speed when it reached the ground

18. Free Fall This means the stone is accelerated
Acceleration is the same for all stones, big or small
Galileo’s experiments showed that if there were NO AIR for them to push their way through, all falling objects near the Earth’s surface would have the same acceleration of 9.8 m/s2

19. Free Fall
In general, the speed of an object falling from rest can be calculated as
Vdownward = g t
v=downward speed
g=acceleration due to gravity
t=time

20. How Far does a Falling Object Fall?
To find out how far, h, the object has fallen in the time, t, use
h=½ g t 2
t2 factor means the “h” increases much faster
than the object’s speed “v”

21. Example 2.7
A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above the water?
Using this formula, you can figure the height of a bridge over water using just a stop watch

22. Distance Traveled when Accelerating
When starting from rest it is D= ½ at2
If tossed vertically h = ½ gt2
When starting with an Initial Velocity v1
D = V1 t + ½ at2
If falling due to gravity, a becomes g ( 9.8m/s2 )

23. Air Resistance Keeps falling things from developing the full g
In air, a stone falls faster than a feather because air resistance affects the stone less
In a vacuum, the stone and feather fall with the same acceleration (9.8m/s2)
Air resistance increases with speed until the object cannot go any faster
It then continues to fall at a constant terminal speed that depends upon the size, shape, and weight

24. Free Fall at terminal Velocity
If a sky diver is falling at a constant velocity i.e, her terminal velocity, and weighs 400N,
What is the force exerted by the AIR on the skydiver?
If the sky diver rolls into a ball, would the force be different?

25. Vacuum vs. Air Resistance
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Figure 2-15

26. Force and Motion What makes something at rest begin to move?
Why do some objects move faster than others?
Why are some accelerated and others not?
Questions like these led Isaac Newton to formulate three principles that summarize behavior of moving bodies

27. Force and Motion
These are known as Newton’s Three Laws of Motion

28. Force and Motion Newton’s First Law of Motion
If no net force acts on it, an object at rest remains at rest and an object in motion remains in motion at constant velocity (that is, at constant speed in a straight line)
An object at rest never begins to move all by itself-a force is needed to start it off
If an object is moving, the object will continue going at constant velocity unless a force acts to slow it down, speed it up, or change its direction
Only a Net Force Can Accelerate
an Object

29. Force, Inertia, Mass
Force is defined as any influence that can change the speed or direction of motion of an object
SI unit of force is the Newton (N)
Inertia is the reluctance of an object to change its state of rest or of uniform motion in a straight line
Mass is the property of matter that shows itself as inertia
The more mass something has, the greater its inertia and the more matter it contains
SI unit of mass is the kilogram (kg)

30. Inertia
Figure 2-19
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31. Force and Motion Newton’s Second Law of Motion
Force is equal to the product of mass and acceleration of an object
The direction of the force is the same as that of the acceleration
F = Force (SI unit is the Newton which
is a (kg)(m / s2)
m=mass (SI unit is the kilogram (kg))
a=acceleration (SI unit m/s2)

32. Newton’s Second Law of Motion
Twice the force means
twice the acceleration
When the same force acts
On different masses, the
Greater mass receives the
Smaller acceleration
Figure 2-22
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33. Mass and Weight
Weight
Force with which something is attracted by the earth’s gravitational pull.
Weight is a force; if you weigh 150 lbs, the Earth is pulling you down with a FORCE of 150 lbs
Although weight and mass are very closely related, weight is different from mass
Mass refers to how much matter something contains

34. Calculating Weight w = mg Newton’s second law of motion says F=ma
In the case of an object at the Earth’s surface, the force gravity exerts on it is its own weight
So, substituting w for F and g for a in the F=ma equation leads to:
w = mg
weight = (mass) (acceleration of gravity)
w = weight
m = mass
g = acceleration of gravity

35. Weight Weight and mass are always proportional to one another
Twice the weight means twice the mass
Mass rather than weight is normally specified in the SI system
SI system unit for weight is the Newton, since weight is a force

36. Weight The weight of 5 kg of potatoes is:
w=mg = (5kg)(9.8m/s2)=49 (kg)(m/s2)=49 N
Mass is a more basic property than weight since the pull of gravity vary from place to place
Pull of gravity is less on a mountaintop than at sea level, less at the equator than near the poles (earth bulges at equator)
Mass remains the same no matter where you are in the universe
Weight changes depending where you are in the universe, since g changes

37. Force and Motion Newton’s Third Law of Motion
When one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object
Another way to state this is for every action force there is an equal and opposite reaction force
This law is responsible for walking-as you move forward the Earth is moving backward
Recoil of a canon
Action of a rocket

38. Newton’s Third Law of Motion
Figure 2-27
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39. Circular Motion
Before we consider how gravity works, we must look into exactly how curved paths come about
Planets orbit the sun in curved paths, not straight lines
A curved path requires an inward pull known as centripetal force

40. Centripetal Force
The velocity vector v is always tangent to the circle
and the centripetal force vector Fc is always directed
toward the center of the circle
Figure 2-31
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41. Centripetal Force
Centripetal force (Fc) is calculated using the following equation where:
m = mass
v = velocity
r = radius of circle

42. What Happens to Centripetal Force when
Mass, Velocity, and Radius are changed?
Figure 2-32
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43. Centripetal Force Example 2.10
Find the centripetal force needed by a 1000-kg car moving at 5 m/s to go around a curve 30 m in radius m=
1000 kg v=
5 m/s r=
30 m
833 N

44. Centripetal Force Example
Figure 2-33
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45. The slaying of the giant
David was told there was a giant needing slain
He selected his 1.0 m sling and his best smooth flat river rock weighing .35 kg
He knew his accuracy suffered if the centripetal force on the sling was more than 80 pounds ( made his arm tired )
How fast can he launch the stone at the giant?
What was the kinetic energy of the stone

46. Newton’s Law of Gravity
Newton arrived at the Law of Gravity that bears his name using Kepler’s 1st and 2nd laws and Galileo’s work on falling bodies
Every object in the universe attracts every other object with a force proportional to both of their masses and inversely proportional to the square of the distance between them

47. Newton’s Law of Gravity
R – distance between the objects
G – Gravitational Constant of nature, the same number everywhere in the universe =
6.670 X N m2/kg2
m - mass of objects

48. Newton’s Law of Gravity
The inverse square – 1/R2 – means the gravitational
force drops off rapidly with increasing R
Figure 2-35
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49. Orbital Velocity
All objects in orbit have a perfect balance of centripetal force and Gravitational Force
Fc = mv2/ r Centripetal Force
F = GMm/ r2 Gravitational Force
Solving for v
v= (GM/r)0.5

50. Weight and Distance Relationship
Figure 2-37
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51. The End

52. EXAMPLES

53. Ex. 2.1

54. Ex. 2.2

55. Ex. 2.3

56. Ex. 2.4

57. Ex. 2.5

58. Ex. 2.6

59. Ex. 2.7

60. Ex. 2.8

61. Ex. 2.9

62. Ex. 2.10

63. Ex. 2.11

64. Ex. 2.12

65. Ex. 2.13

66. Ex. 2.14

67. Ex. 2.15