1. Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.
Chapter 5
Force and Motion–I
Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. 1

2. © 2014 John Wiley & Sons, Inc. All rights reserved.
Goals for this chapter
To understand the meaning of force in physics
To view force as a vector and learn how to combine forces
To understand the behavior of a body on which the forces “balance”
Newton’s THREE Laws of Motion
(Aside – what is a physical LAW?)
© 2014 John Wiley & Sons, Inc. All rights reserved.

3. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's Laws
We will focus on Newton's three laws of motion… but
Newtonian mechanics is valid for “everyday” situations
It is not valid for speeds which are an appreciable fraction of the speed of light
Viewed as an approximation of general relativity
It is not valid for objects on the scale of atomic structure
Viewed as an approximation of quantum mechanics
And not valid for objects in accelerating frames of reference!
© 2014 John Wiley & Sons, Inc. All rights reserved. 3

4. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Before Newtonian mechanics:
Some influence (force) was thought necessary to keep a body moving
The “natural state” of objects was at rest
This seems intuitively reasonable (due to friction)
But envision a frictionless surface
Does not slow an object
The object would keep moving forever at a constant speed
Friction is a force!
© 2014 John Wiley & Sons, Inc. All rights reserved. 4

5. © 2014 John Wiley & Sons, Inc. All rights reserved.
Forces
A force is a push or a pull
A force is an interaction between two objects, or between an object and its environment
A force is a VECTOR quantity, with magnitude and direction.
A net force causes an acceleration!
© 2014 John Wiley & Sons, Inc. All rights reserved. 5

6. © 2014 John Wiley & Sons, Inc. All rights reserved.
Forces
Characteristics of forces:
Unit: N, the newton; 1 N = 1 kg m/s2
Forces are vectors
Net force is the vector sum of all forces on an object
Principle of superposition for forces:
A net force has the same impact as a single force with identical magnitude and direction
© 2014 John Wiley & Sons, Inc. All rights reserved. 6

7. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Superposition Examples
© 2014 John Wiley & Sons, Inc. All rights reserved. 7

8. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Superposition Examples
Answer: (c), (d), (e)
© 2014 John Wiley & Sons, Inc. All rights reserved. 8

9. There are four common types of forces
#1: The normal force: When an object pushes on a surface, the surface pushes back on the object perpendicular to the surface.
This is a contact force.

10. There are four common types of forces
#2: Friction force: This force occurs when a surface resists sliding of an object and is parallel to the surface.
Friction is a contact force. 10

11. There are four common types of forces II
#3: Tension force: A pulling force exerted on an object by a rope or cord.
This is a contact force.

12. There are four common types of forces II
#4: Weight: The pull of gravity on an object.
This is a long-range force, not a contact force, and is also a “field” force. 12

13. What are the magnitudes of common forces?

14. © 2014 John Wiley & Sons, Inc. All rights reserved.
Forces!
A force:
Is a “push or pull” acting on an object
A net force causes acceleration
Newton’s First Law of Motion: If there is no NET force on an object it will remain in the same state of motion
© 2014 John Wiley & Sons, Inc. All rights reserved. 14

15. Newton’s First Law
“An object at rest tends to stay at rest, an object in motion tends to stay in uniform motion.”

16. Newton’s First Law
Mathematically, “A body acted on by zero net force moves with constant velocity and zero acceleration.” 16

17. Newton’s First Law II
In part (a) net force acts, causing acceleration.
In part (b) net force = 0 resulting in no acceleration.

18. Drawing force vectors
Use a vector arrow to indicate the magnitude and direction of the force.

19. Superposition of forces
Several forces acting at a point on an object have the same effect as their vector sum acting at the same point.

20. Decomposing a force into its component vectors
Choose coordinate system with perpendicular x and y axes.
Fx and Fy are components of force along axes.
Use trigonometry to find force components.

21. Notation for the vector sum
Vector sum of all forces on an object is resultant of forces
The net force.

22. Superposition of forces
Force vectors are added using components: Rx = F1x + F2x + F3x + … Ry = F1y + F2y + F3y + … F1 F2 F3

23. Superposition of forces
Force vectors are added using components: Rx = F1x + F2x + F3x + … Ry = F1y + F2y + F3y + … F1 F2 F3
F1x
F3x Rx

24. Superposition of forces
Force vectors are added using components: Rx = F1x + F2x + F3x + … Ry = F1y + F2y + F3y + … F1
F2y
F1y F3
F3y Ry

25. Superposition of forces

26. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Principle of superposition for forces:
A net force has the same impact as a single force with identical magnitude and direction
So we can restate 1st law even more correctly:
© 2014 John Wiley & Sons, Inc. All rights reserved. 26

27. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Newton's first law is true in a non-accelerating frame
Inertial frames:
© 2014 John Wiley & Sons, Inc. All rights reserved. 27

28. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First
Newton's first law is not true in all frames
You go around a corner in a car, and seem to slide SIDEWAYS!?
Air moving south from the north pole towards the equator seems to move to the WEST!!!??
You are on a bus moving away from a stop sign, and your physics books slides backwards with no one touching it!!!!???
© 2014 John Wiley & Sons, Inc. All rights reserved. 28

29. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Newton's first law is not true in accelerating frames
(a): a frictionless puck, pushed from the north pole, viewed from space
(b): the same situation, viewed from the ground
Over long distances, the ground is a non-inertial frame
In (b), a fictitious force would be needed to explain deflection
© 2014 John Wiley & Sons, Inc. All rights reserved. 29

30. When is Newton’s first law valid?
You are on roller skates in a stopped BART car…
The car starts to accelerate forwards.
What happens to you?
If no net force acts on you, you maintain a constant velocity (0!)

31. When is Newton’s first law valid?
You are on roller skates in a moving BART car…
The car starts to slow - accelerate backwards.
What happens to you?
If no net force acts on you, you maintain a constant velocity

32. When is Newton’s first law valid?
If no net force acts on you, you maintains a constant velocity (a vector!)
But as seen in the non-inertial frame of the accelerating vehicle, it appears that you are being pushed to the outside!
Newton’s first law is valid only in non-accelerating inertial frames.

33. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
What is mass?
“the mass of a body is the characteristic that relates a force on the body to the resulting acceleration”
Mass is a measure of a body’s resistance to change in motion
Literally, # of protons, neutrons, & electrons (regardless of how they are grouped into kinds of elements!)
It is not the same as weight, density, size etc.
Same force on LARGER mass produces smaller acceleration!
© 2014 John Wiley & Sons, Inc. All rights reserved. 33

34. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Example Apply identical 8.0 N force to various bodies:
Mass: 1kg → acceleration: 8 m/s2
Mass: 2kg → acceleration: 4 m/s2
Mass: 0.5kg → acceleration: 16 m/s2
And if you saw an acceleration from the application of this force…
Acceleration: 2 m/s2 → mass: 4 kg
© 2014 John Wiley & Sons, Inc. All rights reserved. 34

35. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Summarize these behaviors as:
As an equation, we write:
Identify the body in question, and only include forces that act on that body!
© 2014 John Wiley & Sons, Inc. All rights reserved. 35

36. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
As an equation, we write:
Separate applied forces into components along coordinate system axes
© 2014 John Wiley & Sons, Inc. All rights reserved. 36

37. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
If the net force on a body is zero:
Its acceleration is zero
The forces and the body are in equilibrium
But there may still be forces! They just must cancel!
© 2014 John Wiley & Sons, Inc. All rights reserved. 37

38. Newton’s Second Law
If the net force on an object is zero, the object will not accelerate.

39. Newton’s Second Law
If the net force on an object is not zero, it causes the object to accelerate.

40. Newton’s Second Law
If the net force on an object is not zero, it causes the object to accelerate.

41. An object undergoing uniform circular motion
An object in uniform circular motion is accelerated toward the center of the circle.
So net force on object must point toward the center of the circle.

42. Force and acceleration
Magnitude of acceleration of an object is directly proportional to the net force  on the object.
| | = F/m

43. Mass and acceleration
Magnitude of acceleration of an object is inversely proportional to object’s mass if net force remains fixed.
| | = F/m

44. Newton’s second law of motion
The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the mass of the object.
The SI unit for force is the newton (N).
1 N = 1 kg·m/s2

45. Using Newton’s Second Law
Worker pushes box of mass 40 kg, with constant force of 20N. What is acceleration?

46. Using Newton’s Second Law

47. Using Newton’s Second Law II—Example
Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

48. Using Newton’s Second Law II—Example
Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?

49. Using Newton’s Second Law II—Example
We know:
Displacement in x = +1.0 m
Initial x velocity = +2.8 m/s
Final x velocity = 0 m/s
THREE THINGS!

50. Using Newton’s Second Law II—Example
vf2 = vi2 + 2aDx
So…
a = (vf2 - vi2)/2Dx
a = m/s2
NOTE a points in the direction of f ! +x

51. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
Units of force:
© 2014 John Wiley & Sons, Inc. All rights reserved. 51

52. © 2014 John Wiley & Sons, Inc. All rights reserved.
Free Body Diagrams
To solve problems with forces, we often draw a free body diagram
The only body shown is the one we are solving for
Forces are drawn as vector arrows with their tails on the body
Coordinate system shown
Acceleration is NEVER part of a free body diagram – only forces on a body are present.
© 2014 John Wiley & Sons, Inc. All rights reserved. 52

53. © 2014 John Wiley & Sons, Inc. All rights reserved.
Free Body Diagrams
© 2014 John Wiley & Sons, Inc. All rights reserved. 53

54. © 2014 John Wiley & Sons, Inc. All rights reserved.
Free Body Diagrams
© 2014 John Wiley & Sons, Inc. All rights reserved. 54

55. © 2014 John Wiley & Sons, Inc. All rights reserved.
Free Body Diagrams
© 2014 John Wiley & Sons, Inc. All rights reserved. 55

56. © 2014 John Wiley & Sons, Inc. All rights reserved.

57. © 2014 John Wiley & Sons, Inc. All rights reserved.
Answer: F3 = 2 N to the left in both cases
© 2014 John Wiley & Sons, Inc. All rights reserved.

58. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-1 Newton's First and Second Laws
A system consists of one or more bodies
Any force on the bodies inside a system exerted by bodies outside the system is an external force
Net force on a system = sum of external forces
Forces between bodies in a system: internal forces
Not included in a Free Body Diagram of the system since internal forces cannot accelerate the system
© 2014 John Wiley & Sons, Inc. All rights reserved. 58

59. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
The gravitational force:
A pull that acts on a body, directed toward a second body
Generally we consider situations where the second body is Earth
In free fall (+y direction chosen as UP, with no drag from the air):
© 2014 John Wiley & Sons, Inc. All rights reserved. 59

60. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
In free fall (+y direction chosen as UP, with no drag from the air):
We can write it as a vector:
© 2014 John Wiley & Sons, Inc. All rights reserved. 60

61. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Weight :
The name given to the gravitational force that one body (like the Earth) exerts on an object
It is a force measured in newtons (N)
It is directed downward towards the center
Eq. (5-12)
© 2014 John Wiley & Sons, Inc. All rights reserved. 61

62. © 2014 John Wiley & Sons, Inc. All rights reserved.
Example To relate weight to mass, consider an apple in free fall. The only force on the apple is the gravitational force which results in an acceleration of g. Applying Newton’s 2nd Law
Fnet = ma where Fnet = Fg = W and a =g
© 2014 John Wiley & Sons, Inc. All rights reserved.

63. © 2014 John Wiley & Sons, Inc. All rights reserved.
Example To relate weight to mass, consider an apple in free fall. The only force on the apple is the gravitational force which results in an acceleration of g. Applying Newton’s 2nd Law
Fnet = ma where Fnet = Fg = W and a =g
Fg = W = mg
Thus,
W = mg (mass – weight relationship)
© 2014 John Wiley & Sons, Inc. All rights reserved.

64. Don’t confuse mass and weight!
Keep in mind that the Newton is a unit of force, not mass.
A 2.49 x 104 N Rolls-Royce Phantom traveling in +x direction makes an emergency stop; the x component of the net force acting on its x 104 N. What is its acceleration?

65. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Measuring weight:
Use a balance to compare a body to known masses, find its mass, and compute its weight
Use a spring scale that measures weight on a calibrated scale
Weight is not the same as mass: a pan balance will read the same for different values of g, a scale will read differently for different values of g
© 2014 John Wiley & Sons, Inc. All rights reserved. 65

66. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Weight must be measured when the body is not accelerating vertically
E.g., in your bathroom, or on a train
But not in an elevator
Or on DROP ZONE
Or in orbit….
© 2014 John Wiley & Sons, Inc. All rights reserved. 66

67. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
The normal force:
If you are standing on a surface, the push back on you from the surface (due to deformation) is the normal force
Normal means perpendicular
© 2014 John Wiley & Sons, Inc. All rights reserved. 67

68. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
© 2014 John Wiley & Sons, Inc. All rights reserved. 68

69. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Example Normal force for a block resting on a horizontal surface that is:
Accelerating vertically at ay:
Vertically at rest:
© 2014 John Wiley & Sons, Inc. All rights reserved. 69

70. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Example Normal force for a block resting on a horizontal surface that is:
Accelerating vertically at ay:
Vertically at rest:
Answer: (a) equal to mg (no acceleration)
(b) greater than mg (see 5-13, with positive acceleration)
© 2014 John Wiley & Sons, Inc. All rights reserved. 70

71. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Frictional force or friction:
Occurs when one object slides or attempts to slide over another
Directed along the surface, opposite to the direction of intended motion
Figure 5-8
© 2014 John Wiley & Sons, Inc. All rights reserved. 71

72. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Tension force:
A cord (or rope, etc.) is attached to a body and pulled taut
Cord pulls on the body with force T directed along the cord, AWAY from the body!
The cord is said to be under tension
The tension in the cord is T and is assumed to be the same EVERYWHERE along the cord!
© 2014 John Wiley & Sons, Inc. All rights reserved. 72

73. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Real world – Tension will distort a cord/cable/string! They stretch!
Ideal world - A massless and unstretchable cord exists only as a connection between two bodies
It pulls on both with the same force, T
True even if the bodies and cord are accelerating, and even if the cord runs around a massless, frictionless pulley
These are useful simplifying assumptions
© 2014 John Wiley & Sons, Inc. All rights reserved. 73

74. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Figure 5-9
© 2014 John Wiley & Sons, Inc. All rights reserved. 74

75. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-2 Some Particular Forces
Figure 5-9
Answer: (a) equal to 75 N (b) greater than 75 N (c) less than 75 N
© 2014 John Wiley & Sons, Inc. All rights reserved. 75

76. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Objects interact when they push or pull on each other:
We can write this law as a scalar or vector relation:
We call these two forces a third-law force pair
Any time any two objects interact, there is a third-law force pair
Eq. (5-15)
© 2014 John Wiley & Sons, Inc. All rights reserved. 76

77. These forces act on different bodies.
Newton’s Third Law
If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you.
A force and its reaction force have the same magnitude but opposite directions.
These forces act on different bodies.

78. Applying Newton’s Third Law: Objects at rest
An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

79. Applying Newton’s Third Law: Objects at rest
An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

80. Applying Newton’s Third Law: Objects at rest
An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

81. Applying Newton’s Third Law: Objects at rest
An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.

82. Applying Newton’s Third Law: Objects in motion
A person pulls on a block across the floor. Identify the action- reaction pairs.

83. Applying Newton’s Third Law: Objects in motion
A person pulls on a block across the floor. Identify the action- reaction pairs.

84. Applying Newton’s Third Law: Objects in motion
A person pulls on a block across the floor. Identify the action- reaction pairs.

85. Applying Newton’s Third Law: Objects in motion
A person pulls on a block across the floor. Identify the action- reaction pairs.

86. A paradox?
If an object pulls back on you just as hard as you pull on it, how can it ever accelerate?

87. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
© 2014 John Wiley & Sons, Inc. All rights reserved. 87

88. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Third-law force pairs:
© 2014 John Wiley & Sons, Inc. All rights reserved. 88

89. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
© 2014 John Wiley & Sons, Inc. All rights reserved. 89

90. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Answer: (a) they increase (b) yes (c) they begin to decrease slowly (the gravitational force of Earth decreases with height—negligible in an actual elevator)
(d) yes
© 2014 John Wiley & Sons, Inc. All rights reserved. 90

91. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Sample Problem A block of mass M = 3.3 kg, connected by a cord and pulley to a hanging block of mass m = 2.1 kg, slides across a frictionless surface
Figure 5-12
Figure 5-13
© 2014 John Wiley & Sons, Inc. All rights reserved. 91

92. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Draw the forces involved
Treat the string as unstretchable, the pulley as massless and frictionless, and each block as a particle
Draw a free-body diagram for each mass
Apply Newton's 2nd law (F = ma) to each block → 2 simultaneous eqs.
Eliminate unknowns (T) that are the same, and solve for the acceleration
Figure 5-14
© 2014 John Wiley & Sons, Inc. All rights reserved.

93. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
For the sliding block:
For the hanging block:
Note the direction of “a” for the hanging block!!!
Combining we get:
© 2014 John Wiley & Sons, Inc. All rights reserved.

94. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
For the sliding block:
For the hanging block:
Combining we get:
Plugging in we find a = 3.8 m/s2 and T = 13 N
Does this make sense? Check dimensions are correct, check that a < g, check that T < mg (otherwise acceleration would be upward), check limiting cases (e.g., g = 0, M = 0, m = ∞)
© 2014 John Wiley & Sons, Inc. All rights reserved.

95. © 2014 John Wiley & Sons, Inc. All rights reserved.
5-3 Applying Newton's Laws
Sample Problem A block being pulled up a ramp:
Figure 5-15
© 2014 John Wiley & Sons, Inc. All rights reserved.

96. © 2014 John Wiley & Sons, Inc. All rights reserved.
5 Summary
Newtonian Mechanics
Forces are pushes or pulls
Forces cause acceleration
Force
Vector quantities
1 N = 1 kg m/s2
Net force is the sum of all forces on a body
Newton's First Law
If there is no net force on a body, the body remains at rest if it is initially at rest, or moves in a straight line at constant speed if it is in motion.
Inertial Reference Frames
Frames in which Newtonian mechanics holds
© 2014 John Wiley & Sons, Inc. All rights reserved. 96

97. © 2014 John Wiley & Sons, Inc. All rights reserved.
5 Summary
Mass
The characteristic that relates the body's acceleration to the net force
Scalar quantity
Newton's Second Law
Free-body diagram represents the forces on one object
Eq. (5-1)
Some Particular Forces
Weight:
Normal force from a surface
Friction along a surface
Tension in a cord
Newton's Third Law
Law of force-pairs
If there is a force by B on C, then there is a force by C on B:
Eq. (5-12)
Eq. (5-15)
© 2014 John Wiley & Sons, Inc. All rights reserved. 97