1. Chapter 5
Force and Motion–I 1

2. Mechanics Kinematics Dynamics Kinematics The study of how things move
How far? How Fast? How long?
Dynamics The study of why things move
Force causes motion and changes in motion

3. Newton's First and Second Laws
A force:
Is a “push or pull” acting on an object
Causes acceleration
We will focus on Newton's three laws of motion:
Newtonian mechanics is valid for everyday situations
It is not valid for speeds which are an appreciable fraction of the speed of light
It is not valid for objects on the scale of atomic structure
Viewed as an approximation of general relativity
See “Heads Up” on p. 95 3

4. Newton's First and Second Laws
Before Newton there was Aristotle:
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 Galileo envisioned a frictionless surface
Does not slow an object
The object would keep moving forever at a constant speed
Friction is a force! 4

5. Newton's First and Second Laws
Characteristics of forces:
Unit: N, the newton; 1 N = 1 kg m/s2
Acceleration of a mass is proportional to the exerted force
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
So we can restate more correctly: 5

6. Newton's First and Second Laws
Newton's first law is not true in all frames
Inertial 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 noninertial frame
In (b), a fictitious force would be needed to explain deflection 6

7. Newton's First and Second Laws

8. Newton's First and Second Laws
Generally, assume the ground is an inertial frame
Answer: (c), (d), (e) 8

9. 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 a change in motion (change in velocity)
It is not the same as weight, density, size etc.
Mass is inversely proportional to acceleration
Example Apply an 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
Acceleration: 2 m/s2 → mass: 4 kg 17

10. 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!
Separate the problem axes (they are independent):
Eq. (5-1)
Eq. (5-2) 18

11. Newton's First and Second Laws
The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass.
F = ma
net force = mass  acceleration
Σ 𝐹 represents the vector sum of all external forces acting on the object, or the net force.

12. 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!
Units of force:
Tab. (5-1) 20

13. Newton's First and Second Laws
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.
Components are not shown in the original FBD
Figure 5-3 21

14. Newton's First and Second Laws
Answer: F3 = 2 N to the left in both cases

15. Sample 5.01

16. Sample 5.02

17. Free Body Diagrams FT
FT,1
FT,2 Fg Fg
FT,1
FT,2 Fg Fg

18. Free Body Diagrams Fn
FT,1
FT,2 Fg Fg FT Fn Fn Fa Fg Fg

19. Free Body Diagrams Fn Fn Fs Fg Fg Fn Fr Fg Fg

20. Free Body Diagrams Fn Fk Fg Fg FT Fg Fg

21. Free Body Diagrams FT Fr FT Fg Fg FT FT Fg Fg

22. Free Body Diagrams Fn FT FT Fg Fg FT FT Fg Fg

23. Free Body Diagrams Fn FT FS Fg Fg FS Fn Fn Fg Fg

24. Free Body Diagrams
Fe = kx Fg Fg
Fe = Fg
Fe = Fg Fg Fg

25. 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 FBD of the system since internal forces cannot accelerate the system
Note: do not confuse a free body diagram of an entire system with free body diagrams of individual bodies within a system. 33

26. Concept Check – Newton’s 2nd Law
A force F acts on mass m1 giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2 = 2a1. If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration?
1. 3/4 a1
2. 3/2 a1
3. 1/2 a1
4. 4/3 a1
5. 2/3 a1 F a1 m1
a2 = 2a1 m2 F F m2 m1 a3

27. Concept Check – Newton’s 2nd Law
A force F acts on mass m1 giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2 = 2a1. If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration?
1. 3/4 a1
2. 3/2 a1
3. 1/2 a1
4. 4/3 a1
5. 2/3 a1
Mass m2 must be (1/2)m1 because its acceleration was 2a1 with the same force. Adding the two masses together gives (3/2)m1, leading to an acceleration of (2/3)a1 for the same applied force. F a1 m1
a2 = 2a1 m2 F F m2 m1 a3

28. Some Particular Forces
Gravity Normal Friction Push and Pull Tension
The first force we will investigate is that due to gravity, and we'll call it the gravitational force. We know that the acceleration due to gravity (if on Earth) is approximately g = 9.8 m/s2 . The force, by Newton's Second Law is F = m g
The normal force one which prevents objects from 'falling' into whatever it is they are sitting upon. It is always perpendicular to the surface with which an object is in contact. For example, if there is a crate on the floor, then we say that the crate experiences a normal force by the floor; and because of this force, the crate does not fall into the floor. The normal force on the crate points upward, perpendicular to the floor.
Related to the normal force is the frictional force. The two are related because they are both due to the surface in contact with the body. Whereas the normal force was perpendicular to the surface, the frictional force is parallel. Furthermore, friction opposes motion, and so its vector always points away from the direction of movement. Sliding or contact friction is either kinetic or static.
Another force which may act on an object could be any physical push or pull. This could be caused by a person pushing a crate on the floor, a child pulling on a wagon, or in the case of our example, the wind pushing on the ship. This is often referred to as an applied force.
Tension in an object results if pulling force act on its ends, such as in a rope used to pull a boulder. If no forces are acting on the rope, say, except at its ends, and the rope itself is in equilibrium, then the tension is the same throughout the rope.

29. 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, with no drag from the air):
This force still acts on a body at rest!
We can write it as a vector:
Eq. (5-8)
Eq. (5-9) 45

30. 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) 46

31. Some Particular Forces
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)

32. 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
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 48

33. 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
Figure 5-7 49

34. Some Particular Forces
Example Normal force for a block resting on a horizontal surface that is:
Accelerating vertically at ay:
Vertically at rest:
Eq. (5-13)
Eq. (5-14)
Answer: (a) equal to mg (no acceleration)
(b) greater than mg (see 5-13, with positive acceleration) 50

35. 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 51

36. 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
The cord is said to be under tension
The tension in the cord is T
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 52

37. Some Particular Forces
Figure 5-9
Answer: (a) equal to 75 N (b) greater than 75 N (c) less than 75 N 53

38. Objects interact when they push or pull on each other:
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) 54

39. Action and Reaction Forces
Action-reaction pairs do not imply that the net force on either object is zero.
The action-reaction forces are equal and opposite, but either object may still have a net force on it.
Consider driving a nail into wood with a hammer. The force that the nail exerts on the hammer is equal and opposite to the force that the hammer exerts on the nail. But there is a net force acting on the nail, which drives the nail into the wood.
If A acts on B, then B acts back on A

40. Third-law force pairs:
Applying Newton's Laws
Figure 5-11
Third-law force pairs:
This includes the gravitational forces between Earth and the cantaloupe! 56

41. 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 57

42. Concept Check – Newton’s 3rd Law
When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that??
1. this slows your initial velocity, which is already upward
2. you don’t go up, you’re too heavy
3. you’re not really pulling down – it just seems that way
4. the rope actually pulls you up
5. you are pulling the ceiling down

43. Concept Check – Newton’s 3rd Law
When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that??
1. this slows your initial velocity, which is already upward
2. you don’t go up, you’re too heavy
3. you’re not really pulling down – it just seems that way
4. the rope actually pulls you up
5. you are pulling the ceiling down
When you pull down on the rope, the rope pulls up on you!! It is actually this upward force by the rope that makes you move up! This is the “reaction” force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton’s 3rd Law.

44. Concept Check – Newton’s 3rd Law
A small car collides with a large truck. Which experiences the greater impact force?
1. the car
2. the truck
3. both the same
4. it depends on the velocity of each
5. it depends on the mass of each

45. Concept Check – Newton’s 3rd Law
A small car collides with a large truck. Which experiences the greater impact force?
1. the car
2. the truck
3. both the same
4. it depends on the velocity of each
5. it depends on the mass of each

46. Concept Check – Newton’s 3rd Law
A small car collides with a large truck. Which experiences the greater acceleration?
1. the car
2. the truck
3. both the same
4. it depends on the velocity of each
5. it depends on the mass of each

47. Concept Check – Newton’s 3rd Law
A small car collides with a large truck. Which experiences the greater acceleration?
1. the car
2. the truck
3. both the same
4. it depends on the velocity of each
5. it depends on the mass of each
We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car has the larger acceleration, since it has the smaller mass.

48. Newton’s 2nd and 3rd Laws SF m a = SF SF a = a = m m SF m a = SF SF a
2nd Law
Car
Truck SF m a = SF SF a = a = m m
2nd Law
You
Earth SF m a = SF SF a = a = m m

49. Concept Check – Newton’s 3rd Law
In outer space, a bowling ball and a ping-pong ball attract each other due to gravitational forces. How do the magnitudes of these attractive forces compare?
1. the bowling ball exerts a greater force on the ping-pong ball
2. the ping-pong ball exerts a greater force on the bowling ball
3. the forces are equal
4. the forces are zero because they cancel out
5. there are actually no forces at all
F12
F21

50. Concept Check – Newton’s 3rd Law
In outer space, a bowling ball and a ping-pong ball attract each other due to gravitational forces. How do the magnitudes of these attractive forces compare?
1. the bowling ball exerts a greater force on the ping-pong ball
2. the ping-pong ball exerts a greater force on the bowling ball
3. the forces are equal
4. the forces are zero because they cancel out
5. there are actually no forces at all
F12
F21
The forces are equal and opposite by Newton’s 3rd Law!

51. Concept Check – Newton’s 3rd Law
In outer space, a bowling ball and a ping-pong ball attract each other due to gravitational forces. How do the accelerations of the objects compare?
1. they do not accelerate because they are weightless
2. accelerations are equal, but not opposite
3. accelerations are opposite, but bigger for the bowling ball
4. accelerations are opposite, but bigger for the ping-pong ball
5. accelerations are equal and opposite
F12
F21

52. Concept Check – Newton’s 3rd Law
In outer space, a bowling ball and a ping-pong ball attract each other due to gravitational forces. How do the accelerations of the objects compare?
1. they do not accelerate because they are weightless
2. accelerations are equal, but not opposite
3. accelerations are opposite, but bigger for the bowling ball
4. accelerations are opposite, but bigger for the ping-pong ball
5. accelerations are equal and opposite
F12
F21
The forces are equal and opposite -- this is Newton’s 3rd Law!! But acceleration is F/m and so the smaller mass has the bigger acceleration.
Follow-up: Where will the balls meet if they are released from this position?

53. 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 69

54. Draw the forces involved
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

55. Plugging in we find a = 3.8 m/s2 and T = 13 N
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 that 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 = ∞)
Eq. (5-18)
Eq. (5-20)
Eq. (5-21)
Eq. (5-22)

56. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Elevator at rest
Elevator moving up or down at constant velocity

57. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Elevator moving up, speeding up
Elevator moving up, slowing down

58. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Elevator moving down, speeding up
Elevator moving down, slowing

59. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
At rest on a surface or sliding with no friction
Pushed on a surface

60. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Pushed down at an angle on a surface (no friction)

61. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Pulled up at an angle no friction

62. Net Force equations from Free Body Diagrams
Description
FBD
Net Force Equations
Sliding down an incline (no friction)

63. Sample 5.04

64. Sample 5.04

65. Sample 5.05

66. Sample 5.06

67. Sample 5.07

68. Inertial Reference Frames
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 84

69. Some Particular Forces Newton's Third Law
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) 85