1. Forces and Newton’s Laws of Motion
Chapter 4
Forces
and
Newton’s Laws of Motion

2. 4.1 The Concepts of Force and Mass
1) A force is a push or a pull.
Contact forces arise from physical
contact .
Action-at-a-distance forces do not
require contact and include gravity and electrical forces.

3. 4.1 The Concepts of Force and Mass
Arrows are used to represent forces. The length of the arrow
is proportional to the magnitude of the force.
15 N
5 N

4. 4.1 The Concepts of Force and Mass
2) Mass is a measure of the amount
of “stuff” contained in an object.
SI Unit of Mass: kilogram (kg)

5. Galileo vs. Aristotle
In our experience, objects must be pushed in order to keep moving. So a force would be needed to have a constant velocity. This is what Aristotle claimed in his in his series of books entitled "Physics", written 2400 years ago.
But 400 years ago, another scientist and astronomer, Galileo, proposed the following thought experiment which revealed another perspective.

6. Thought Experiment
Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

7. Thought Experiment
Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

8. Thought Experiment
Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

9. Thought Experiment
Imagine two perfectly smooth ramps connected together by a perfectly smooth surface. If a ball is let go at the top of the one ramp, what will happen?

10. Thought Experiment
If a ball rolls down one ramp, it keeps rolling up the other side until it reaches the same height.

11. Now repeat that experiment, but make the second ramp less steep.
Thought Experiment
Now repeat that experiment, but make the second ramp less steep.
What Will Happen?

12. Now repeat that experiment, but make the second ramp less steep.
Thought Experiment
Now repeat that experiment, but make the second ramp less steep.
What Will Happen?

13. Now repeat that experiment, but make the second ramp less steep.
Thought Experiment
Now repeat that experiment, but make the second ramp less steep.
What Will Happen?

14. Now repeat that experiment, but make the second ramp less steep.
Thought Experiment
Now repeat that experiment, but make the second ramp less steep.
What Will Happen?

15. Thought Experiment
It will still keep rolling until it reaches the same height, but it has to roll farther!

16. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

17. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

18. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

19. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

20. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

21. Thought Experiment
Finally, make the ramp flat.
Now what will happen?

22. Thought Experiment
It will keep rolling forever, no external force is necessary.

23. Galileo vs. Aristotle It's not that Aristotle was wrong.
In everyday life, objects do need to keep being pushed in order to keep moving.
Push a book across the table. When you stop pushing, it stops moving. Aristotle is right in terms of what we see around us every day.

24. Force and Motion
It's just that Galileo, and later Newton, imagined a world where friction could be eliminated.
Fapplied
Ffriction
Friction represents an external force acting on the object, just as your push is an external force.
In the absence of all external forces, an object's velocity remains constant. Two equal and opposite forces have the same effect, they cancel to create zero net force.

25. 4.2 Newton's 1st Law of Motion

26. Sir Isaac Newton
Galileo's observations were more fully formed in 1687 by the 'father of physics, ' Sir Isaac Newton, who called this observation "The First Law of Motion".

27. 4.2 Newton’s First Law of Motion
An object at rest remains at rest, and an object in motion remains in motion, unless acted on by a net external force.
In other words, an object maintains its velocity (both speed and direction) unless acted upon by a nonzero net force.
Having zero velocity, being at rest, is not special, it is just one possible velocity…a velocity which is no more special than any other.

28. 4.2 Newton’s First Law of Motion
3) The net force on an object is the vector sum of all forces acting on that object.
The SI unit of force is the Newton (N).
Individual Forces
Net Force
4 N
10 N
6 N

29. Mathematically, the net force is written as
where the Greek letter sigma denotes the vector sum.

30. 4.2 Newton’s First Law of Motion
Individual Forces
Net Force
5 N
3 N
4 N

31. In the absence of an external force, a moving object will1
In the absence of an external force, a moving object will c A
stop immediately. c B
slow down and eventually come to a stop. c C
go faster and faster. c D
move with constant velocity.
Ans: D

32. 2
When the rocket engines on a spacecraft are suddenly turned off while traveling in empty space, the starship will c A
stop immediately. c B
slowly slow down, and then stop. c C
go faster and faster. c D
move with constant velocity.
Ans: D

33. 3
A rocket moves through empty space in a straight line with constant speed. It is far from the gravitational effect of any star or planet. Under these conditions, the force that must be applied to the rocket in order to sustain its motion is c A
equal to its weight. c B
equal to its mass. c C
dependent on how fast it is moving. c D
zero.
Ans: D

34. 4
You are standing in a moving bus, facing forward, and you suddenly fall forward. You can infer from this that the bus‘s c A
velocity decreased. c B
velocity increased. C
speed remained the same, but it's turning to the right. c D
speed remained the same, but it's turning to the left. c
Ans: A

35. 5
You are standing in a moving bus, facing forward, and you suddenly fall forward as the bus comes to an immediate stop. What force caused you to fall forward? c A
gravity c B
normal force due to your contact with the floor of the bus c C
force due to friction between you and the floor of the bus c D
There is not a force leading to your fall.
Ans: D

36. 4.2 Newton’s First Law of Motion
4) Inertia is the natural tendency of an
object to remain at rest or in motion at
a constant speed along a straight line
(constant velocity).
Inertia is the resistance of any physical object to any
change in its state of motion, including changes to its
speed and direction. 
The mass of an object is a quantitative measure of inertia.

37. 4.2 Newton’s First Law of Motion
5) All Newton's laws are only valid in
inertial reference frames
An inertial reference frame is one which is not accelerating or rotating.
It is a space in which every body remains in a state of rest unless acted on by an external unbalanced force.
Newton’s First Law is also called Law of inertia

38. 6) Relative Motion
Relative motion – motion depends on your frame of reference
Are you moving if you are sitting 100% still in your chair??
YES! The earth is moving and you are on the earth, so you are moving relative to the other planets, the sun, etc.
NO! Relative to the floor, you are not moving
It all depends on your frame of reference

39. Check your understanding

40. 4.3 Newton’s Second Law of Motion

41. Newton’s Second Law of Motion
An object doesn't change its velocity unless a force acts on it.
How does an object respond to a force when it is applied?

42. 4.3 Newton’s Second Law of Motion
When a net external force acts on an object
of mass m,
the acceleration that results has a magnitude that is directly proportional to the net force and inversely proportional to the mass.
The direction of the acceleration is
the same as the direction of the net force.

43. 4.3 Newton’s Second Law of Motion
SI Unit for Force

44. 4.3 Newton’s Second Law of Motion

45. A free-body-diagram is a diagram that
represents the object and the forces that
act on it.

46. 4.3 Newton’s Second Law of Motion
The net force in this case is:
275 N N – 560 N = +110 N
and is directed along the + x axis of the coordinate system.

47. 4.3 Newton’s Second Law of Motion
If the mass of the car is 1850 kg then, by
Newton’s second law, the acceleration is

48. Rules for free body diagram:
Identify the object--represent the object by a box or a circle
draw the force arrow from the object outward in the direction that the force is acting.
label each force arrow according to its type.
Choose coordinate direction.

49. https://phet.colorado.edu/en/simulation/forces-and-motion-basics

50. 6
A 3.5 kg object experiences an acceleration of 0.5 m/s2. What net force does the object feel?

51. 7
A 12 N net force acts on a 36 kg object? How much does it accelerate?

52. 8
How much net force is required to accelerate a 0.5 kg toy car, initially at rest to a velocity of 2.4 m/s in 6 s?

53. 9
A net force F accelerates a mass m with an acceleration a. If the same net force is applied to mass 2m, then the acceleration will be c A 4a c B 2a c C
a/2 c D
a/4

54. A constant net force acts on an object. The object moves with:10
A constant net force acts on an object. The object moves with: c A
constant acceleration c B
constant speed c C
constant velocity c D
increasing acceleration

55. 11
A net force F acts on a mass m and produces an acceleration a. What acceleration results if a net force 2F acts on mass 4m? c A
a/2 B 8a c c C 4a c D 2a

56. The acceleration of an object is inversely proportional to:12
The acceleration of an object is inversely proportional to: c A
the net force acting on it. c B
its position. c C
its velocity. c D
its mass.

57. 4.3 Newton’s Second Law of Motion---
Example: A 5.0 kg object is being acted on by a 20N force to the right (F1), and a 30N force, also to the right (F2). What is the net force on the object? F2 F1
The second force, F2, acts to the right also, with a greater magnitude of 30N. This is drawn slightly larger than F­1.

58. 4.3 Newton’s Second Law of Motion--
Example: A 5.0 kg object is being acted on by a 20N force to the right (F1), and a 30N force, also to the right (F2). What is the net force on the object?
To add vectors, move the second vector so it starts where the first one ends. F1 F2
The sum is a vector which starts where the first vector started, and ends where the last one ends.

59. 4.3 Newton’s Second Law of Motion---
Example: A 5.0 kg object is being acted on by a 20N force to the right (F1), and a 30N force, also to the right (F2). What is the net force on the object?
These free body diagrams are critically important to our work. Once done, the problem can be translated into an algebra problem. F1 F2 ΣF

60. Newton’s Second Law of Motion
For example: A 5.0 kg object is being acted on by a 20N force to the right (F1), and a 30N force, also to the right (F2). What is the net force on the object? F1 F2 ΣF
First we will define "to the right" as positive.
Then we can interpret our diagram to read:
ΣF = F1 + F2
ΣF = 20N + 30N
ΣF = 50N to the right
we get the direction from our diagram and from our positive answer, which we defined as meaning "to the right"

61. Force is a vector, so ΣF = ma is true along each coordinate axis.
4.3 Newton’s Second Law of Motion
Force is a vector, so ΣF = ma is true along each coordinate axis.
That means we can add up all the forces in the vertical direction and those will equal "ma" in the vertical direction.
And then can do the same thing in the horizontal direction. F1 F2 F3
a = 1 m/s2 F1 F2
F1 +(-F2) = m*a
F1 - F2 = 0 F3
F3 = m*a
F3 = (2kg)(1 m/s2)
F3 = 2 N
a = 1 m/s2

62. 13
Two forces act on an object. One force is 40N to the west and the other force is 40N to the east. What is the net force acting on the object?

63. Two forces act on an object. One force is 8.0 14
Two forces act on an object. One force is 8.0
N to the north and the other force is 6.0N to the south. What is the net force acting on the object? c A
14 N to the north c B
14 N to the south c C
2 N to the north c D
2 N to the south

64. 15
A force F1 = 50N acts to the right on a 5.0 kg object. Another force, F2 = 30N, acts to the left.
Find the acceleration of the object:

65. 16
A force F1 = 350N pushes upward on 20.0 kg object. Another force, F2 = 450N pulls downward.
Find the acceleration of the object:

66. 17
An object accelerates downward at a rate of 4.9 m/s2. If the downward force on the object is 500N and the upward force is 250N, what is the mass of the object?

67. 4.4 The Vector Nature of Newton’s Second Law
The direction of force and acceleration vectors
can be taken into account by using x and y
components.
is equivalent to

68. 4.4 The Vector Nature of Newton’s Second Law

69. 4.4 The Vector Nature of Newton’s Second Law
The net force on the raft can be calculated
in the following way:
Force
x component
y component
+17 N
+(15 N) cos67
0 N
+(15 N) sin67
+23 N
+14 N

70. 4.4 The Vector Nature of Newton’s Second Law

71. 4.4 Gravitational force,
Weight

72. 1) The Gravitational Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on every
other particle.
A particle is a piece of matter, small enough in size to be
regarded as a mathematical point.
The force that each exerts on the other is directed along the line
joining the particles.

73. 1) The Gravitational Force
For two particles that have masses m1 and m2 and are separated by a distance, then there will be gravitational force acting on each mass by the other,

74. 4.4 The Gravitational Force

75. 2) Weight – the Force of Gravity
Weight is the force exerted on an object by gravity. Close to the surface of Earth, where the gravitational acceleration is nearly constant, weight can be calculated with:
Fg = mg
Near the surface of Earth, g is 9.8 m/s2 downwards.

76. SI Unit of Weight: newton (N)
The weight of an object on or above the earth is the gravitational force that the earth exerts on the object.
The weight always acts downwards, toward the center
of the earth.
On or above another astronomical body, the weight is the
gravitational force exerted on the object by that body.
SI Unit of Weight: newton (N)

77. 18
Determine the Force of Gravity (weight) of a 6.0 kg bowling ball.

78. 19
Determine the weight of a small car with a mass of 900 kg.

79. 20
Using a spring scale, you find that the weight of a friction block in the lab is around 24 N. What is the mass of the block, in kilograms?

80. 21
A 120 lb woman has a mass of about 54.5 kg.
What is her weight?

81. 22
What is the weight of a 25 kg object located near the surface of Earth?

82. 23
Which of the following properties of an object is likely to change on another planet? c A
Mass c B
Weight c C
Color c D
Volume (size and shape)

83. The acceleration due to gravity is lower on the Moon than on Earth
The acceleration due to gravity is lower on the Moon than on Earth. Which of the following is true about the mass and weight of an astronaut on the Moon's surface, compared to Earth? 24 c A
Mass is less, weight is same c B
Mass is same, weight is less c C
Both mass and weight are less c D
Both mass and weight are the same

84. 4.5 the Normal Force
An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? FG

85. Normal Force
An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there?
The force exerted perpendicular to a surface is called the normal force.
It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!)
The words "normal" and "perpendicular" are synonyms. FN FG

86. 25
A 14 N brick is sitting on a table. What is the normal force supplied by the table? c A
14 N upwards B
28 N upwards c c C
14 N downwards D
28 N downwards c

87. 26
What normal force is supplied by a desk to a 2.0 kg box sitting on it?

88. 3) The Normal Force

89. Static and Kinetic Frictional Forces

90. Friction - A Resistive Force
There are many different types of forces that occur in nature, but perhaps none is more familiar to us than the force of friction (Ffr).
Friction is a resistive force that opposes the motion of an object.
What does sandpaper have to do with friction?
Friction is resistance to the relative or tendency of relative motion between the object and the contact surface.

91. Friction - A Resistive Force
Friction is the reason objects stop rolling or sliding along a surface. It is the reason it is difficult to start pushing a heavy box along the floor.
There are many different types of friction:
Friction between solid objects and air is often called air resistance.
Friction between two fluids is called viscosity, and so on.

92. Static and Kinetic Frictional Forces
When an object is in contact with a surface there is a force
acting on that object. Frictional force is the component of
this force that is
parallel to the surface.

93. 1) Static Friction Force
Static friction is the frictional force between two surfaces that are not moving along each other.
Static friction keeps objects from moving when a force is first applied.
Fapplied
v = 0

94. 1) Static Frictional Forces
When the two surfaces are
not sliding across one another
the friction is called
static friction.

95. Static Frictional Forces
The magnitude of the static frictional force can have any value
from zero up to a maximum value.
is called the coefficient of static friction.

96. *
Friction Force
The static frictional force increases as the applied force increases, always equal to the net applied force.
Until it reaches its maximum, μsFN.
Then the object starts to move, and the kinetic frictional force takes over, μKFN . 10 30 20 50 40 60 70
Friction force, f
Applied force, FA
f = μS FN
μk FN
no motion
sliding

97. 4.9 Static and Kinetic Frictional Forces
Note that the magnitude of the frictional force does
not depend on the contact area of the surfaces.

98. 2) Kinetic Frictional Forces
While Static friction opposes the impending relative motion between two objects.
Kinetic friction opposes the relative sliding motion motions that actually does occur.
is called the coefficient of kinetic friction.

99. 4.6 Static and Kinetic Frictional Forces

100. 4.6 Static and Kinetic Frictional Forces
The sled comes to a halt because the kinetic frictional force
opposes its motion and causes the sled to slow down.

101. 4.6 Static and Kinetic Frictional Forces
Suppose the coefficient of kinetic friction is 0.05 and the total
mass is 40kg. What is the kinetic frictional force?

102. Example:
The force of friction between an object and the surface upon which it is sliding is 8 N. The mass of the object is 20kg.
How much is the object’s weight?
How much is the normal force?
What is the coefficient of kinetic friction?

103. Example:
The minimum horizontal force to move an object on a surface is 400N. The force of friction between an object and the surface upon which it is sliding is 360N. The mass of the object is 95kg. What is the coefficient of kinetic friction? What is the coefficient of static friction?.

104. 4.7 The Tension Force Cables and ropes transmit
forces through tension.

105. A massless rope will transmit tension undiminished from one
4.7 The Tension Force
A massless rope will transmit
tension undiminished from one
end to the other.
If the rope passes around a
massless, frictionless pulley, the
tension will be transmitted to
the other end of the rope
undiminished.

106. 4.8 Air resistance force--Fair
special type of frictional force 
oppose the motion of an object
It is most noticeable for objects that travel at high speeds
Usually is speed related.

107. 4.9 Spring force--Fspring
force exerted by a compressed or stretched spring upon any object that is attached to it
to its rest or equilibrium position
Hook’s Law-magnitude of the force is directly proportional to the amount of stretch or compression of the spring

108. Practice of free body diagram and problem solving
Draw free body diagram:
Determine net force:

109. Fnet= F2 – F1=60-40=20N a=Fnet/m=20/5.0=4.0 m/s/s 13
Two forces act on an object with mass of 5.0 kg. One force is 40N to the west and the other force is 60N to the east. What is the net force acting on the object? What is the object acceleration? F1 F2
F1=40N, F2=60N
Fnet= F2 – F1=60-40=20N
a=Fnet/m=20/5.0=4.0 m/s/s

110. 15
A force F1 = 50N acts to the right on a 5.0 kg object. Another force, F2 = 30N, acts to the left.
Find the acceleration of the object:

111. 16
A force F1 = 350N pushes upward on 20.0 kg object. Another force, F2 = 450N pulls downward.
Find the acceleration of the object:

112. 17
A 250 kg object is sliding on a flat table under a horizontal force of 100 N applied to the object. The object also experience friction force of 60N from the table surface. How much is the object acceleration?
Fapp=100N
Ff=60N
m=250kg
Fnorm
Fapp Ff Fg
Fnet = Fapp - Ff
=100-60
= 40N
Then a=40/250=0.16m/s/s

113. 4.5 Newton’s Third Law of Motion
Whenever one body exerts a force on a
second body, the second body exerts an
oppositely directed force of equal magnitude on the first body.
For every action, there is an equal, opposite reaction. This is another way to state Newton's 3rd Law.
It is important to remember that the forces (or actions) are always applied to two different objects.

114. About action and reaction force:
All forces come in action-reaction pairs
Action and reaction forces are equal in size
Action and reaction forces are opposite in direction
They are same type of force
They acted on different objects
will never cancel out each other

115. Newton’s Third Law of Motion
A key to the correct application of the third law is that the forces are exerted on different objects.
Make sure you don’t use them as if they were acting on the same object. Then they would add to zero!
Force on hands
Force on floor

116. 4.5 Newton’s Third Law of Motion
Suppose that the magnitude of the force is 36 N. If the mass
of the spacecraft is 11,000 kg and the mass of the astronaut
is 92 kg, what are the accelerations?

117. 4.5 Newton’s Third Law of Motion
Acceleration of spacecraft:
Acceleration of astronaut:

118. Newton’s Third Law of Motion
Rocket propulsion can also be explained using Newton’s third law. Hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.
Note that the rocket does not need anything to “push” against.

119. Newton’s Third Law of Motion
Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source.
Horizontal force exerted on the ground by person's foot
FGP
Horizontal force exerted on the person's foot by ground
FPG
Subscripts help keep your ideas and equations clear.
FGP = -FPG

120. When you sit on a chair, the net external force on you is27
When you sit on a chair, the net external force on you is c A
zero. c B
dependant on your weight. c C
up. c D
down.

121. 28
An object of mass m sits on a flat table. The Earth pulls on this object with force mg, which we will call the action force. What is the reaction force? c A
The table pushing up on the object with force mg c B
The object pushing down on the table with force mg c C
The table pushing down on the floor with force mg
The object pulling upward on the Earth with force mg D c

122. 29
A 20-ton truck collides with a 1500-lb car and causes a lot of damage to the car. Since a lot of damage is done on the car A
the force on the truck is greater then the force on the car c B c
the force on the truck is equal to the force on the car C
the force on the truck is smaller than the force on the car c
the truck did not slow down during the collision c D

123. 30
As you are sitting in a chair, you feel the chair pushing up on you. The reaction force in this situation is: c A
The chair pushing down on the ground c B
Gravity pulling down on you c C
You pushing down on the chair c D
The ground pushing up on the chair

124. 31
A student is doing push-ups in gym class. A reaction pair of forces is best described as: c A
The student pushes down on the ground -
The ground pushes up on the student B
Gravity is pulling the student down -
The ground is pushing the student up c c C
Gravity is pulling the student down -
The student's arms push the student up c D
The student's hands push down on the ground -
The students arms push the student up

125. (Note: there may be more than one answer. Be prepared to explain WHY!)33
If you blow up a balloon, and then release it, the balloon will fly away. This is an illustration of:
(Note: there may be more than one answer. Be prepared to explain WHY!) c A
Newton's first law c B
Newton's second law c C
Newton's third law c D
Galileo's law of inertia