Forces

1
Chapter 4

• Forces
• and
• Newtons 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
Thought Experiment
Now repeat that experiment, but make the second
ramp less steep. What Will Happen?
12
Thought Experiment
Now repeat that experiment, but make the second
ramp less steep. What Will Happen?
13
Thought Experiment
Now repeat that experiment, but make the second
ramp less steep. What Will Happen?
14
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.
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 Newtons First Law of Motion
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
velocitya velocity which is no more special than
any other.
28
4.2 Newtons 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
10 N
4 N
6 N
29
Net Force Mathematically, the net force is
written as
where the Greek letter sigma denotes the vector
sum.
 
30
4.2 Newtons 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 will
1
A
stop immediately.
c
c
B
slow down and eventually come to a stop.
c
C
go faster and faster.
D
move with constant velocity.
c
Ans D
32
When the rocket engines on a spacecraft are
suddenly turned off while traveling in empty
space, the starship will
2
A
stop immediately.
c
c
B
slowly slow down, and then stop.
C
go faster and faster.
c
D
move with constant velocity.
c
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
A
equal to its weight.
c
B
equal to its mass.
c
C
dependent on how fast it is moving.
c
D
zero.
c
Ans D
34
You are standing in a moving bus, facing forward,
and you suddenly fall forward. You can infer
from this that the buss
4
A
velocity decreased.
c
B
velocity increased.
c
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?
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.
c
Ans D
36
4.2 Newtons 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 Newtons 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.
Newtons 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
• http//www.phy.ntnu.edu.tw/ntnujava/index.php?topi
  c140

39
Check your understanding http//www.physicsclassr
oom.com/getattachment/curriculum/newtlaws/newtl2.p
df http//www.physicsclassroom.com/class/newtlaws
/Lesson-1/Inertia-and-Mass
40
4.3 Newtons Second Law of Motion
41
Newtons 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 Newtons 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 Newtons Second Law of Motion
SI Unit for Force
 
44
4.3 Newtons Second Law of Motion
45
4.4 Free body diagram
A free-body-diagram is a diagram that represents
the object and the forces that act on it.
46
4.3 Newtons Second Law of Motion
The net force in this case is 275 N 395 N
560 N 110 N and is directed along the x
axis of the coordinate system.
47
4.3 Newtons Second Law of Motion
If the mass of the car is 1850 kg then, by
Newtons 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 https//phet.colorado.edu/en/simu
lation/forces-1d https//phet.colorado.edu/en/si
mulation/forces-and-motion
50
A 3.5 kg object experiences an acceleration of
0.5 m/s2. What net force does the object feel?
6

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
A
4a
c
B
2a
c
c
C
a/2
D
a/4
c
54
10
A constant net force acts on an object. The
object moves with
A
constant acceleration
c
B
constant speed
c
C
constant velocity
c
D
increasing acceleration
c
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?
A
a/2
c
B
8a
c
C
4a
c
D
2a
c
56
12
The acceleration of an object is inversely
proportional to
A
the net force acting on it.
c
B
its position.
c
C
its velocity.
c
D
its mass.
c
57
4.3 Newtons 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 Newtons 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 Newtons 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.
60
Newtons 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?
First we will define "to the right" as
positive. Then we can interpret our diagram to
read SF F1 F2 SF 20N 30N SF 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
4.3 Newtons Second Law of Motion
Force is a vector, so SF 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.
a 1 m/s2
F1 (-F2) ma F1 - F2 0
F3 ma 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
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
B
14 N to the south
c
C
2 N to the north
c
D
2 N to the south
c
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 Newtons 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 Newtons Second Law
69
4.4 The Vector Nature of Newtons 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 Newtons Second Law
71
4.4 Gravitational force, Weight
72
1) The Gravitational Force
Newtons 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
Near the surface of Earth, g is 9.8 m/s2
downwards.
76
4.6.2 weight
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?
A
Mass
c
c
B
Weight
c
C
Color
D
Volume (size and shape)
c
83
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
A
Mass is less, weight is same
c
B
Mass is same, weight is less
c
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?
A
14 N upwards
c
B
28 N upwards
c
C
14 N downwards
c
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
4.6 Friction
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.
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 .
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
objects 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
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
• Hooks 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 http//www.physicsclassroo
m.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Di
agrams
Determine net force http//www.physicsclassroom.c
om/class/newtlaws/Lesson-2/Determining-the-Net-For
ce
109
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?
F140N, F260N
F1
F2
Fnet F2 F160-4020N aFnet/m20/5.04.0 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?
Fapp100N Ff60N m250kg
Fnorm
Fapp
Ff
Fg
Fnet Fapp - Ff 100-60 40N Then
a40/2500.16m/s/s
113
4.5 Newtons 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
Newtons 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 dont use them as if
they were acting on the same object. Then they
would add to zero!
116
4.5 Newtons 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 Newtons Third Law of Motion
Acceleration of spacecraft
Acceleration of astronaut
118
Newtons Third Law of Motion
Rocket propulsion can also be explained using
Newtons 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
Newtons Third Law of Motion
Helpful notation the first subscript is the
object that the force is being exerted on the
second is the source.
Subscripts help keep your ideas and equations
clear.
FGP -FPG
120
When you sit on a chair, the net external force
on you is
27
A
zero.
c
B
dependant on your weight.
c
C
up.
c
c
D
down.
121
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?
28
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
c
The object pulling upward on the Earth with force
mg
D
c
122
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
29
A
the force on the truck is greater then the force
on the car
c
B
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
c
the truck did not slow down during the collision
D
c
123
30
As you are sitting in a chair, you feel the chair
pushing up on you. The reaction force in this
situation is
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
c
124
A student is doing push-ups in gym class. A
reaction pair of forces is best described as
31
The student pushes down on the ground - The
ground pushes up on the student
c
A
Gravity is pulling the student down - The ground
is pushing the student up
B
c
Gravity is pulling the student down - The
student's arms push the student up
C
c
The student's hands push down on the ground - The
students arms push the student up
D
c
125
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!)
A
Newton's first law
c
B
c
Newton's second law
C
c
Newton's third law
D
c
Galileo's law of inertia