Chapter 4
Forces and the Laws of Motion
Section 1 Changes in Motion
Section 2 Newton's First Law
Section 3 Newton's Second and Third Laws
Section 4 Everyday Forces
Chapter 4
Section 1 Changes in Motion
 Describe how force affects the motion of an
object.
 Interpret and construct free body diagrams.
Chapter 4
Section 1 Changes in Motion
 A force is an action exerted on an object which
may change the object’s state of rest or motion.
 Forces can cause accelerations.
 The SI unit of force is the newton, N.
 Forces can act through contact or at a distance.
Chapter 4
Section 1 Changes in Motion
 The effect of a force depends on both
magnitude and direction.Thus, force is a
vector quantity.
 Diagrams that show force vectors as arrows are
called force diagrams.
 Force diagrams that show only the forces
acting on a single object are called free-body
diagrams.
Chapter 4
Section 1 Changes in Motion
Force Diagram
In a force diagram,
vector arrows represent
all the forces acting in a
situation.
Free-Body Diagram
A free-body diagram
shows only the forces
acting on the object of
interest—in this case, the
car.
Chapter 4
Section 2 Newton’s First Law
 Explain the relationship between the motion of
an object and the net external force acting on
the object.
 Determine the net external force on an object.
 Calculate the force required to bring an object
into equilibrium.
Chapter 4
Section 2 Newton’s First Law
 An object at rest remains at rest, and an object
in motion continues in motion with constant
velocity (that is, constant speed in a straight
line) unless the object experiences a net
external force.
 In other words, when the net external force on
an object is zero, the object’s acceleration (or
the change in the object’s velocity) is zero.
Chapter 4
Section 2 Newton’s First Law
 Newton's first law refers to the net force on
an object.The net force is the vector sum of
all forces acting on an object.
 The net force on an object can be found by
using the methods for finding resultant
vectors.
Although several forces are acting on
this car, the vector sum of the forces
is zero. Thus, the net force is zero,
and the car moves at a constant
velocity.
Chapter 4
Section 2 Newton’s First Law
Determining Net Force
Derek leaves his physics book on top of a drafting
table that is inclined at a 35° angle. The free-body
diagram below shows the forces acting on the book.
Find the net force acting on the book.
Chapter 4
Section 2 Newton’s First Law
1. Define the problem, and identify the
variables.
Given:
Fgravity-on-book = Fg = 22 N
Ffriction = Ff = 11 N
Ftable-on-book = Ft = 18 N
Unknown:
Fnet = ?
Chapter 4
Section 2 Newton’s First Law
2. Select a coordinate system, and apply it
to the free-body diagram.
Choose the x-axis parallel to and the y-axis perpendicular to
the incline of the table, as shown in (a). This coordinate
system is the most convenient because only one force needs
to be resolved into x and y components.
Tip: To simplify the problem, always
choose the coordinate system in which as
many forces as possible lie on the x- and
y-axes.
Chapter 4
Section 2 Newton’s First Law
3. Find the x and y components of all
vectors.
Draw
a sketch, as shown in (b), to help find
the components of the vector Fg. The angle 
is equal to 180– 90 – 35 = 55.
cos  
Fg , x
Fg
sin  
Fg , y
Fg
Fg , x  Fg cos 
Fg , y  Fg sin 
Fg , x  (22 N )(cos 55 )
Fg , x  (22 N )(sin 55 )
Fg , x  13 N
Fg , x  18 N
Add both components to the free-body diagram, as shown in (c).
Chapter 4
Section 2 Newton’s First Law
4. Find the net force in both the x and y directions.
Diagram (d) shows another free-body
diagram of the book, now with forces
acting only along the x- and y-axes.
For the x direction:
SFx = Fg,x – Ff
SFx = 13 N – 11 N
SFx = 2 N
For the y direction:
SFy = Ft – Fg,y
SFy = 18 N – 18 N
SFy = 0 N
Chapter 4
Section 2 Newton’s First Law
5. Find the net force.
Add the net forces in the x and y directions together as
vectors to find the total net force. In this case, Fnet = 2 N in
the +x direction, as shown in (e). Thus, the book
accelerates down the incline.
Chapter 4



Section 2 Newton’s First Law
Inertia is the tendency of an object to resist
being moved or, if the object is moving, to resist
a change in speed or direction.
Newton’s first law is often referred to as the
law of inertia because it states that in the
absence of a net force, a body will preserve its
state of motion.
Mass is a measure of inertia.
Chapter 4
Section 2 Newton’s First Law
Chapter 4



Section 2 Newton’s First Law
While inertia causes
passengers in a car to
continue moving forward
as the car slows down,
inertia also causes seat belts
to lock into place.
The illustration shows how
one type of shoulder
harness operates.
When the car suddenly
slows down, inertia causes
the large mass under the
seat to continue moving,
which activates the lock on
the safety belt.
Chapter 4



Section 2 Newton’s First Law
Equilibrium is the state in which the net force on
an object is zero.
Objects that are either at rest or moving with
constant velocity are said to be in equilibrium.
Newton’s first law describes objects in equilibrium.
Tip: To determine whether a body is in equilibrium, find the net force. If the net
force is zero, the body is in equilibrium. If there is a net force, a second force
equal and opposite to this net force will put the body in equilibrium.
Chapter 4
Section 3 Newton’s Second and
Third Laws
 Describe an object’s acceleration in terms of its
mass and the net force acting on it.


Predict the direction and magnitude of the
acceleration caused by a known net force.
Identify action-reaction pairs.
Chapter 4
Section 3 Newton’s Second and
Third 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.
SF = ma
net force = mass  acceleration
SF represents the vector sum of all external forces acting
on the object, or the net force.
Chapter 4
Section 3 Newton’s Second and
Third Laws
Chapter 4



Section 3 Newton’s Second and
Third Laws
If two objects interact, the magnitude of the
force exerted on object 1 by object 2 is equal
to the magnitude of the force simultaneously
exerted on object 2 by object 1, and these two
forces are opposite in direction.
In other words, for every action, there is an
equal and opposite reaction.
Because the forces coexist, either force can be
called the action or the reaction.
Chapter 4


Section 3 Newton’s Second and
Third Laws
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.
Chapter 4
Section 3 Newton’s Second and
Third Laws
Chapter 4




Section 4 Everyday Forces
Explain the difference between mass and
weight.
Find the direction and magnitude of normal
forces.
Describe air resistance as a form of friction.
Use coefficients of friction to calculate frictional
force.
Chapter 4



Section 4 Everyday Forces
The gravitational force (Fg) exerted on an
object by Earth is a vector quantity,
directed toward the center of Earth.
The magnitude of this force (Fg) is a scalar
quantity called weight.
Weight changes with the location of an
object in the universe.
Chapter 4

Section 4 Everyday Forces
Calculating weight at any location:
Fg = mag
ag = free-fall acceleration at that location

Calculating weight on Earth's surface:
ag = g = 9.81 m/s2
Fg = mg = m(9.81 m/s2)
Chapter 4
Section 4 Everyday Forces
Chapter 4


Section 4 Everyday Forces
The normal force acts on a surface in a
direction perpendicular to the surface.
The normal force is not always opposite
in direction to the force due to gravity.
– In the absence of other forces, the
normal force is equal and opposite
to the component of gravitational
force that is perpendicular to the
contact surface.
– In this example, Fn = mg cos .
Chapter 4
Section 4 Everyday Forces
Chapter 4



Section 4 Everyday Forces
Static friction is a force that resists the
initiation of sliding motion between two
surfaces that are in contact and at rest.
Kinetic friction is the force that opposes the
movement of two surfaces that are in contact
and are sliding over each other.
Kinetic friction is always less than the
maximum static friction.
Chapter 4
Section 4 Everyday Forces
Chapter 4



Section 4 Everyday Forces
In free-body diagrams, the force of friction is
always parallel to the surface of contact.
The force of kinetic friction is always opposite
the direction of motion.
To determine the direction of the force of static
friction, use the principle of equilibrium. For
an object in equilibrium, the frictional force
must point in the direction that results in a net
force of zero.
Chapter 4


Section 4 Everyday Forces
The quantity that expresses the dependence of
frictional forces on the particular surfaces in
contact is called the coefficient of friction, m.
Coefficient of kinetic friction:
mk 
Fk
Fn
• Coefficient of static friction:
ms 
Fs,m ax
Fn
Chapter 4
Section 4 Everyday Forces
Chapter 4
Section 4 Everyday Forces
Overcoming Friction
A student attaches a rope to a 20.0 kg box of
books.He pulls with a force of 90.0 N at an angle of
30.0° with the horizontal. The coefficient of kinetic
friction between the box and the sidewalk is 0.500.
Find the acceleration of the box.
Chapter 4
Section 4 Everyday Forces
1. Define
Given:
m = 20.0 kg
mk = 0.500
Fapplied = 90.0 N at  = 30.0°
Unknown:
a= ?
Diagram:
Chapter 4
Section 4 Everyday Forces
2. Plan
Choose a convenient coordinate system, and find
the x and y components of all forces.
The diagram on the right shows the
most convenient coordinate
system, because the only force to
resolve into components is Fapplied.
Fapplied,y = (90.0 N)(sin 30.0º) = 45.0 N (upward)
Fapplied,x = (90.0 N)(cos 30.0º) = 77.9 N (to the right)
Chapter 4
Section 4 Everyday Forces
Choose an equation or situation:
A. Find the normal force, Fn, by applying the condition of
equilibrium in the vertical direction:
SFy = 0
B. Calculate the force of kinetic friction on the box:
Fk = mkFn
C. Apply Newton’s second law along the horizontal direction to
find the acceleration of the box:
SFx = max
Chapter 4
Section 4 Everyday Forces
3. Calculate
A. To apply the condition of equilibrium in the vertical direction,
you need to account for all of the forces in the y direction:
Fg, Fn, and Fapplied,y. You know Fapplied,y and can use the box’s
mass to find Fg.
Fapplied,y = 45.0 N
Fg = (20.0 kg)(9.81 m/s2) = 196 N
Next, apply the equilibrium condition,
SFy = 0, and solve for Fn.
SFy = Fn + Fapplied,y – Fg = 0
Fn + 45.0 N – 196 N = 0
Fn = –45.0 N + 196 N = 151 N
Tip: Remember to pay
attention to the
direction of forces.
In this step, Fg is
subtracted from Fn
and Fapplied,y
because Fg is directed
downward.
Section 4 Everyday Forces
Chapter 4
B. Use the normal force to find the force of kinetic friction.
Fk = mkFn = (0.500)(151 N) = 75.5 N
C. Use Newton’s second law to determine the horizontal
acceleration.
SFx  Fapplied  Fk  ma x
ax 
Fapplied , x  Fk
m

77.9 N  75.5 N
2 0.0 kg
a = 0.12 m/s2 to the right

2.4 N
20.0 kg

2.4 kg  m /s
20.0 kg
2
Chapter 4
Section 4 Everyday Forces
4. Evaluate
The box accelerates in the direction of the
net force, in accordance with Newton’s
second law. The normal force is not equal
in magnitude to the weight because the y
component of the student’s pull on the
rope helps support the box.
Chapter 4


Section 4 Everyday Forces
Air resistance is a form of friction. Whenever
an object moves through a fluid medium, such
as air or water, the fluid provides a resistance
to the object’s motion.
For a falling object, when the upward force of
air resistance balances the downward
gravitational force, the net force on the object
is zero. The object continues to move
downward with a constant maximum speed,
called the terminal speed.
Chapter 4

There are four fundamental forces:





Section 4 Everyday Forces
Electromagnetic force
Gravitational force
Strong nuclear force
Weak nuclear force
The four fundamental forces are all field
forces.
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
1. What is the acceleration of the two blocks?
A.
B.
a 
a
F
m1
F
m2
C. a 
D. a 
F
m1  m 2
F
( m 1 )( m 2 )
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
1. What is the acceleration of the two blocks?
A.
B.
a 
a
F
m1
F
m2
C. a 
D. a 
F
m1  m 2
F
( m 1 )( m 2 )
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
2.
What is the horizontal force acting on m2?
F. m1a
G. m2a
H. (m1 + m2)a
J. m1m2a
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each
other on a smooth, horizontal surface. Block m1 is on the left of
block m2. A constant horizontal force F to the right is applied to
m1.
2.
What is the horizontal force acting on m2?
F. m1a
G. m2a
H. (m1 + m2)a
J. m1m2a
Chapter 4
3.
Standardized Test Prep
A crate is pulled to the right with a force of 82.0 N, to the left with a force
of 115 N, upward with a force of 565 N, and downward with a force of 236
N. Find the magnitude and direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis
B. 3.30 N at 6° counterclockwise from the positive x-axis
C. 3.30 x 102 at 96° counterclockwise from the positive x-axis
D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
Chapter 4
3.
Standardized Test Prep
A crate is pulled to the right with a force of 82.0 N, to the left with a force
of 115 N, upward with a force of 565 N, and downward with a force of 236
N. Find the magnitude and direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis
B. 3.30 N at 6° counterclockwise from the positive x-axis
C. 3.30 x 102 at 96° counterclockwise from the positive x-axis
D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
Chapter 4
4.
Standardized Test Prep
A ball with a mass of m is thrown into the air, as shown in the
figure below. What is the force exerted on Earth by the ball?
A. mballg directed down
B. mballg directed up
C. mearthg directed down
D. mearthg directed up
Chapter 4
4.
Standardized Test Prep
A ball with a mass of m is thrown into the air, as shown in the
figure below. What is the force exerted on Earth by the ball?
A. mballg directed down
B. mballg directed up
C. mearthg directed down
D. mearthg directed up
Chapter 4
5.
Standardized Test Prep
A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a
constant pull of 7.5 x 105 N, how long would it take to increase the speed
of the train from rest to 85 km/h? (Disregard friction.)
A. 4.7 x 102s
B. 4.7s
C. 5.0 x 10-2s
D. 5.0 x 104s
Chapter 4
5.
Standardized Test Prep
A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a
constant pull of 7.5 x 105 N, how long would it take to increase the speed
of the train from rest to 85 km/h? (Disregard friction.)
A. 4.7 x 102s
B. 4.7s
C. 5.0 x 10-2s
D. 5.0 x 104s
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 6–7.
A truck driver slams on the brakes and skids
to a stop through a displacement Dx.
6.
If the truck’s mass doubles, find the truck’s skidding distance
in terms of Dx. (Hint: Increasing the mass increases the normal
force.)
A. Dx/4
B. Dx
C. 2Dx
D. 4Dx
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 6–7.
A truck driver slams on the brakes and skids
to a stop through a displacement Dx.
6.
If the truck’s mass doubles, find the truck’s skidding distance
in terms of Dx. (Hint: Increasing the mass increases the normal
force.)
A. Dx/4
B. Dx
C. 2Dx
D. 4Dx
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 6–7.
A truck driver slams on the brakes and skids
to a stop through a displacement Dx.
7.
If the truck’s initial velocity were halved, what would be the
truck’s skidding distance?
A. Dx/4
B. Dx
C. 2Dx
D. 4Dx
Chapter 4
Standardized Test Prep
Use the passage below to answer questions 6–7.
A truck driver slams on the brakes and skids
to a stop through a displacement Dx.
7.
If the truck’s initial velocity were halved, what would be the
truck’s skidding distance?
A. Dx/4
B. Dx
C. 2Dx
D. 4Dx
Chapter 4
Standardized Test Prep
Use the graph at right to
answer questions 8–9. The
graph shows the relationship
between the applied force and
the force of friction.
8.
What is the relationship between the forces at point A?
F. Fs=Fapplied
G. Fk=Fapplied
H. Fs<Fapplied
I. Fk>Fapplied
Chapter 4
Standardized Test Prep
Use the graph at right to
answer questions 8–9. The
graph shows the relationship
between the applied force and
the force of friction.
8.
What is the relationship between the forces at point A?
F. Fs=Fapplied
G. Fk=Fapplied
H. Fs<Fapplied
I. Fk>Fapplied
Chapter 4
Standardized Test Prep
Use the graph at right to
answer questions 8–9. The
graph shows the relationship
between the applied force and
the force of friction.
9.
What is the relationship between the forces at point B?
A. Fs, max=Fk
B. Fk> Fs, max
C. Fk>Fapplied
D. Fk<Fapplied
Chapter 4
Standardized Test Prep
Use the graph at right to
answer questions 8–9. The
graph shows the relationship
between the applied force and
the force of friction.
9.
What is the relationship between the forces at point B?
A. Fs, max=Fk
B. Fk> Fs, max
C. Fk>Fapplied
D. Fk<Fapplied
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
10.
How long does the ball take to hit the ground?
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
10.
How long does the ball take to hit the ground?
Answer: 6.00 s
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
11. How far from the building does the ball hit the
ground?
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
11. How far from the building does the ball hit the
ground?
Answer: 72.0 m
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
12. When the ball hits the ground, what is its speed?
Chapter 4
Standardized Test Prep
Base your answers to questions 10–12 on the
information below.
A 3.00 kg ball is dropped from rest from the
roof of a building 176.4 m high.While the ball
is falling, a horizontal wind exerts a constant
force of 12.0 N on the ball.
12. When the ball hits the ground, what is its speed?
Answer: 63.6 m/s
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the
motion of the crate relative to the ground, the motion
of the crate relative to the truck, and whether the crate
will hit the front wall of the truck bed, the back wall,
or neither. Disregard friction.
13. Starting at rest, the truck accelerates to the right.
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the
motion of the crate relative to the ground, the motion
of the crate relative to the truck, and whether the crate
will hit the front wall of the truck bed, the back wall,
or neither. Disregard friction.
13. Starting at rest, the truck accelerates to the right.
Answer: at rest, moves to the left, hits back wall
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the
motion of the crate relative to the ground, the motion
of the crate relative to the truck, and whether the crate
will hit the front wall of the truck bed, the back wall,
or neither. Disregard friction.
14. The crate is at rest relative to the truck while the
truck moves with a constant velocity to the right.
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the motion of the crate
relative to the ground, the motion of the crate relative to the truck, and
whether the crate will hit the front wall of the truck bed, the back wall, or
neither. Disregard friction.
14. The crate is at rest relative to the truck while the
truck moves with a constant velocity to the right.
Answer: moves to the right, at rest, neither
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the motion of the
crate relative to the ground, the motion of the crate relative to the
truck, and whether the crate will hit the front wall of the truck
bed, the back wall, or neither. Disregard friction.
15. The truck in item 14 slows down.
Chapter 4
Standardized Test Prep
Base your answers to questions 13–15 on the
passage.
A crate rests on the horizontal bed of a pickup truck.
For each situation described below, indicate the motion of the crate
relative to the ground, the motion of the crate relative to the truck, and
whether the crate will hit the front wall of the truck bed, the back wall, or
neither. Disregard friction.
15. The truck in item 14 slows down.
Answer: moves to the right, moves to the right,
hits front wall
Chapter 4
Standardized Test Prep
16. A student pulls a rope attached to a 10.0 kg wooden
sled and moves the sled across dry snow. The student
pulls with a force of 15.0 N at an angle of 45.0º.
If mk between the sled and the snow is 0.040, what
is the sled’s acceleration? Show your work.
Chapter 4
Standardized Test Prep
16. A student pulls a rope attached to a 10.0 kg wooden
sled and moves the sled across dry snow. The student
pulls with a force of 15.0 N at an angle of 45.0º.
If mk between the sled and the snow is 0.040, what
is the sled’s acceleration? Show your work.
Answer: 0.71 m/s2
Chapter 4
Standardized Test Prep
17. You can keep a 3 kg book from dropping by pushing
it horizontally against a wall. Draw force diagrams,
and identify all the forces involved. How do they
combine to result in a zero net force? Will the force
you must supply to hold the book up be different for
different types of walls? Design a series of
experiments to test your answer. Identify exactly
which measurements will be necessary and what
equipment you will need.
Chapter 4
Standardized Test Prep
17. You can keep a 3 kg book from dropping by pushing
it horizontally against a wall. Draw force diagrams,
and identify all the forces involved. How do they
combine to result in a zero net force? Will the force
you must supply to hold the book up be different for
different types of walls? Design a series of experiments to test your
answer. Identify exactly
which measurements will be necessary and what
equipment you will need.
Answer: Plans should involve measuring forces such
as weight, applied force, normal force, and friction.
Chapter 4
Section 1 Changes in Motion
Chapter 4
Section 2 Newton’s First Law