Newton’s Laws Examples
Physics 6A
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Newton’s Laws of Motion
These three rules govern the motion of any object.
1: Law of Inertia
The velocity of an object will not change unless it is acted upon by a nonzero net force.
2: This is the formula we will use to calculate the effect of forces on objects.


F  m  a
3: Forces always come in action-reaction pairs.
You have probably heard this as “for every action there is an equal and opposite reaction”.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
v0
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this? No, of course it slows down
and then stops. So is Newton’s first law violated?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this? No, of course it slows down
and then stops. So is Newton’s first law violated?
Here it is again – does the motion of the eraser follow this rule?
1: Law of Inertia
The velocity of an object will not change unless it is acted upon by a nonzero net force.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this? No, of course it slows down
and then stops. So is Newton’s first law violated?
Here it is again – does the motion of the eraser follow this rule?
1: Law of Inertia
The velocity of an object will not change unless it is acted upon by a nonzero net force.
There must some net force acting on the eraser since it changed its velocity
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this? No, of course it slows down
and then stops. So is Newton’s first law violated?
Here it is again – does the motion of the eraser follow this rule?
1: Law of Inertia
The velocity of an object will not change unless it is acted upon by a nonzero net force.
There must some net force acting on the eraser since it changed its velocity
What force(s) are exerted on the eraser?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
You may think that Newton’s first law (inertia) would
tell us that the eraser should continue forward at
speed v0 indefinitely.
v0
Does the eraser do this? No, of course it slows down
and then stops. So is Newton’s first law violated?
Here it is again – does the motion of the eraser follow this rule?
1: Law of Inertia
The velocity of an object will not change unless it is acted upon by a nonzero net force.
There must some net force acting on the eraser since it changed its velocity
What force(s) are exerted on the eraser?
We can draw a picture of the eraser and all the forces that act on it.
This is one of your most important tools – we call it a “free-body diagram”
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
Here is the force diagram for the eraser
friction
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
‘Normal’ means perpendicular
Here is the force diagram for the eraser
Assuming that the normal force and the weight
are the same magnitude, which direction is the
net force on the eraser?
friction
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
‘Normal’ means perpendicular
Here is the force diagram for the eraser
Assuming that the normal force and the weight
are the same magnitude, which direction is the
net force on the eraser?
The net force is to the left (in the direction of
the friction force). What does this tell you
about the acceleration of the eraser?
friction
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
‘Normal’ means perpendicular
Here is the force diagram for the eraser
Assuming that the normal force and the weight
are the same magnitude, which direction is the
net force on the eraser?
The net force is to the left (in the direction of
the friction force). What does this tell you
about the acceleration of the eraser?
friction
weight
Yes, the acceleration is also to the left. This
will always happen – the acceleration will be
the same direction as the net force (this is from
Newton’s 2nd law)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
‘Normal’ means perpendicular
Here is the force diagram for the eraser
Assuming that the normal force and the weight
are the same magnitude, which direction is the
net force on the eraser?
The net force is to the left (in the direction of
the friction force). What does this tell you
about the acceleration of the eraser?
friction
weight
Yes, the acceleration is also to the left. This
will always happen – the acceleration will be
the same direction as the net force (this is from
Newton’s 2nd law)
At this point it should be clear why the eraser
slowed down and stopped. The acceleration
was to the left – opposite the velocity, so the
speed decreased.
We will return to this example and do some
calculations after we learn more about friction.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
friction
Does each force in our diagram have an
‘equal and opposite’ reaction force?
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
friction
Let’s think about the friction force first.
What objects are interacting to make the friction
force happen?
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
Frail on eraser
Let’s think about the friction force first.
What objects are interacting to make the friction
force happen? It is the rough surface of the eraser
rubbing against the metal chalk rail. How would
you describe the ‘reaction’ to this force?
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
F rail on eraser
F eraser on rail,x
Let’s think about the friction force first.
What objects are interacting to make the friction
force happen? It is the rough surface of the eraser
rubbing against the metal chalk rail. How would
you describe the ‘reaction’ to this force?
weight
The ‘reaction’ is always the same 2 objects, with
their roles reversed. So we can consider the force
that the eraser exerts on the rail as the
corresponding reaction.
This was not in our free-body diagram because our
diagram only had forces on the eraser.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
F rail on eraser
F eraser on rail,x
What about the weight? What is the reaction to
that force?
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
What about the weight? What is the reaction to
that force? What objects are interacting to make
the weight of the eraser?
F rail on eraser
F eraser on rail,x
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
What about the weight? What is the reaction to
that force? What objects are interacting to make
the weight of the eraser?
F rail on eraser
F eraser on rail,x
Fearth on eraser
The weight is the force of gravity exerted on the
eraser by the earth.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
What about the weight? What is the reaction to
that force? What objects are interacting to make
the weight of the eraser?
F rail on eraser
F eraser on rail,x
Fearth on eraser
The weight is the force of gravity exerted on the
eraser by the earth.
So how would you describe the reaction force? Is
it the normal force?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
What about the weight? What is the reaction to
that force? What objects are interacting to make
the weight of the eraser?
F rail on eraser
F eraser on rail,x
Fearth on eraser
The weight is the force of gravity exerted on the
eraser by the earth.
So how would you describe the reaction force? Is
it the normal force? NO (why not??)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
F rail on eraser
What about the weight? What is the reaction to
that force? What objects are interacting to make
the weight of the eraser?
F eraser on rail,x
Fearth on eraser
The weight is the force of gravity exerted on the
eraser by the earth.
So how would you describe the reaction force? Is
it the normal force? NO (why not??)
The reaction has to be the same objects with their
roles reversed. The weight was the earth pulling
downward on the eraser, so the reaction should be
the eraser pulling upward on the earth. (same 2
objects, opposite direction)
Feraser on earth
EARTH (not to scale)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Normal
force
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
Ok, last one – what is the reaction that
corresponds to the normal force? First identify
which 2 objects are interacting.
F rail on eraser
F eraser on rail,x
Fearth on eraser
Feraser on earth
EARTH (not to scale)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Frail on eraser,y
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
Ok, last one – what is the reaction that
corresponds to the normal force? First identify
which 2 objects are interacting. This time it is the
eraser and the chalk rail, but in the vertical (y)
direction.
F rail on eraser,x
F eraser on rail,x
Fearth on eraser
Feraser on earth
EARTH (not to scale)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail
The eraser in the diagram is pushed giving it an initial velocity v0, then released and
allowed to slide until it stops. We will put some numbers in later. For now, we will
consider what Newton’s Laws tell us about this motion.
Frail on eraser,y
One more idea with this eraser example:
How does Newton’s 3rd law apply here?
Does each force in our diagram have an ‘equal
and opposite’ reaction force?
Ok, last one – what is the reaction that
corresponds to the normal force? First identify
which 2 objects are interacting. This time it is the
eraser and the chalk rail, but in the vertical (y)
direction.
F rail on eraser,x
F eraser on rail,x
Fearth on eraser
Feraser on rail,y
The opposite to this force is a downward force on
the chalk rail due to the eraser.
Feraser on earth
EARTH (not to scale)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
y
Normal
force
x
120 N
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
y
Normal
force
We can use Newton’s 2nd law to
calculate the acceleration.
x
120 N
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
y
Normal
force
We can use Newton’s 2nd law to
calculate the acceleration.
x
120 N
We can write down separate equations
for the x- and y-directions:
x  direction
Fx  m  a x
y  direction
Fy  m  a y
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
y
Normal
force
We can use Newton’s 2nd law to
calculate the acceleration.
x
120 N
We can write down separate equations
for the x- and y-directions:
x  direction
Fx  m  a x
y  direction
Fy  m  a y
120N  60kg  a x
Normal  Weight  0
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Pushing a box across the floor.
A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton
force. Draw a free-body diagram for the box. Find the resulting acceleration.
y
Normal
force
We can use Newton’s 2nd law to
calculate the acceleration.
x
120 N
We can write down separate equations
for the x- and y-directions:
x  direction
Fx  m  a x
y  direction
Fy  m  a y
120N  60kg  a x
Normal  Weight  0
a x  2 m2
s
weight
Notice that we could determine that the normal force
equals the weight, but in this problem we don’t really
care (if there were friction we would need this fact)
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail.
A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes
to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail.
A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes
to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.
Normal
force
Here is the free-body diagram again. Notice that the
only horizontal force is friction.
friction
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail.
A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes
to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.
Normal
force
Here is the free-body diagram again. Notice that the
only horizontal force is friction. We can write down
Newton’s 2nd law for the x-direction:
 Fx  Ffriction  m  ax
friction
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail.
A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes
to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.
Normal
force
Here is the free-body diagram again. Notice that the
only horizontal force is friction. We can write down
Newton’s 2nd law for the x-direction:
 Fx  Ffriction  m  ax
friction
We can use kinematics to find the acceleration:
v2  v20  2a  (x  x 0 )
0
a
(4 m
)2 
s
2.7 m2
s
2a  (3m)
weight
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: An eraser sliding on the chalk rail.
A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes
to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.
Normal
force
Here is the free-body diagram again. Notice that the
only horizontal force is friction. We can write down
Newton’s 2nd law for the x-direction:
 Fx  Ffriction  m  ax
friction
We can use kinematics to find the acceleration:
v2  v20  2a  (x  x 0 )
0
a
(4 m
)2 
s
2.7 m2
s
weight
2a  (3m)
Put this value in to find the friction force:
 Ffriction  (0.1kg)  (2.7 m2 )
s
Ffriction  0.27N
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB