Newton’s Third Law of Motion 3.

4
Examine the photograph in Figure 1 of an Atlas V rocket during liftoff. What forces
are acting on the rocket? An obvious one is gravity pulling the rocket down. The
rocket is accelerating upward in the picture. This means that the net force must be
up according to Newton’s second law. What is this upward force? You might suggest
that the ground is pushing up on the rocket with the normal force. This cannot be
the answer because the normal force is a contact force and the rocket is no longer in
contact with the ground. In this section, you will learn about this upward force as you
learn about Newton’s third law of motion.

Action and Reaction Forces

If you reach out and push this book away from you, you can actually feel the book
pushing back on you. This is an example of a set of action and reaction forces. The
action force is you pushing on the book, and the reaction force is the book pushing
back on you. An easy way to experience action and reaction forces is by pushing on
the boards when you are skating in an ice rink. When you push on the boards (the
action force), the boards push back on you (reaction force). It is the reaction force
that causes you to accelerate away from the boards.
These action and reaction forces are all around us and go unnoticed most of the
time. When you push a door open, the door pushes back on you. When you walk
forward across the floor, you push backwards on the ground and the ground pushes
Figure 1  An Atlas V rocket was
forward on you. In fact, whenever one object exerts a force on another, the second
launched in June 2009. As the rocket
object exerts another force back. lifted up off the launch pad, what force
Another simple way to demonstrate action and reaction forces is to have a person caused it to accelerate upward?
standing at rest on a skateboard suddenly step forward (Figure 2). When this hap-
pens, the person and the skateboard will accelerate in opposite directions. According
to Newton’s second law, both the person and the skateboard have net forces acting on
them because they are accelerating. What causes these forces?
The net force on the skateboard is caused by the person’s feet pushing backwards
on the skateboard. The person’s feet exert the action force on the skateboard. The net
force on the person is caused by the skateboard pushing forward on the person. The
skateboard exerts the reaction force on the person.
Keep in mind that these action and reaction forces are simultaneous. It is incorrect to V of person
imply that the action force happens first and then the reaction force happens. These are
contact forces, and both the action and reaction forces start whenever contact is made.
Newton’s third law of motion deals with these action and reaction forces. For this V of skateboard
reason, it is sometimes called the action–reaction law.
Figure 2  As a person jumps off
a skateboard in one direction, the
Third Law of Motion skateboard will accelerate in the other
For every action force, there is a simultaneous reaction force that is equal in magnitude, direction.
but opposite in direction.

We can now explain how a rocket can accelerate up off the launch pad. During third law of motion  each action force
liftoff, the rocket engines burn rocket fuel, creating tremendous pressure, which causes has a reaction force that is equal in
the expanding hot gases to accelerate from the bottom of the rocket (action force). magnitude and opposite in direction
At the same time, the expanding hot gases push up on the rocket (reaction force),
causing the rocket to accelerate up. According to Newton’s third law, the action force
caused by the expanding hot gases is equal in magnitude to the reaction force of the
expanding hot gases on the rocket. If the reaction force up on the rocket from the
expanding hot gases is greater than the force of gravity pulling the rocket down, then
the rocket will accelerate up. In the following Tutorial, you will apply Newton’s third law
to problems involving motion.

NEL 3.4 Newton’s Third Law of Motion   137

 Tutorial 1 Explaining Motion Using Newton’s Third Law
In the following Sample Problem, we will clarify Newton’s third law and demonstrate how it
can be used to explain motion when objects exert forces on each other.

Sample Problem 1
Explain each event in terms of Newton’s third law. (b) As the rubber in the balloon contracts, it forces air out the
(a) A swimmer moves through the water. back of the balloon (action force). According to Newton’s
(b) A small balloon releases air and flies around the classroom. third law, the reaction force is caused by the air pushing
(c) You start walking across the floor. back on the balloon, which accelerates the balloon
forward.
Solution (c) The bottom of your shoe exerts a horizontal backward action
(a) The swimmer’s arms and legs exert an action force force on the floor. According to Newton’s third law, the
backwards on the water, causing the water to accelerate reaction force is caused by friction when the floor pushes
backwards. According to Newton’s third law, the water forward on your feet. Friction causes you to accelerate
exerts an equal but opposite force forward on the swimmer, forward.
propelling the swimmer forward through the water.

Practice
1. Explain each event in terms of Newton’s third law. K/U

(a) A rocket can accelerate in outer space.

(b) A motorboat accelerates east in the water.
(c) Football player 1 tackles football player 2.

Mini Investigation
Demonstrating the Third Law
SKILLS
Skills: Predicting, Performing, Observing, Analyzing, Communicating HANDBOOK A2.1

In this investigation, you will perform and observe several actions (c) Stand on a bathroom scale placed beside a desk. Put
that involve Newton’s third law. Your task is to predict what will your hands on the desk and push down.
happen at each station, observe carefully what actually happens, (d) Stand on a bathroom scale. Push down on your own
and explain why it happens. head with your hands.
Equipment and Materials: office chair with wheels; bathroom (e) Use a spring-loaded ballistics cart to fire a ball
scale; desk; ballistics cart; fan cart with removable sail horizontally.
(f) Obtain a fan cart (Figure 3(a)) with no sail. Direct the
1. Create a table similar to Table 1 to record your observations.
fan away from the cart. Turn the fan cart on.
Add six rows to the table.
(g) Obtain a fan cart (Figure 3(b)) with a sail. Direct the fan
Table 1 toward the sail. Turn the fan cart on.
sail
Action and reaction
Activity Prediction Observation forces

2. Read through the descriptions of activities (a) through (g).

For each activity, predict what you think will happen and
record your predictions in your table. (a) (b)
3. Perform activities (a) to (g) (or observe a classmate Figure 3
performing these activities). Record your observations.
(a) Sit on an office chair and push gently against a wall with A. Use Newton’s third law to describe the action and reaction
both hands. forces you observed in each activity. T/I
(b) Sit on the chair, not touching the wall. Use your hands to
pull horizontally on your own shoulders, away from the wall.

138 Chapter 3 • Newton’s Laws of Motion NEL

 You may have noticed that objects will not always accelerate or the reading on a
scale will not always change when a force is applied to an object. What is different
about these situations? The difference is that in each of these situations there is no
external net force acting on the object.
Does this mean that action and reaction forces cancel and we can never accelerate?
Definitely not. Action and reaction forces always act on different objects, or different
parts of a single object. When two objects are involved, the two forces are not added
together and each object can accelerate.
For example, if a ballistics cart pushes backwards on a ball (action force), the
ball accelerates backwards because the applied force causes a net force on the ball.
CAREER LInK
According to Newton’s third law, the ball will also cause a reaction force on the cart
in the opposite direction. This reaction force causes a net force on the cart, making To learn about becoming a forensic
it accelerate the other way. The action and reaction forces do not cancel because they technician and a forensic scientist,
do not act on the same object. When you draw the FBD for each object, the action
go T o N ELSoN S C i EN C E
and reaction forces will appear in separate FBDs (Figure 4).
FBD of ball FBD of cart
F�N
F�N

F�g
F�g
(a) before
FBD of ball FBD of cart
F�N
F�N

F�a F�a
F�g
F�g

(b) after
Figure 4 (a) Diagram and FBDs of a ball inside a ballistics cart before firing (b) Diagram and FBDs
after firing the ball. The action and reaction forces do not cancel because they act on different
objects.

tario Physics 11 U
Tutorial 2 Using Newton’s Third Law in Calculations
76504338 In the following Sample Problem, we will clarify Newton’s third law and demonstrate how it
can be used to explain motion when objects exert forces on each other.
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Sample Problem 1: One Skater Pushing on Another
Two skaters are standing on ice facing each other (Figure 5).
ss 4th Pass (1st pass 7381-A)
Skater 1 pushes on skater 2 with a force of 70 N [E]. Assume
proved
that no friction acts on either skater. The mass of skater 1 is
t Approved 50 kg and the mass of skater 2 is 70 kg.
(a) State the action and reaction forces.
(b) Draw the FBD of each skater.
(c) Describe what will happen to each skater.
(d) Calculate the acceleration of each skater. skater 1 skater 2
ntario Physics 11 U Figure 5

76504338 NEL 3.4 Newton’s Third Law of Motion 139

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 Solution (d) For each skater, the normal force and the force of gravity
(a) The action force is skater 1 pushing with 70 N [E] on cancel. This means that the applied force is equal to the net
skater 2. The reaction force is skater 2 pushing with 70 N force. For skater 1,
S S
[W] on skater 1. F net 5 F a
(b) Choose east as positive. So west is negative.
m1a1 5 270 N
150 kg2 a1 5 270 N
skater 1 skater 2
a1 5 21.4 m/s2
F�N1 F�N2 The acceleration of skater 1 is 1.4 m/s2 [W].
Similarly, for skater 2,
F a � �70 N F a � �70 N S S
F net 5 F a
m2a2 5 170 N
170 kg2 a2 5 70 N
F�g F�g a2 5 11.0 m/s2
1 2

The acceleration of skater 2 is 1.0 m/s2 [E].

(c) Skater 1 will accelerate west and skater 2 will accelerate east.
Notice that the two skaters accelerate in opposite directions
and with different accelerations. The accelerations do not have
the same magnitude because the skaters’ masses are different.

Practice
1. Given the action force, describe the reaction force for each 3. A horse is tethered to a cart to pull it forward. A student
situation. K/U C claims, “According to Newton’s third law, when the horse
(a) You push forward on a book with 5.2 N. pulls forward on the cart, the cart will also pull backwards
(b) A boat exerts a force of 450 N [W] on the water. on the horse. The two objects are attached together, so they
(c) A hockey player hits the boards with a force of 180 N cannot accelerate.” Discuss the validity of this statement.
[toward the boards]. K/U C

2. Nobel and Maaham are wearing inline skates. Nobel has 4. A student stands on a skateboard and pushes on a wall with
a mass of 62 kg and pushes on Maaham, whose mass is a force of 87 N [S]. The total mass of the student and the
54 kg. Maaham accelerates at 1.2 m/s2 [left]. Assume that skateboard is 58 kg. K/U T/I
no friction acts on either person. T/I (a) Calculate the acceleration of the student. [ans: 1.5 m/s2 [N]]
(a) Determine the force that Nobel exerts on Maaham. (b) Explain why the wall does not move.
s 11 U [ans: 65 N [left]]
(b) Determine Nobel’s acceleration. [ans: 1.0 m/s2 [right]]

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UNiT TASK BOOKMARK 3.4 Summary
5th Pass (1st pass 7381-A)
You can apply what you have learned
• Newton’s third law always involves situations where two objects exert forces
about Newton’s third law to the Unit
on each other.
Task on page 204.
• Newton’s third law states that for every action force there is a simultaneous
reaction force equal in magnitude but opposite in direction.
• When applying Newton’s third law, the action and reaction forces will appear on
separate FBDs. Since they are on separate FBDs, they are not added together.

140 Chapter 3 • Newton’s Laws of Motion NEL

 3.4 Questions
1. Given each action force, state the reaction force. K/U 6. A toy car (200 g) moves by shooting a plastic ball (50 g)
(a) A tire pushes on the road with a force of horizontally out the back. The average acceleration of the
240 N [backwards]. car is 1.2 m/s2 [E] and there is negligible friction acting on
(b) You pull on a desk with a force of 25 N [N]. each part of the toy. T/I C
2. Explain each event below in terms of Newton’s third law. K/U
(a) Draw an FBD for each object.
(a) A squid moves through the water by taking in water (b) Identify the action and reaction forces on each part
and expelling it. of the toy.
(b) Walking on a wagon is dangerous. 7. Two figure skaters are moving east together during a
(c) A helicopter can hover above the ground. performance. Skater 1 (78 kg) is behind skater 2 (56 kg)
3. During a space walk, an astronaut notices that her tether when skater 2 pushes on skater 1 with a force of
is not attached and she is drifting away from the space 64 N [W]. Assume that no friction acts on either
station. Explain each statement below using Newton’s skater. T/I
third law. K/U C (a) Determine the acceleration of each skater.
(a) She can pull herself back to the space station if she (b) What will happen to the motion of each skater?
can reach the space station and pull on it. Explain your reasoning.
(b) She cannot push herself back to the station by pulling 8. A milk carton filled with water is hanging from a string
forward on her space suit. (Figure 8). What will happen if you punch two holes in
(c) She can get back to the space station even if she opposite sides of the carton at the opposite corners?
cannot reach it if she is holding a tool. Explain your reasoning. T/I
4. Figure 6 shows a photograph of an early naval cannon tied
to a ship. Explain why the ropes are necessary. A

Figure 6

5. Figure 7 shows a fan cart. K/U

(a) Explain why the fan cart cannot accelerate.
(b) Explain why the fan cart can accelerate if the rigid sail
is removed. Figure 8

sail 9. A male astronaut (82 kg) and a female astronaut (64 kg)
are floating side by side in space. T/I
(a) Determine the acceleration of each astronaut if the
woman pushes on the man with a force of 16 N [left].
(b) How will your answers change if the man pushes with
16 N [right] on the woman instead?
(c) How will your answers change if they both reach out
and push on each other’s shoulders with a force of
16 N?

Figure 7

NEL 3.4 Newton’s Third Law of Motion 141