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Physics Factsheet
www.curriculum-press.co.uk
Number 108
Where Students Make Mistakes:
Balanced Forces and Action-Reaction pairs
Newton’s third law of motion states, “For every action, there is an
equal and opposite reaction.” This means forces always act in
pairs. In an exam question, the tricky part can be working out just
what the pair is.
For every action, there is an equal and opposite
reaction (forces act in pairs)
Force of foot acting on the ball
To start with, we’ll use several simple examples to help you
understand Newton’s third law.
Force of ball acting on the foot
What about a bullet fired from a gun? The gun forces the bullet
forwards. The bullet forces the gun backwards. Our hand or
shoulder feels a kick from this “recoil” (although there are mechanical
ways to deal with this).
Force of earth acting on
the sprinter
Force of sprinter acting on
the earth
Force of gun acting on the bullet
What happens when a sprinter begins their race? They push off
from their starting blocks. If the sprinter is pushing backwards
against the earth, what’s the other half of the force pair? The earth
must be pushing the sprinter forwards, with a force of exactly the
same size. But if the forces are equally sized and in opposite
directions, how can the sprinter move?
Force of bullet acting on the gun
Example Exam Question: An Olympic pistol marksman fires at
×106ms-2. Assume his
a target. The 10g bullet accelerates at 2×
gun has a mass of 2kg. Explain and calculate the acceleration
the gun undergoes.
Answer
Action of the gun on the bullet has an equal and opposite
reaction of the bullet on the gun. Gun’s mass is 200 times
greater than the bullet, so the gun’s acceleration will be 200
times less.
2×106ms-2
= 1×104ms-2
a=
200
The sprinter moves because only one of the forces acts on him. The
other acts on the Earth.
The sprinter pushes the earth backwards and the earth pushes the
sprinter forwards. But the sprinter is tiny compared to the earth.
We notice the sprinter moving forwards but we don’t see the earth
moving backwards.
Exam Hint: Even though force-pairs are always equal and
opposite, always balanced, there can still be movement. As we
walk, we are pushed forwards and the earth is pushed
backwards. Because the earth is so huge, this backward motion
is tiny and we don’t see it.
Force of exhaust
gases acting on the
rocket
A footballer kicks a ball forwards. What is the other half of the force
pair? The ball pushes the foot backwards. If we kick the ball
forwards hard, the backward force acting on the foot could break a
toe!
Force of rocket
acting on the exhaust
gases
How does a rocket move? Many people think it takes off by pushing
against the ground. So how can it work in space? A rocket engine
produces high speed exhaust gases which are forced backwards by
the rocket. The exhaust gases push the rocket forwards.
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Physics Factsheet
108 . Where Students Make Mistakes: Balanced Forces and Action-Reaction pairs
Now, what happens if an object is moved up or down?
Exam Hint: A rocket does NOT travel by pushing off against
the ground. The exhaust gases moving backwards push the
rocket forwards.
Think about travelling in a lift. In the first example, the lift is not moving.
Now, what is the force pair in this picture?
Wp We R p Re
Stationary lift
You may be tempted to say the weight of the book is balanced by
the contact force from the ground. Although this IS true, there are
TWO separate force pairs here. We need to understand both pairs
before going further.
According to Newton’s first law of motion, something will stay still
unless an unbalanced force acts. In this case, the man’s weight
(Wp) is balanced by the upwards contact force (Re). He stays where
he is. However, Newton’s first law goes on to say that something
will stay at a steady speed in a straight line unless an unbalanced
force acts. In the first example, the lift could be moving up or down
at a steady speed.
Gravity is an attraction between any objects with mass. The book
and the earth are attracting each other. For a small object, we usually
think only about the force of the earth pulling the book
DOWNWARDS, causing weight. But the book is also attracting
the earth UPWARDS, with a force of exactly the same size (but in
the opposite direction). Because the earth is so much larger than
the book, we don’t notice the effect of the book on the earth.
When an object on a surface is at rest or moving
vertically at a steady speed, the upward contact force is equal
and opposite to the weight of the object.
If the lift accelerates upwards or downwards, the weight of the man
due to the earth (Wp) and the earth due to the man (We) DO NOT
CHANGE.
Weight acts in a force pair. An object is attracted down
to the earth and so the object attracts the earth upwards. The
forces are equal in size, but in opposite directions.
In the second example, the man is being forced upwards. The
upwards contact force must be bigger than his weight downwards.
This overall unbalanced upward force causes upward acceleration.
In more simple terms the floor is pushing him upwards.
The book and the ground are also pushing against each other.
These are contact forces. Everyday matter consists of atoms. An
atom consists of a positive nucleus surrounded by shells of negative
electrons. A simple way to consider contact forces is that if you
bring two surfaces close together, the outer electrons repel each
other. The reason a book does not fall through a table is because
the outer electrons in the book and the table repel each other. In
reality, they’re not actually touching. The electrostatic repulsion
causes the book to “float” above the table.
Wp We R p Re
Lift accelerates upwards
Wearth
W book
Cearth
C book
1) weight force pair 2) contact force pair
Cearth
In the third example, the lift is moving down. The upward push due
to contact force is less. The overall unbalanced force is downwards
and he accelerates downwards. In more simple terms, the floor is
“falling away” below him.
W book
3) forces acting on book
Contact forces act in a force pair. The outer electrons
in two surfaces repel each other.
Exam Hint: The weight of an object and the upward contact
force are not a force pair. The earth-object attraction is one
force pair and the contact force pair is caused by the two
surfaces repelling each other.
Wp We R p Re
Lift accelerates downwards
Exam Hint: When an object is resting on a surface, the upward
contact force will reduce if the surface accelerates downwards
and increase if the surface accelerates upwards.
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Physics Factsheet
108 . Where Students Make Mistakes: Balanced Forces and Action-Reaction pairs
Answers
1) Newton’s third law of motion states that for every action, there
is an equal and opposite reaction. This means forces always act
in pairs, equal in size and opposite in direction.
How does the upward contact force alter during exercise, say, if a
woman is repeatedly squatting and standing? In the initial part of
the squat, the woman accelerates downwards. Is the contact force
greater or less than her weight? The overall unbalanced force must
be downwards, which means the upward contact force is SMALLER.
As she reaches the bottom of the squat, she decelerates to a stop.
The overall unbalanced force must be upwards. The upwards
contact force must be BIGGER than her weight. If she pauses here,
the upward contact force will BALANCE her weight again. As she
rises, she accelerates upwards, so upward contact force is GREATER.
As she decelerates to a stop again, the upward contact force must
be LESS.
2) When we walk, we push back against the earth. According to
Newton’s third law of motion, the earth pushes us with the same
force in the opposite direction. If we remove friction, then we
reduce our ability to push backwards and then be pushed
forward.
3) The gun forces the bullet forwards so the bullet forces the gun
backwards. The mass of the gun is 250 times greater than the
bullet, so the acceleration is 250 times less.
5 × 106ms-2
a=
= 2 × 104ms-2
250
Forces acting on man accelerating upwards
4)
Wp Re
Force of the ball
acting on the bat
Try this for yourself on a set of scales. You need to explain why the
needle wobbles as you squat and rise.
Force of the bat
acting on the ball
5) A rocket engine produces exhaust gases which are forced out at
a high velocity. The rocket forces the exhaust gases backwards
and the exhaust gases force the rocket forwards.
Questions
1) Explain Newton’s third law of motion in your own words.
6) The two force pairs acting on an object resting on the ground
are weight and contact force. Objects with mass attract each
other by gravity, causing weight. The weight of the object caused
by the earth is exactly equal and opposite to the weight of the
earth caused by the object. Contact forces occur because the
outer electrons in the atoms of the object and the ground repel
each other via electrostatic repulsion.
2) Use Newton’s third law of motion to explain why it is difficult to
walk on a slippery surface.
3) Explain and calculate the acceleration of a 5kg rifle when a 20g
bullet is fired with an acceleration of 5 × 106ms-2.
4) Use a vector diagram to show the forces involved in striking a
cricket ball with a bat.
7) Let’s say the scales read 50kg (really, they’re measuring 500N
weight but the scale is written in kg). As you accelerate
downwards, the upward contact force is reduced. The scales
would dip below 50kg (although your mass and weight ISN’T
CHANGING!). Then as you decelerate to a stop, the upward
contact force is greater; the pointer would increase above 50kg.
When paused, the pointer would be at 50kg, as the upward
contact force and your weight balance. As you accelerate
upwards, the upward contact force is greater and the pointer
goes up. Decelerating to a finish causes the upward contact
force to decrease and the scales would go below 50 kg. When
stopped, the pointer reads 50kg again as your weight is balanced
by the upward contact force.
5) In your own words, explain how a rocket moves.
6) Explain the two forces pairs acting on an object resting on the
ground.
7) Describe and explain how the pointer on a set of bathroom scales
would change if you squatted and then stood.
Acknowledgements:
This Physics Factsheet was researched and written by Jermey Carter
The Curriculum Press, Bank House, 105 King Street, Wellington, Shropshire, TF1 1NU
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ISSN 1351-5136
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