Forces and motion 2:
The link between force
and motion
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The link between force and motion
The questions in this set probe pupils’ understanding of the relationship between
forces and motion. All the questions deal with motion in a straight line only.
The key ideas tested are:
• if an object is speeding up, there is a resultant force in the direction it is going;
• if an object is slowing down, there is a resultant force in the direction opposite to
its motion;
• if an object is at rest, the resultant force on it is zero;
• if an object is travelling at a steady speed, the resultant force on it is zero.
In the questions, the term ‘total force’ is used rather than ‘resultant force’. The former
is the term used in National Curriculum tests and GCSE papers and is more likely to
be familiar to pupils.
The statements above go from the observed motion to a conclusion about the resultant
(or total) force. Pupils should also be able to reason in the other direction, from the
force to a conclusion about the motion:
• if the total force on an object is zero, the object is either at rest or travelling at a
steady speed;
• if the total force on an object is not zero, it will experience a change of motion in
the direction of the total force (i.e. if the total force is in the direction in which it is
already moving, it will speed up; if the total force is in the direction opposite to its
motion, it will slow down).
These ideas relate directly to National Curriculum Key Stage 3, statement Sc4/2c.
They also relate very directly to the ideas covered in QCA Scheme of work Unit 9K,
Speeding up. None of the questions in this set uses the terms ‘velocity’ or
‘acceleration’, which are first introduced in the National Curriculum at Key Stage 4
(in statements Sc4/2c-e).
Questions 1-8
Six of these questions are about the motion of a car, subject to two main forces, a
driving force and a counter force. Q1-3 ask about the relative sizes of these, and about
the direction of the total force, when a car is speeding up, going at a steady speed, and
slowing down. Pupils are likely to find the speeding up case the easiest; most will
think the driving force is larger. Q2 is a more difficult case, and many are likely to
choose the answer that the driving force is bigger (either a lot or a little) than the
counter force. In the slowing down case (Q3), some may again think the total force
still has to be forwards, as that is the direction in which the car is moving. Q4-5
present the same situations in different combinations: Q4 asks about the sizes of
driving force and counter force in each situation in turn (speeding up, steady speed,
slowing down), whilst Q5 asks about the total force. Q6 is a repeat of Q2, but now
using the context of cycling. Questions similar to Q1 and Q3 for the cycling context
are not included, but would be easy to write. Q7 deals with a different example of
steady motion – pushing a box against a friction force. The ideas involved are again
the same as in Q2 and Q6. Finally Q8 returns to the context of the car, but now asks
pupils to reason in the other direction – from information about the relative size of the
forces to a conclusion about the motion.
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Note:
Several of these questions ask about the sizes of driving force and counter force and
about the total force acting. We might expect pupils’ answers to these to be
consistent, even where they are incorrect. If they are not, this might indicate a
misunderstanding of what is meant by ‘total force’, which should be followed up.
Question 9
This five-part question is about the motion of a spacecraft. In this context, there is no
friction or air resistance, which simplifies matters. On the other hand, we have no
first-hand experience of the situation, on which to base predictions. Parts (a)-(c) give
information on the motion and ask about the forces needed to produce it; parts (d)-(e)
give information about the forces and ask about the motion that will result. The
common misconception here is that a force in the direction of motion is needed to
maintain steady motion – with a larger force causing a larger steady speed. In this
way of thinking, force is associated with speed, rather than with change of speed
(acceleration).
Questions 10-13
These probe understanding of a situation that many pupils find difficult to interpret –
an object that has been set in motion and is now slowing down.
Q10-12 look in different ways at the motion of a football that has been kicked. Q10
helps to identify the forces pupils think are acting here – with many preferring to
indicate a force in the direction of motion instead of (or as well as) one in the opposite
direction. Q11 checks first on how pupils think the ball is actually moving. It then
focuses on the horizontal forces only, offering a smaller number of options than Q10.
Q12 also probes understanding of the motion itself, before going on to look at how
this might be explained. Q23 (see below) also deals with this context.
Q13 is very similar to Q11, probing understanding of the same ideas in a different
context. In both of these questions, it is important to check that pupils’ answers to
parts (b) and (c) are consistent – and to explore this further if they are not.
Questions 14-17
Q14-17 deal with vertical motion – a ball thrown vertically upwards. Q14 asks about
the forces involved when the ball is on the way up. This situation is similar to those
probed in Q11 and Q13. Many pupils are likely to include an upwards force ‘of the
throw’. Again, it is important to check that pupils’ answers to parts (b) and (d) are
consistent – and to explore this further if they are not. Compared with Q14, pupils are
likely to find Q16 easier – as the total force now is in the direction of motion. For this
reason, this question is not so good for diagnosing understanding/misunderstanding.
The hardest situation for many pupils to interpret correctly is the instant when the ball
is at the highest point of its motion. This is explored in Q15. If pupils concentrate on
the interactions that are giving rise to the forces involved, they are more likely to get
parts (b) and (d) right – there must still be a gravity force on the ball. But if they
focus too strongly on the motion, they may be distracted by the fact that the ball has
zero speed at this instant. There is, in fact, no finite period of time when its speed is
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zero. The ball can be said to have zero speed at this instant, but it does not have zero
speed for an instant (or for any finite period of time).
Q17 looks at the total force in these three situations again. It can be useful as a check,
to see if pupils can deal with all three cases in quick succession. However, compared
to Q14-16, it does not give as much insight into pupils’ thinking.
Questions 18-19
The key idea tested by these questions is that, when external forces are removed, an
object travels in a straight line in the direction it was going at the instant the forces
became zero. Many pupils have an intuition that objects in situations like these will
continue to move in a curved path, or move directly away from the centre.
Questions 20-23
Many of the questions in this set could be used as small-group tasks, but this group of
four is specifically designed to be used in this way. One suggestion is to give each
pupil a question sheet and allow them 5-10 minutes to write their own individual
answers. Then put pupils into groups of three, and give each triad another blank copy
of the question, perhaps enlarged to A3 size as a mini-poster. Encourage each group
to discuss their answers and write the group’s agreed ‘best answer’ on the new sheet.
This might take 10-15 minutes. It is important that every member of the group is
prepared to explain and justify this group answer. Then the groups’ answers can be
pinned up on the wall, so everyone can see the whole set – and the whole class can
discuss what the answers to the question should be. In this way, pupils may come to a
better understanding of the ideas involved here, and of ways of representing them.
These questions involve ideas that are also probed by questions in the set, Forces 1:
Identifying forces. They could be useful for reinforcing these ideas, as well as probing
understanding of the relationship between forces and motion. Q21 and 22 are quite
demanding, in that they ask about situations where the size of one force is changing.
Q23 probes the same ideas as Q10-12 earlier in the pack.
Questions 24-25
These two concept cartoons deal with these ideas. They could be used as posters that
pupils might discuss informally while this topic is being taught. Or they could be used
as individual or small-group activities, using the response sheets provided with each to
make pupils think about their response to the comments of the cartoon characters.
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1
We can think of the forces acting on a car when it is moving as:
• the driving force caused by the engine
• the counter force caused by air resistance
and friction
(a)
A driver has just left a 30 mph zone and is speeding up. Which of the
following best describes the size of the driving force and counter force,
while the car is speeding up?
Tick ONE box ( )
The driving force is bigger
than the counter force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(b)
The total force on the car is the sum of all the forces acting on it.
Which of the following best describes the total force acting on the car while it is
is speeding up?
Tick ONE box ( )
The total force is forwards.
The total force is zero.
The total force is backwards.
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2
We can think of the forces acting on a car when it is moving as:
• the driving force caused by the engine
• the counter force caused by air resistance
and friction
(a)
This car is travelling along a level road at a steady speed.
Which of the following best describes the size of the driving force and
counter force, while the car is travelling at a steady speed?
Tick ONE box ( )
The driving force is a lot
bigger than the counter
force.
The driving force is a little bit
bigger than the counter
force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(b)
The total force on the car is the sum of all the forces acting on it.
Which of the following best describes the total force acting on the car while it is
travelling along a level road at a steady speed?
Tick ONE box ( )
The total force is quite a
large force forwards.
The total force is a small
force forwards.
The total force is zero.
The total force is backwards.
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3
We can think of the forces acting on a car when it is moving as:
• the driving force caused by the engine
• the counter force caused by air resistance and
friction
(a)
A driver is approaching a village where there is a 30 mph speed limit.
She is slowing down from 60 mph to 30 mph, to go through the village.
Which of the following best describes the size of the driving force and
counter force, while the car is slowing down?
Tick ONE box ( )
The driving force is bigger
than the counter force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(b)
The total force acting on the car is the sum of the driving force and the counter
force.
Which of the following best describes the total force acting on the car while it is
slowing down?
Tick ONE box ( )
The total force is forwards.
The total force is zero.
The total force is backwards.
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4
We can think of the forces acting on a car when it is moving as:
• the driving force caused by the engine
• the counter force caused by air resistance
and friction
(a)
A driver has just left a 30 mph zone and is speeding up.
Which of the following best describes the size of the driving force and
counter force, while the car is speeding up?
Tick ONE box ( )
The driving force is bigger
than the counter force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(b)
The car is travelling along a level road at a steady speed.
Which of the following best describes the size of the driving force and
counter force, while the car is travelling at a steady speed?
Tick ONE box ( )
The driving force is a lot
bigger than the counter
force.
The driving force is a little bit
bigger than the counter
force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(c)
The driver is now approaching a village where there is a 30 mph speed
limit. She is slowing down from 60 mph to 30 mph, to go through the
village.
Which of the following best describes the size of the driving force and
counter force, while the car is slowing down?
Tick ONE box ( )
The driving force is bigger
than the counter force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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5
We can think of the forces acting on a car when it is moving as:
• the driving force caused by the engine
• the counter force caused by air resistance
and friction
The total force on the car is the sum of these two forces.
(a)
A driver has just left a 30 mph zone and is speeding up. Which of the
following best describes the total force acting on the car while it is
speeding up?
Tick ONE box ( )
The total force is forwards.
The total force is zero.
The total force is backwards.
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(b)
The car is travelling along a level road at a steady speed.
Which of the following best describes the total force acting on the car while it is
travelling at a steady speed?
Tick ONE box ( )
The total force is forwards.
The total force is zero.
The total force is backwards.
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(c)
The driver is now approaching a village where there is a 30 mph speed
limit. She is slowing down from 60 mph to 30 mph, to go through the
village.
Which of the following best describes the total force on the car, while it
is slowing down?
Tick ONE box ( )
The total force is forwards.
The total force is zero.
The total force is backwards.
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6
A cyclist is riding along
a level road at a steady speed.
We can think of the forces acting
on the bicycle as:
• a driving force caused by the cyclist pedalling
• a counter force caused by air resistance and friction.
(a)
The bicycle is travelling at a steady speed. Which of the following best
describes the size of these two forces?
Tick ONE box ( )
The driving force is a lot
bigger than the counter
force.
The driving force is a little bit
bigger than the counter
force.
The driving force is exactly
the same size as the counter
force.
The driving force is smaller
than the counter force.
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(b)
What is the total force acting on the bicycle, while it is travelling at a steady
speed?
Tick ONE box ( )
The total force is quite a
large force forwards.
The total force is a small
force forwards.
The total force is zero.
The total force is backwards.
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box moving along at steady speed
Bilal is pushing a heavy box
across the floor.
The box is moving along
at a steady speed.
(a)
Which of the following best describes the horizontal forces acting on the
box while it is moving along at a steady speed?
Tick ONE box ( )
The only force acting on the
box is Bilal’s push.
The only force acting on the
box is the friction force from
the floor.
There are two forces: Bilal’s
push and friction. Bilal’s
push is bigger.
There are two forces: Bilal’s
push and friction. They are
the same size.
There are two forces: Bilal’s
push and friction. The friction
force is bigger.
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(b)
The total force on the box is the sum of all the forces acting on it.
Which of the following best describes the total force on the box while it is
moving along at a steady speed?
Tick ONE box ( )
The total force acting on the
box is towards the right.
The total force acting on the
box is zero.
The total force acting on the
box is towards the left.
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8
A car is travelling along a level road. We can think of the forces acting on the
car as:
• a driving force caused by the engine
• a counter force caused by air resistance and friction
counter force
(a)
driving force
At one stage in the car’s motion, the driving force is bigger than the
counter force. How is the car moving?
Tick ONE box ( )
The car is getting faster. Its speed is increasing.
The car is travelling at a steady speed.
The car is getting slower. Its speed is decreasing.
(b)
At another stage in the car’s motion, the driving force is equal to the
counter force. How is the car moving now?
Tick ONE box ( )
The car is getting faster. Its speed is increasing.
The car is travelling at a steady speed.
The car is getting slower. Its speed is decreasing.
The car is stopped.
(c)
At another stage in the car’s motion, the counter force is bigger than
the driving force. How is the car moving now?
Tick ONE box ( )
The car is getting faster. Its speed is increasing.
The car is travelling at a steady speed.
The car is getting slower. Its speed is decreasing.
The car has turned round and is going in the other direction.
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9
A spacecraft is drifting through space. It is very far away from all other
objects, so there are no gravity forces acting on it. There is no air in space, so
there is no friction or air resistance. The spacecraft is moving in a straight line
at a steady speed.
moving at
steady speed
The captain of the spacecraft can exert a force on the spacecraft by firing the
rockets.
(a) What force must be exerted on the spacecraft to keep it moving in this
direction at a steady speed?
Tick ONE box ( )
No force is needed.
A small steady force towards the right.
A large steady force towards the right.
(b) The captain of the spacecraft wants to make it move in the same direction,
but with its speed getting steadily greater (a constant acceleration).
What force must be exerted on the spacecraft to make this happen?
Tick ONE box ( )
No force is needed.
A steady force towards the right.
A gradually increasing force towards the right.
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(c) Later, the captain of the spacecraft wants to make it slow down.
What force must be exerted on the spacecraft to make this happen?
Tick ONE box ( )
No force is needed. The spacecraft will do this if he switches off the
rockets and just waits.
A force to the left, opposite to its motion, until the spacecraft has
stopped.
(d) At one point during the spacecraft’s journey, it is travelling at a steady
speed. The captain fires its rockets for a short time. As a result, a steady
force is exerted on the spacecraft, towards the right.
How will the spacecraft move while this force is acting?
Tick ONE box ( )
It will continue moving at the same speed.
It will move at a higher steady speed.
Its speed will keep increasing, while the rockets are firing.
(e) After a few minutes, the captain switches the rockets off again.
How will the spacecraft move now?
Tick ONE box ( )
It will immediately slow down again, to its original speed before the
rockets were fired.
It will gradually slow down again, until it is back at its original
speed before the rockets were fired.
It will continue travelling at the speed it had reached when the
rockets were switched off.
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10
Desmond kicks a football across a level pitch. It rolls to the point X and then
stops.
Think about the football when it is in the middle and still moving.
stopped
moving
X
(a) The pictures below show the forces acting on the football while it is
moving. The arrows just indicate the direction of the forces, not their size.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Which picture best shows the forces acting on the moving football?
Write one letter in the box.
(b) In this box, draw a
larger copy of the
diagram you think is
correct, and label the
forces to show what
each one is.
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Desmond kicks a football across a level pitch. It rolls to the point B and then
stops.
moving
A
(a)
stopped
B
How would you describe the motion of the ball at the point A?
Tick ONE box ( )
It is getting faster.
It is moving at a steady speed.
It is slowing down.
(b)
Which of the following diagrams best shows the horizontal forces on the
ball at point A? (The vertical forces are not shown.)
The length of the arrow indicates the size of each force.
Tick ONE box ( )
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(c)
Which of the following best describes the total force acting on the ball at
A?
Tick ONE box ( )
The total force on the ball is forwards, towards B.
The total force on the ball is zero.
The total force on the ball is backwards, towards Desmond.
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Desmond kicks a football across a level pitch. It rolls to the point X and then
stops.
stopped
X
A
B
C
(a) Where is the football moving fastest?
Tick ONE box ( )
At A, just after it leaves Desmond’s foot.
At B, about a quarter of the way to X.
At C, halfway to X.
(b) During what period of time does Desmond exert a force on the ball?
Tick ONE box ( )
Just while his foot is in contact with the ball.
While the ball is speeding up – until somewhere around point B.
Up to the halfway point, when the ball starts to slow down.
All the time the ball is moving.
(c) Look at each of the following statements about the ball’s motion. For each,
tick one column ( ), to show if you think the statement is true or false.
True
i
Desmond’s kick gives the ball a forward force which gradually
wears out. By the time the ball reaches X, all the force has gone.
ii
Desmond’s kick gives the ball some momentum in the forward
direction. This gradually gets less, because of friction. By the
time the ball reaches X, all its momentum has gone.
iii
Desmond’s foot exerts a force on the ball while it is in contact with
it. This starts the ball moving. After that, friction and air
resistance are the only horizontal forces on the ball.
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False
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13
A sledge slides down a slope and then on to some level snow. It travels to the
point B before it stops.
moving
stops here
B
A
(a)
How would you describe the motion of the sledge at the point A?
Tick ONE box ( )
It is getting faster.
It is moving at a steady speed.
It is slowing down.
(b)
Which of the following diagrams best shows the horizontal forces on the
sledge at point A? (The vertical forces are not shown.)
To simplify the diagrams, the sledge is just shown as a dot. The length
of the arrow indicates the size of each force.
Tick ONE box ( )
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(c)
Which of the following best describes the total force acting on the
sledge at A?
Tick ONE box ( )
The total force on the sledge is forwards,
Towards B.
The total force on the sledge is zero.
The total force on the sledge is backwards,
Towards the slope.
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14
highest point
Kim throws a tennis ball straight up
into the air. It goes up and comes
back down into her hand.
A
ball going up
Think about the moment when
the ball is at A, on the way up
to its highest point.
(a)
How would you describe the motion of the ball at this instant?
Tick ONE box ( )
It is getting faster.
It is moving at a steady speed.
It is slowing down.
(b)
Which of the following diagrams best shows the vertical forces on the
ball when it is at point A on the way up?
(The length of the arrow indicates the size of each force.)
Tick ONE box ( )
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(c)
Which of the following best describes the forces acting on the ball when
it is at point A on the way up?
Tick ONE box ( )
The only force acting on the ball is the upward force of the throw.
The only force acting on the ball is the downward force of gravity.
The forces acting on the ball are the force of gravity, and the air
resistance.
The forces acting on the ball are the force of gravity, the air
resistance, and the force of the throw.
There are no forces acting on the ball.
(d)
highest point
Which of the following diagrams
best shows the total force acting
on the ball when it is at point A
on the way up?
A
ball going up
Tick ONE box ( )
total force
no force
total force
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15
highest point
Kim throws a tennis ball straight up
into the air. It goes up and comes
back down into her hand.
Think about the moment when
the ball is at its highest point.
(a)
How would you describe the motion of the ball at this instant?
Tick ONE box ( )
It is getting faster.
It is moving at a steady speed.
It is slowing down.
Its speed is zero.
(b)
Which of the following diagrams best shows the vertical forces on the
ball at the instant when it is at its highest point?
(The length of the arrow indicates the size of each force.)
Tick ONE box ( )
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(c)
Which of the following best describes the forces acting on the ball at the
instant when it is at its highest point?
Tick ONE box ( )
The only force acting on the ball is the upward force of the throw.
The only force acting on the ball is the downward force of gravity.
The forces acting on the ball are the force of gravity, and the air
resistance.
The forces acting on the ball are the force of gravity, the air
resistance, and the force of the throw.
There are no forces acting on the ball.
(d)
highest point
Which of the following diagrams
best shows the total force acting
on the ball when it is at its
highest point?
Tick ONE box ( )
total force
no force
total force
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16
highest point
Kim throws a tennis ball straight up
into the air. It goes up and comes
back down into her hand.
A
ball coming down
Think about the moment when
the ball is at A, on the way down
again from its highest point.
(a)
How would you describe the motion of the ball at this instant?
Tick ONE box ( )
It is getting faster.
It is moving at a steady speed.
It is slowing down.
(b)
Which of the following diagrams best shows the vertical forces on the
ball when it is at point A on the way down?
(The length of the arrow indicates the size of each force.)
Tick ONE box ( )
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(c)
Which of the following best describes the forces acting on the ball when
it is at point A on the way down?
Tick ONE box ( )
The only force acting on the ball is the upward force of the throw.
The only force acting on the ball is the downward force of gravity.
The forces acting on the ball are the force of gravity, and the air
resistance.
The forces acting on the ball are the force of gravity, the air
resistance, and the force of the throw.
There are no forces acting on the ball.
(d)
highest point
Which of the following diagrams
best shows the total force acting
on the ball when it is at point A
on the way down?
A
ball coming down
Tick ONE box ( )
total force
no force
total force
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17
Kim throws a tennis ball straight up into the air for a short distance and
catches it when it comes down again.
(a) In the diagrams below, the ball is on the way up. Which diagram best
shows the total force on the ball? Put a circle round one letter (A, B, or
C) to show your answer.
total force
zero
A
B
C
(b) In the diagrams below, the ball is right at the top of its flight. Which
diagram best shows the total force on the ball? Put a circle round one
letter (D, E or F) to show your answer.
total force
zero
D
E
F
(c) In the diagrams below, the ball is on the way down. Which diagram best
shows the total force on the ball? Put a circle round one letter (G, H or I)
to show your answer.
total force
zero
G
114
H
I
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A curved tube is laid on a level table top. In the diagram below, you are
looking down on this from above.
A marble is fired into the tube at point P. The force of friction is so small that it
can be ignored. The marble travels round the tube at a steady speed.
P
O
R
Q
Which path in the diagram below best shows how the marble would move
after it comes out of the tube and rolls across the table top?
Write one letter (A, B, C, D or E) in the box:
B
C
A
D
O
E
R
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19
A heavy ball is tied to a rope. An athlete swings the ball round in a circle, as
shown in the diagram. This is looking down on the athlete from above.
P
When the ball is at the point P in the diagram, the rope suddenly breaks near
the ball.
Which path in the diagram below best shows how the ball would move after
the rope breaks?
Write one letter (A, B, C, D or E) in the box:
B
A
C
D
P
E
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Forces on a stone
Each of these diagrams shows a stone,
in different situations.
To each diagram, add arrows to show
all the forces acting on the stone
when it is:
(a) falling through the air,
(b) at rest, hanging from a string,
(c) at rest, sitting on the floor,
(d) sliding along the floor, after a push
that started it moving.
Represent forces:
• by drawing arrows
to show the direction
of each force,
• with the length of the arrow
representing the size of the force.
Label each force to indicate what it is.
(a) falling through the air.
(b) at rest, hanging from the ceiling.
(c) at rest, sitting on the floor.
(d) sliding along the floor, after a
push that started it moving.
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21
Forces on a tin of beans
A tin of beans is dropped from about
10 cm above a foam cushion.
On the diagrams below, draw all the
forces acting on the tin:
(a) just before it touches the cushion,
(b) when it has touched the cushion
and is moving down into it,
(c) when it has come to rest on the
cushion,
(d) when it is lying on a table.
Represent forces:
• by drawing arrows
to show the direction
of each force,
• with the length of the arrow
representing the size of the force.
Label each force to indicate what it is.
(a) just before it touches the cushion.
(b) moving down into the cushion.
(c) finally at rest on the cushion.
(d) at rest on a table.
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22
Box on a spring
A box is attached to a spring. The top
end of the spring is fixed to the ceiling.
Represent forces:
• by drawing arrows
On the diagrams below, draw all the
to show the direction
forces acting on the box:
of each force,
(a) just after the box has been
released,
• with the length of the arrow
(b) while the box is moving
representing the size of the force.
downwards,
(c) when the box has stopped moving. Label each force to indicate what it is.
Mark all the forces on the box
(a) the box has just been released. The
spring has not yet begun to stretch.
(b) the box is moving downwards, and the
spring is stretching.
(c) the box has stopped moving. The spring
is stretched.
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23
Kicking a football
A footballer kicks a football across a level pitch. It rolls to the point X and then
stops.
moving
stopped
Y
X
On the diagrams below, draw all the
forces acting on the football:
(a) when it is at the point Y and still
moving,
(b) when it is at the point X and has
stopped.
Represent forces:
• by drawing arrows
to show the direction
of each force,
• with the length of the arrow
representing the size of the force.
Label each force to indicate what it is.
(a) football at point Y, still moving.
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(b) football at point X, stopped.
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24
Cycling along
Tom is cycling along a level road. He is riding along at a steady
speed. What are the forces involved here, and how big are they?
When Tom pedals, he
exerts a driving force. This
has to be bigger than the
friction and air resistance
forces to keep the bike
moving.
If the speed is steady,
the driving force must
be exactly equal to the
friction and air
resistance forces.
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The total force
must be forwards,
or the bike would
stop.
If the driving force
was bigger than
friction and air
resistance, the bike
would speed up.
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Cycling along
What do you think?
Tick a box in each row to show if you agree or disagree with each
of the pupils:
Agree
Andy
Beth
Disagree
Not sure
When Tom pedals, he exerts
a driving force. This has to
be bigger than the friction
and air resistance forces to
keep the bike moving.
The total force must be
forwards, or the bike would
stop.
Carla
If the speed is steady, the
driving force must be exactly
equal to the friction and air
resistance forces.
Derek
If the driving force was bigger
than friction and air
resistance, the bike would
speed up.
Please explain your answer in the space below:
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25
Freewheeling
Tom is cycling along a level road. He stops pedalling and
freewheels. He gradually slows down until he stops. How would
you explain this?
For anything to move,
there has to be a force in
the direction it is going.
It is the force of gravity
that slows him down
and eventually makes
him stop.
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He stops because
he runs out of
force.
The friction force
changes his motion,
and makes his speed
get less.
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Freewheeling
What do you think?
Tick a box in each row to show if you agree or disagree with each
of the pupils:
Agree
Anya
For anything to move, there
has to be a force in the
direction it is going.
Bill
He stops because he runs out
of force.
Cara
It is the force of gravity that
slows him down and
eventually makes him stop.
Dave
The friction force changes his
motion, and makes his speed
get less.
Disagree
Not sure
Please explain your answer in the space below:
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Answers and discussion
The link between force and motion
In the discussion below, answer options are referred to by number (1, 2, 3 …), in the
order in which they appear in the question.
1
(a)
(b)
1
1
2
(a) 3
(b) 3
An answer pattern showing a total force in the forward direction (either 1 or 2 for
both (a) and (b)) suggests that the student associates force with motion, rather
than with change of motion.
3
(a) 3
(b) 3
A student choosing option 1 for part (b) may be associating force with motion,
rather than with change of motion.
4
(a)
(b)
(c)
1
3
3
5
(a)
(b)
(c)
1
2
3
Note: For Questions 4 and 5, the comments above on Q2 and Q3 again apply.
6
(a) 3
(b) 3
An answer pattern showing a total force in the forward direction (either 1 or 2 for
both (a) and (b)) suggests that the student associates force with motion, rather
than with change of motion.
7
(a) 4
(b) 2
An answer pattern showing a total force in the forward direction (1/1 or 3/1)
suggests that the student associates force with motion, rather than with change of
motion.
8
(a) 1
(b) 2
(c) 3
Answer pattern 2/3/4 might suggest that the student associates force with motion,
rather than with change of motion.
9
(a)
(b)
1
2
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(c) 2
(d) 3
(e) 3
Answer pattern (a) 2 or 3; (b) 3; (c) 1; (d) 2; (e) 1 or 2 might suggest that the
student associates force with motion, rather than with change of motion.
10 (a) M
Common distractors here are likely to be O, J and A. All of these suggest that the
student feels there has to be a force in the direction of motion. This again
suggests that the student associates force with motion, rather than with change of
motion.
(b) The downward force should be labelled ‘force exerted by the Earth
(gravity)’, or ‘gravity force’, or perhaps ‘weight’. The upward force is ‘force
exerted by the ground (reaction)’ or ‘reaction force’, or ‘normal reaction’. The
force towards the left is ‘force exerted by the ground and the air (friction and air
resistance)’ or simply ‘friction’ and ‘air resistance’. In this situation, the air
resistance force will be small.
11 (a) 3
(b) 5
(c) 3
The purpose of part (a) here is to find out how students think the ball is moving
after the kick. Some may believe it continues to speed up for the first part of its
motion. If so, their answers to the remaining parts (and to Q10) might then be
consistent with their (incorrect) understanding of the motion. Answers to parts
(b) and (c) need to be interpreted in the light of the answer given to (a). Some
students who realise the ball is slowing down may still choose: (b) 1 or 2 or 3 or 4
and (c) 1, suggesting that they associate force with motion, rather than with
change of motion.
12 (a) 1
(b) 1
(c) (i) false; (ii) true; (iii) true.
This question may help to show if a student thinks of a force as arising only
during an interaction (in this case, the kick). Students who think that a moving
object ‘has’, or ‘contains’, force may choose incorrect options here.
13 (a) 3
(b) 5
(c) 3
This question involves exactly similar ideas and reasoning to Q11, so the same
comments apply.
14 (a) 3
(b) 5
(c) 3
(d) 3
Key ideas in this question (and in Q15 and 16) are:
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-
Gravity is an interaction between two masses, in this case the Earth and the
ball. It acts at a distance. So there is a force of gravity acting on the ball all
the time.
- There is an interaction between the thrower’s hand and the ball only while
they are in contact.
- At the instant when the ball is at its highest point, its speed is zero. So there
is no air resistance at this instant, as this is caused by motion through the air.
Parts (a), (b) and (d) of this question involve similar ideas and reasoning to Q11
and Q13, so the same comments apply. Part (c) may help you to interpret the
thinking behind students’ answers to part (b).
15 (a)
(b)
(c)
(d)
4
5
2
3
16 (a) 1
(b) 4
(c) 3
(d) 3
Students are likely to find this easier than Q14 or 15, as the total force is now in
the direction of motion.
17 (a) A
(b) D
(c) G
A common answer pattern here is B, F, G. This suggests that the student
associates force with motion, rather than with change of motion. There are two
ways to work out the right answer here. One is to think about the interactions
involved: after the ball leaves the thrower’s hand, the only interactions involved
are gravity and air resistance (which is a lot smaller). The force of gravity on the
ball is always downwards; the force of air resistance on the ball is always in the
opposite direction to its motion. The resultant (or total) force is therefore always
downwards. For parts (a) and (c), you can reach the same conclusion by thinking
about the change of motion of the ball. On the way up (part (a)), the speed of the
ball is getting less. This requires a resultant force in the direction opposite to its
motion. On the way down (part (c)), the speed of the ball is increasing. So the
resultant force acting on it is in its direction of motion. It is not so easy to explain
from the motion why the resultant force is downwards in part (b). It is easier to
deduce this from thinking about the interactions involved. Gravity is not
suddenly switched off at this instant – so the resultant force is downwards, due to
gravity.
18 C. When it leaves the tube, the only horizontal force acting on the ball is friction,
which is in the direction exactly opposite to its motion. It moves in a straight
line, in the direction it was going at the moment the sideways forces stopped
acting.
19 C. The reason is similar to that for Q18.
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20 (a)
(b)
force exerted
by the string
force exerted by the
air (air resistance)
force exerted by
the Earth (gravity)
force exerted by
the Earth (gravity)
(c)
(d)
force exerted by the
floor (reaction)
force exerted by
the Earth gravity)
force exerted by the
floor (reaction)
force exerted
by the floor
(friction)
force exerted by
the Earth (gravity)
Note that in (b) and (c) the two forces are equal in size. In (a), the upward force
is smaller than the downward one. In (d), the two vertical forces are equal. The
friction force is likely to be smaller than the gravity force, but there is no way of
knowing its relative size. It will depend on the materials the stone and floor are
made of. The crucial thing in (d) is to mark a force in the direction opposite to
the motion, not in the direction of motion. In (d), students who indicate a force in
the direction the stone is moving may associate force with motion rather than
with change of motion. The two vertical forces in (c) and (d) should really be in
line. They are drawn slightly apart so that their lengths are clearer.
21
Ignoring air resistance, which will be very much smaller than the gravity force in
this instance (because the distance of the fall is small and so the speed of the can
is low), the answers are:
(a)
(b)
force exerted by
the cushion
(reaction)
force exerted
by the Earth
(gravity)
force exerted
by the Earth
(gravity)
(c)
force exerted by the
cushion (reaction)
force exerted
by the Earth
(gravity)
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(d)
force exerted by the
table (reaction)
force exerted
by the Earth
(gravity)
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The two forces in (b), (c) and (d) should really be in line. They are drawn slightly
apart so that their lengths are clearer. In (c) and (d), the two forces are equal in
size. In (b) the upwards force is smaller. The force exerted by the cushion
depends on how much it is compressed.
If air resistance is included, there would be a second, small upward force in (a)
and (b). It would be much smaller than the downward gravity force.
22
(a)
(b)
force exerted
by the Earth
(gravity)
(c)
force exerted
by the spring
force exerted
by the spring
force exerted
by the Earth
(gravity)
force exerted
by the Earth
(gravity)
In part (c), the two forces should be equal. In (b), the upwards force is smaller
than the gravity force. The size of the spring force depends on its extension.
23
(a)
force exerted by
the ground
(reaction)
force exerted by
the ground
(friction)
force exerted
by the Earth
(gravity)
(b)
force exerted by
the ground
(reaction)
force exerted
by the Earth
(gravity)
The two vertical forces are equal in both diagrams. The friction force is likely to
be smaller than this, but it is not possible to say exactly how big it will be,
relative to the gravity (or reaction) forces. It will depend on the properties of the
ball and the ground. The two vertical forces in (a) and (b) should really be in
line. They are drawn slightly apart so that their lengths are clearer.
24 Andy’s comment is incorrect. When the bike is moving at a steady speed, the
total force acting on it is zero. So the driving force only has to be equal to the
friction and air resistance forces. Beth’s comment is incorrect. If the total force
on an object is zero, its motion will not change. So if it is moving, it will keep
moving at the same speed and in the same direction. Carla’s and Derek’s
comments are both correct.
25 Anya’s comment is incorrect, though this is a common misconception. Bill also
expresses a common misconception. A moving object does not ‘have force’,
which it can ‘run out of’. A force arises only when there is an interaction
between two objects. Bill would be better to say that the cyclist has momentum,
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which gets less. Cara’s comment is interesting. If she means that gravity directly
slows the cyclist down, this is incorrect. The force of gravity acts vertically
downwards and cannot affect the cyclist’s horizontal motion. Dave’s comment is
correct; it is the friction force (at the hubs and tyres), and also the air resistance,
that changes the bike’s motion. The size of this friction force, however, will
depend on the weight of the bike and the cyclist. This may be what Cara means,
but she needs to explain the connection more clearly to show that she understands
the situation.
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Acknowledgements
Some of the questions in this pack are based on probes used by science education
researchers to explore learners’ understanding of key ideas about forces and motion.
These have been modified, often quite substantially, to improve their clarity or to
make them easier to use in class. Others are new questions, written for EPSE Project
1: Using Diagnostic Assessment to Enhance Teaching and Learning in Science.
Questions which are knowingly based on previous probes are listed below, with an
indication of the original source. If precursors of any questions in this pack are not
acknowledged below, we would be grateful to have this pointed out, so that it can be
rectified in any subsequent publication.
Q10
Part (a) is based on an unpublished idea from Jon Ogborn.
Q17
Based on a question in:
Osborne, R., Schollum, B. & Hill, G. (1981). Learning in Science Project Working
Paper No. 33. University of Waikato: LISP Project.
Q18-19 Based on questions 4 and 10 in the Force Concept Inventory (FCI):
Hestenes, D., Wells, M. & Swackhamer, G. (1992). Force Concept Inventory. The
Physics Teacher, 30, 141-159.
Q20-23 The format of these questions is based on an idea developed by Pam Mulhall and
Brian McKittrick at Monash University. They refer to items of this format as
Conceptual Understanding Procedures (CUPs). A selection can be downloaded
from URL: http://www.education.monash.edu.au/projects/physics/
Q21 is very slightly modified from one of their examples; the others here are new
items using the same format.
Q20
This question was influenced by:
Court, J.E. (1993). Free-body diagrams. The Physics Teacher, 31, 104-108.
Court, J.E. (1999). Free-body diagrams revisited - I. The Physics Teacher, 37, 427-433.
Q24-25 These are new items, but are based on the Concept Cartoon format developed by
Stuart Naylor and Brenda Keogh:
Naylor, S. & Keogh, B. (2000). Concept Cartoons in Science Education. Sandbach:
Millgate House Publishers.
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