Forces and motion 5: Forces in pairs: Newton’s Third La · Forces in pairs: Newton’s Third Law The questions in this set probe pupils’ understanding of the fact that forces

Forces and motion 5: Forces in pairs: Newton’s Third Law

© University of York 2003 193

Forces in pairs: Newton’s Third Law The questions in this set probe pupils’ understanding of the fact that forces always come in pairs. If A pushes B, then B pushes back on A, with an equal force. This applies to both steady forces, and to short-lived forces such as those that arise in a collision or sudden impact. The forces are always equal, at every instant during an interaction, and regardless of the sizes of the objects involved, or their motion. This idea is specifically stated in a National Curriculum Statement at Key Stage 4 (Sc4/2g). However, some understanding that forces arise from interactions and always come in pairs is essential to make sense of the ideas required at Key Stage 3. There is a strong case for teaching these ideas earlier than Key Stage 4. Understanding that forces arise in pairs, each acting on a different object, is also probed by many of the questions in the set Identifying forces. The questions in this set differ in probing more thoroughly the pupils’ understanding of the sizes of the two forces that arise in an interaction. Common misunderstandings are likely to include the following: • that whilst you experience a push ‘back’ if you push an object and it doesn’t

move, there is less force back (or none at all) if it does move; • that if you push an object in a situation where there is very little friction, there is

no ‘push back’ by the object; • that the ‘passive’ partner in an interaction doesn’t exert a force; • that the sizes of the forces in a pair depend on the masses of the objects, or their

motion. Questions 1-3 These look at very similar situations – pushing a box. Pupils are most likely to recognise a push back force in Q1, where the box is not moving. If you ask more than one of these questions at the same time, you should be aware that people have a tendency to change the answer they give to a second question that seems similar to a previous one – assuming (not unreasonably) that the questioner would not have asked the second one if the situation was not different in some way. It takes confidence to give the same answer several times to a series of similar looking questions. Questions 4-7 These deal with situations that you could explore practically (with care!) in class, as a demonstration. The difference between Q4 and 5 is that in the second, the masses are unequal. Some pupils may be reluctant to say that the passive partner in Q4-5 ‘exerts’ a force; you may need to discuss what we mean by ‘exerts’ here. Indeed it may be easier to see that the rope (in Q6) exerts a force on both boys. Q7 is a variant of Q6 in which the rope is tied to the second trolley. Questions 8-10 These explore the idea of forces in pairs in the context of field forces (rather than ‘contact’ forces). The first level of understanding here is to appreciate that both

194 © University of York 2003

objects in these situations experience a force. A second level is to appreciate that the forces are of equal size, even where the objects are very different (as in Q10). Questions 11-14 These look at forces during collisions. The questions are designed to separate the issue of what forces are present, from that of their relative sizes. Questions 15-17 These return to situations involving steady forces, but have been placed here because they deal with situations more like those of Q11-14. Pupils are likely to find these difficult, particularly Q16. This is, in fact, a similar situation to that of Q2-3, so it may be useful to see how consistent pupils’ answers to questions about these quite different contexts are. Questions 18-20 Q18-20 are quite challenging questions which many pupils will find difficult. It is important to emphasise that the length of the arrows is an indication of the size of the forces. These questions are suitable for small-group and whole class discussion. One way of using them 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.


1 A large box is sitting on a level floor. Sam exerts a force forwards on the box but it does not move. Think about the force exerted by the box on Sam while he is pushing. Which of the following statements is correct? Tick ONE box ( )

While Sam is pushing, he exerts a force on the box. The box does not exert a force on Sam. While Sam is pushing, he exerts a force on the box. The box also exerts a force on Sam in the opposite, ie. ( ), direction. The force exerted on Sam by the box is smaller. While Sam is pushing, he exerts a force on the box. The box also exerts a force on Sam in the opposite, ie. ( ), direction. The two forces are the same size. While Sam is pushing, he exerts a force on the box. The box also exerts a force on Sam in the opposite, ie. ( ), direction. The force exerted on Sam by the box is bigger.

box not moving


2 A large box is sitting on a level floor. Sam exerts a force forwards on the box, and it moves at a steady speed across the floor. moving at a steady speed Think about the forces exerted by the box on Sam while he is pushing. Which of the following statements is correct? Tick ONE box ( )



3 A large box is sitting on an ice rink. Sam exerts a force forwards on the box, and it moves across the ice. The ice is very smooth. The friction force on the box is so small that it can be ignored.

moving across the ice

friction is so small it can be ignored

ice Think about the forces acting on Sam while he is pushing. Which of the following statements is correct? Tick ONE box ( )



4 Aisha and Ben are sitting on office chairs which move easily on castors. Aisha pushes with her bare feet on Ben’s knees. Ben Aisha (a) What do you think will happen? Tick ONE box ( )

Ben will move away from Aisha. Aisha will not move.

Aisha will move away from Ben. Ben will not move.

Aisha and Ben will both move away from each other.

(b) Look at the following statements about the forces acting on Ben and

Aisha. Which statement is correct? Tick ONE box ( )

Aisha exerts a force on Ben. Ben does not exert a force on Aisha.

Ben exerts a force on Aisha. Aisha does not exert a force on Ben.

Aisha exerts a force on Ben. Ben also exerts a force on Aisha. The two forces are the same size.

Aisha exerts a force on Ben. Ben also exerts a force on Aisha. The force exerted by Aisha is bigger.

Aisha exerts a force on Ben. Ben also exerts a force on Aisha. The force exerted by Ben is bigger.


5 Paolo and Alice are sitting on office chairs which move easily on castors. Paolo has a mass of 75kg and Alice has a mass of 50kg. Paolo pushes with his bare feet on Alice’s knees. Paolo Alice (a) What do you think will happen? Tick ONE box ( )

Alice will move away from Paolo. Paolo will not move.

Paolo will move away from Alice. Alice will not move.

Alice and Paolo will both move away from each other.

(b) Look at the following statements about the forces acting on Paolo and

Alice. Which statement is correct? Tick ONE box ( )

Paolo exerts a force on Alice. Alice does not exert a force on Paolo.

Alice exerts a force on Paolo. Paolo does not exert a force on Alice.

Paolo exerts a force on Alice. Alice also exerts a force on Paolo. The two forces are the same size.

Paolo exerts a force on Alice. Alice also exerts a force on Paolo. The force exerted by Paolo is bigger.

Paolo exerts a force on Alice. Alice also exerts a force on Paolo. The force exerted by Alice is bigger.


6 Bilal and Tim are sitting on two lab trolleys which move easily on castors. Both boys hold the ends of a rope. Bilal pulls on the rope; Tim just holds his end.

Tim Bilal (a) What do you think will happen? Tick ONE box ( )

Tim will move towards Bilal. Bilal will not move.

Bilal will move towards Tim. Tim will not move.

Both Bilal and Tim will start to move towards each other.

(b) Look at the following statements about the forces acting on Bilal and

Tim. Which statement is correct? Tick ONE box ( )

The rope exerts a force on Tim. The rope does not exert a force on Bilal.

The rope exerts a force on Bilal. The rope does not exert a force on Tim.

The rope exerts a force on both Tim and Bilal. The two forces are the same size.

The rope exerts a force on both Tim and Bilal. The force it exerts on Tim is bigger.

The rope exerts a force on both Tim and Bilal. The force it exerts on Bilal is bigger.


7 Kwai and Tom are sitting on two lab trolleys which move easily on castors. Kwai holds one end of the rope. The other end is tied to Tom’s trolley. Kwai pulls on the rope. Tom

Kwai (a) What do you think will happen? Tick ONE box ( )

Tom will move towards Kwai. Kwai will not move.

Kwai will move towards Tom. Tom will not move.

Both Kwai and Tom will start to move towards each other.

(b) Look at the following statements about the forces involved. Which

statement is correct? Tick ONE box ( )

The rope exerts a force on Tom’s trolley. The rope does not exert a force on Kwai.

The rope exerts a force on Kwai. The rope does not exert a force on Tom’s trolley.

The rope exerts a force on Kwai and on Tom’s trolley. The two forces are the same size.

The rope exerts a force on Kwai and on Tom’s trolley. The force it exerts on Kwai is bigger.

The rope exerts a force on Kwai and on Tom’s trolley. The force it exerts on Tom’s trolley is bigger.


8 Two magnets are placed on a flat table. Magnet A is three times as strong as magnet B. The two magnets attract each other.

A B three times as strong (a) Look at each of the following statements. For each statement, tick one

box ( ) to show if you think it is true or false. True False Magnet A exerts a force on magnet B.

Magnet B exerts a force on magnet A.

If you have ticked ‘TRUE’ for both statements, please answer part (b).

(b) How do the sizes of the two forces compare? Tick ONE box ( )

The force exerted by A on B is bigger than the force exerted by B on A. The force exerted by A on B is the same size as the force exerted by B on A. The force exerted by A on B is smaller than the force exerted by B on A.


9 A magnet and an iron nail are placed on a flat table. Iron is a magnetic substance and so it is attracted towards the magnet. (a) Look at each of the following statements. For each statement, tick one

box ( ) to show if you think it is true or false. True False The magnet exerts a force on the nail.

The nail exerts a force on the magnet.



The force exerted by the magnet on the nail is bigger than the force exerted by the nail on the magnet. The force exerted by the magnet on the nail is the same size as the force exerted by the nail on the magnet. The force exerted by the magnet on the nail is smaller than the force exerted by the nail on the magnet.


10

Earth

A spacecraft is in orbit round the Earth. spacecraft (a) Look at each of the following statements. For each statement, tick one

box ( ) to show if you think it is true or false. True False The Earth exerts a force on the spacecraft.

The spacecraft exerts a force on the Earth.



The force exerted by the Earth on the spacecraft is bigger than the force exerted by the spacecraft on the Earth. The force exerted by the Earth on the spacecraft is the same size as the force exerted by the spacecraft on the Earth. The force exerted by the Earth on the spacecraft is smaller than the force exerted by the spacecraft on the Earth.


11 A car skids on an icy road and crashes into a wall. (a) Look at each of the following statements about the crash. For each

statement, tick one box to show if you think it is true or false. True False During the collision, the car exerts a force on the wall.

During the collision, the wall exerts a force on the car.

There are no forces involved. The car is smashed because the wall gets in its way.

If you have ticked ‘TRUE’ for the first two statements above, please answer part (b).


The force exerted by the car on the wall is bigger than the force exerted by the wall on the car. The force exerted by the car on the wall is the same size as the force exerted by the wall on the car. The force exerted by the car on the wall is smaller than the force exerted by the wall on the car.


12 A car skids on an icy road and crashes into a wall. The collision knocks the wall over. (a) Look at each of the following statements about the crash. For each

statement, tick one box to show if you think it is true or false. True False During the collision, the car exerts a force on the wall.

During the collision, the wall exerts a force on the car.

There are no forces involved. The car is smashed because the wall gets in its way.



The force exerted by the car on the wall is bigger than the force exerted by the wall on the car. The force exerted by the car on the wall is the same size as the force exerted by the wall on the car. The force exerted by the car on the wall is smaller than the force exerted by the wall on the car.


13 A car skids on an icy road and crashes into a large lorry coming the other way. (a) Look at each of the following statements about the crash. For each

statement, tick one box to show if you think it is true or false. True False During the collision, the car exerts a force on the lorry.

During the collision, the lorry exerts a force on the car.

There are no forces involved. The car is smashed because it gets in the way of the lorry.



The force exerted by the car on the lorry is bigger than the force exerted by the lorry on the car. The force exerted by the car on the lorry is the same size as the force exerted by the lorry on the car. The force exerted by the car on the lorry is smaller than the force exerted by the lorry on the car. The size of the forces depends on the speed of the two vehicles. As you are not told this, you cannot say which force is bigger.


14 In an accident, a white car crashes into a red car of the same type travelling in the opposite direction. The cars have exactly the same mass. Before the collision the white car was travelling at 10 mph and the red car was travelling at 20 mph.

white red 20 mph

10 mph

(a) Look at each of the following statements about the crash. For each

statement, tick one box to show if you think it is true or false. True False During the collision, the white car exerts a force on the red car.

During the collision, the red car exerts a force on the white car.

There are no forces involved. The cars are smashed because each gets in the way of the other.



The force exerted by the white car on the red car is bigger than the force exerted by the red car on the white car. The force exerted by the white car on the red car is the same size as the force exerted by the red car on the white car. The force exerted by the white car on the red car is smaller than the force exerted by the red car on the white car.


15 A lorry breaks down on the road and is pushed back to town by a small car. In this diagram, the car has just started to push the lorry, and it is still speeding up. (a) Look at each of the following statements. For each statement, tick one

box to show if you think it is true or false. True False While the car and lorry are speeding up, the car exerts a force on the lorry.

While the car and lorry are speeding up, the lorry exerts a force on the car.

There are no forces involved. The lorry moves because it is in the way of the car.



The force exerted by the car on the lorry is bigger than the force exerted by the lorry on the car. The force exerted by the car on the lorry is the same size as the force exerted by the lorry on the car. The force exerted by the car on the lorry is smaller than the force exerted by the lorry on the car.


16 A lorry breaks down on the road and is pushed back to town by a small car. In this diagram, the car has got the lorry moving and is now pushing it along at a constant speed. (a) Look at each of the following statements. For each statement, tick one

box to show if you think it is true or false. True False While the car and lorry are moving at a constant speed, the car exerts a force on the lorry.

While the car and lorry are moving at a constant speed, the lorry exerts a force on the car.

There are no forces involved. The lorry moves because it is in the way of the car.



The force exerted by the car on the lorry is bigger than the force exerted by the lorry on the car. The force exerted by the car on the lorry is the same size as the force exerted by the lorry on the car. The force exerted by the car on the lorry is smaller than the force exerted by the lorry on the car.


17 A construction worker pushes two boxes along the floor. He is able to move them slowly along at a steady speed. moving at a steady speed

B A

(a) Look at each of the following statements. For each statement, tick one

box to show if you think it is true or false. True False While the construction worker is pushing, Box A exerts a force on Box B.

While the construction worker is pushing, Box B exerts a force on Box A.



The force exerted by Box A on Box B is bigger than the force exerted by Box B on Box A. The force exerted by Box A on Box B is the same size as the force exerted by Box B on Box A. The force exerted by Box A on Box B is smaller than the force exerted by Box B on Box A.


A B 18 Two wrestlers are pushing each other. Wrestler A is winning. He is pushing wrestler B back. In the boxes below, you are asked to mark the forces acting on each wrestler.

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) On this diagram, mark all the horizontal forces acting on wrestler A. (Ignore any vertical forces.) (b) On this diagram, mark all the horizontal forces acting on wrestler B. (Ignore any vertical forces.) (c) On this diagram, mark all the horizontal forces acting on the ground. (Ignore any vertical forces.)


19 A driver is pushing her car which has broken down. The car is moving along slowly. In the boxes below, you are asked to mark the forces acting on each object involved in this situation.



(a) On this diagram, mark all the horizontal forces acting on the car. (Ignore any vertical forces.) (b) On this diagram, mark all the horizontal forces acting on the driver. (Ignore any vertical forces.) (c) On this diagram, mark all the horizontal forces acting on the ground. (Ignore any vertical forces.)


Paolo Pete 20 Paolo and Pete are playing tug-of-war. Paolo is winning. In the boxes below, you are asked to mark the forces acting on different objects in this situation.



(a) On this diagram, mark all the horizontal forces acting on Paolo. (Ignore any vertical forces.) (b) On this diagram, mark all the horizontal forces acting on Pete. (Ignore any vertical forces.)


(c) On this diagram, mark all the horizontal forces acting on the rope. (Ignore any vertical forces.) (d) On this diagram, mark all the horizontal forces acting on the ground. (Ignore any vertical forces.)


Answers and discussion Forces in pairs: Newton’s Third Law 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 3 2 3 This answer may feel counter-intuitive for some students. But this is an

absolutely fundamental idea about forces: forces arise from an interaction involving two objects; every interaction give rise to a force pair; the two forces of a pair are equal in size, opposite in direction, and one acts on each of the interacting objects.

3 3 See comment on Q2 above. When the box is on ice, with no friction, this may be

even more counter-intuitive. But the same reasoning applies. Note that, as there is no counter-force due to friction in this case, the speed of the box will increase steadily.

4 (a) 3 (b) 3 5 (a) 3 (b) 3

Note that, although the masses of Paolo and Alice are different, the two forces of the interaction pair are equal in size. The accelerations (or changes of momentum) of Paolo and Alice will, of course, be different, because of their different masses.

6 (a) 3 (b) 3 7 (a) 3 (b) 3 8 (a) true, true (b) 2 9 (a) true, true (b) 2 10 (a) true, true (b) 2 11 (a) true, true, false (b) 2


12 (a) true, true, false (b) 2 13 (a) true, true, false (b) 2 14 (a) true, true, false (b) 2

It is, of course, true that the absolute size of the forces involved does depend on the speed of the vehicles. But the two forces in the pair are always equal. It does not matter which vehicle is moving, or moving faster – the two forces of the interaction pair are always the same size as each other.

15 (a) true, true, false (b) 2

This answer may puzzle some students, who will ask: ‘so how do they ever get moving?’ The answer is best seen by looking separately at the forces on the car and on the lorry. There are two main horizontal forces on the car: a forward force exerted by the ground as a result of the rotation of the car’s driving wheels; and a force exerted by the lorry in the opposite direction. (There may also be some air resistance but, as they are moving slowly, this will be relatively very small and can be ignored.) When the speed of the car is increasing, the forward force due to its engine is bigger than the backward force exerted by the lorry. Similarly, for the lorry, there are two main horizontal forces: a forward force exerted by the car, and a backward force exerted by the ground (friction). When the speed of the lorry is increasing, the forward force due to the car is bigger than the backward force of friction. (Note: Qs 18-20 deal with situations that are very similar to this, by looking at the forces on each of the objects involved in this way.)

16 (a) true, true, false (b) 2 17 (a) true, true (b) 2 18 (a) (b)

force exerted by wrestler A

force exerted by wrestler B

force exerted by the

ground (friction) force exerted by the ground (friction)

218 University of York 2003

(c)

force exerted by wrestler A (friction)

force exerted by wrestler B (friction)

The force exerted by wrestler B on wrestler A, and the force exerted by wrestler A on wrestler B are equal in size and opposite in direction. Wrestler A starts to move forward if the force exerted on him by the ground is bigger than the force exerted on him by wrestler B. Similarly, wrestler B starts to move backwards if the force exerted on him by the ground is smaller than the force exerted on him by wrestler A. The two friction forces on the ground are the second halves of two force pairs – and must be the same size as the other force in each pair (the force exerted on the ground by the wrestler). At any time when the motion of the wrestlers is changing, the forces acting on the ground are not equal (they are not an interaction pair, but arise from two separate interactions) – but these are only two of the many forces acting in this situation.

19 (a) (b) force exerted

by car force exerted by driver

force exerted by ground (friction)


(c) force exerted by

driver (friction) force exerted by the car (friction)

The force exerted by the driver on the car, and the force exerted by the car on the driver are equal in size and opposite in direction. The driver starts to move forward because the force exerted on her by the ground is bigger than the force exerted on her by the car. When she is moving at a steady speed, these forces are equal. Similarly, the car starts to move forwards if the force exerted on it by the driver is bigger than the force exerted on it by the ground. When it is moving at a steady speed, the two forces acting on it are equal. The two friction forces on the ground are the second halves of two force pairs – and each must be the same size as the other force in each pair.


20 (a) (b)

force exerted by rope force exerted

by rope



(c) force exerted by Paolo force exerted by Pete

(d)

force exerted by Paolo (friction)

force exerted by Pete (friction)

The force exerted by Paolo on the rope, and the force exerted by the rope on Paolo are equal in size and opposite in direction. The same is true of the forces exerted by Pete on the rope and by the rope on Pete. Also, the two forces exerted on the rope must be the same size – as a rope must have the same tension throughout. So how is it possible for anyone to move? The answer is that Paolo started to move backwards because the force exerted on him by the ground is bigger than the force exerted on him by the rope. Pete started to move forwards because the force exerted on him by the ground is smaller than the force exerted on him by the rope. The two friction forces on the ground are the second halves of two force pairs – and must be the same size as the other force in each pair. At any time when the motion of Paolo and Pete is changing, the forces on the ground are not equal (they are not an interaction pair, but arise from two separate interactions) – but these are only two of the many forces acting in this situation.


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 were then 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. Q4-5 Based on question 11 in the Force Concept Inventory (FCI):

Hestenes, D., Wells, M. & Swackhamer, G. (1992). Force Concept Inventory. The Physics Teacher, 30, 141-159.

Q15-16 Based on questions 13-14 in the Force Concept Inventory (FCI):

Hestenes, D., Wells, M. & Swackhamer, G. (1992). Force Concept Inventory. The Physics Teacher, 30, 141-159.

Q18-20 The format of these question 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/

Q18-19 Based on questions discussed in: Viennot, L. (2001). Reasoning in Physics (p. 75). Dordrecht: Kluwer Academic.


The Evidence-informed Practice in Science Education (EPSE) Research Network is a collaboration between four universities: York, King’s College London, Leeds and Southampton. It was funded by the UK Economic and Social Research Council (ESRC) from January 2000 to June 2003, as part of the Teaching and Learning Research Programme. The Network has carried out four related research projects, looking in different ways at how evidence obtained from research can improve the effectiveness of science education.


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Forces and motion 5: Forces in pairs: Newton’s Third La · Forces in pairs: Newton’s Third Law The questions in this set probe pupils’ understanding of the fact that forces