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### Action and reaction - Newton's third law

## Action and reaction - Newton's third law

Practical Activity for 14-16

Students are easily confused by the glib terms 'action' and 'reaction'. This law needs careful teaching if students are to understand and appreciate it.

**Demonstration**

Convincing kinaesthetic experience that forces come in pairs.

Apparatus and Materials

- Large demonstration trolleys or skateboards or roller skates, 2
- Rope, 6 m in length

Health & Safety and Technical Notes

If a level section of playground is not available, this activity is better done in the school hall.

Read our standard health & safety guidance

Since the motions of the two trolleys are essentially the same in all three cases, it is not necessary to make friction negligible – nor is that possible with large trolleys or roller skates. However, it is important to make the friction drags as regular and repeatable as possible. And it is good to make them relatively small.

Procedure

- Arrange two students, A and B, on trolleys or roller skates, far apart at the sides of the room facing each other so that they can move towards each other on their wheels as freely as possible. Mark definite starting-points on the floor.
- Get the students to hold the rope taut between them. Tell them not to ‘skate’ but just use the rope as follows:

- Student A merely holds the rope whilst B hauls the rope in until the trolleys collide. Both come to rest and their positions are noted.
- Repeat this, but with student A hauling whilst student B merely holds the rope.
- Finally, both students haul on the rope.

Teaching Notes

- Take care to see that both trolleys start each time from the same position. It will then be found that the collision occurs at the same place however the pulling is done.
- The experiment could be tried with two students on each trolley, or with two on one trolley and one on the other.

*This experiment was safety-tested in April 2006*

### Up next

### Action and reaction with a metre rule

**Demonstration**

Illustrating Newton's Third Law of Motion.

Apparatus and Materials

- Metre rule

Health & Safety and Technical Notes

Arrange furniture and observers to minimise the possibility of injury if one side pulls harder than expected.

Read our standard health & safety guidance

Procedure

The teacher and a student (or two students) pull at either end of a metre rule.

Teaching Notes

- This very simple demonstration is the basis for a discussion which will probably need much repetition, as students begin to understand the application of Newton’s Third Law.
- With you and student pulling on the metre rule ask:
*"Which way am I pulling you?"**"Which way are you pulling me?"**"Is it possible for me to pull you without you pulling me?"*- These two forces do not cancel each other out and come to no pull at all. You are able to feel the student’s pull quite well and the student can feel your pull. Only one of the forces acts on the teacher and one on the student.
You pulling on the student

andthe student pulling on you

form a ‘Newton pair’ of forces.- If the student objects that there are three bodies involved (two people plus the metre rule), then dispense with the metre rule and pull each other directly.
- If you do not wish to discuss the role of the meter rule as a connector, then explain that you pull the rule and the rule pulls you. A tension force is transmitted along the rule until, at the other end, the rule pulls the student and the student pulls the rule. Tension forces depend on the material being able to
hold itself together

, otherwise the forces between the atoms and molecules would part company and the rule would break. - The reason why neither you nor the student is accelerated is because of the frictional force acting on your shoes. This balances the pull - unless one of you is standing on ice where friction is not great enough to prevent motion.
- Newton's Third Law concerns pairs of forces that act on two different bodies. Body A acts on body B, and body B acts on body A. The forces acting are equal in size but opposite in direction.

*This experiment was safety-tested in March 2005*

### Up next

### Skateboard forces

**Demonstration**

Forces on a student and skateboard are equal and opposite.

Apparatus and Materials

- Skateboards or demonstration trolleys, 2
- Board, with one dimension larger than the skateboard wheelbase, with screw-eye fixed to it
- Ball bearings
- Rope

Health & Safety and Technical Notes

The activity should be done well away from hard edges such as those of lab furniture, with participating students wearing safety protection as recommended by skateboard manufacturers.

Read our standard health & safety guidance

Use demonstration trolleys (either bought or home-made) or skateboards.

Procedure

- A student walks, from in front or behind, towards a stationary skateboard. She/he steps on to the skateboard and stops walking.
- A student steps onto the trolley from the side, and then starts to walk forwards.
- A student walks towards a skateboard as in step 1, but carries on walking.
- Place the board onto the ball bearings and the skateboard onto the board, with the screw-eye at the front. Fix the rope to the screw-eye. Pull the rope to exert a force on the board.
- Two students sit or stand, facing each other a few metres apart, on two skateboards. Each takes one end of the rope and both pull. Repeat this with one student pulling actively and the second merely responding. Then the second pulls while the first responds.

Teaching Notes

- In step 1, the student and skateboard experience equal and opposite forces. The skateboard experiences a forwards acceleration and the student experiences a backwards acceleration. The student's acceleration is much smaller because of his or her greater mass. The walker stops relative to the skateboard, she/he and the trolley together move forwards.
- In step 2, forces on student and skateboard are again equal and opposite. The student experiences positive acceleration while the skateboard experiences negative acceleration.
- In step 3, the skateboard motion after the event is very similar to that before. As the student steps onto the skateboard, student and skateboard experience equal and opposite forces. The same happens as the student steps off. The skateboard experiences first a forwards force and then a backwards force, and these are approximately the same.
- In step 4, there is little friction between the lower board and the skateboard. So the lower board is unable to exert much force on the skateboard. The student remains stationary relative to the ground.
- This can also be shown with a
normal

experiment trolley on a sheet of card placed on rollers. Pull the card suddenly. The trolley gains little motion and just drops off the card as it is moved. - In step 5, forces are, as always, equal and opposite. Whichever student pulls, the other experiences a force of the same size and in the opposite direction, and the collision occurs at the same place.

*This experiment was safety-tested in April 2006*

### Up next

### Newton's laws of motion

## First and second laws

If you are considering the forces acting on just one body, either law I or law II will apply.

**The first law** describes what happens when the forces acting on a body are balanced (no resultant force acts) – the body remains at rest or continues to move at constant velocity (constant speed in a straight line).

If a book is placed on a table, it stays at rest. This is an example of Newton’s first law. There are two forces on the book and they happen to balance owing to the elastic properties of the table. The table is slightly squashed by the book and it exerts an elastic force upwards equal to the weight of the book. You can show this by placing a thick piece of foam rubber on a table and placing a book on top of it. The foam rubber squashes.

Galileo was the first person to challenge the common sense notion that steady motion requires a steady force. He looked beyond the obvious and was able to say *if* there was no friction then

an object would continue to move at constant velocity. In other words, he put forward a hypothesis. He could see that a motive force is generally needed to keep an object moving in order to balance frictional forces opposing the motion.

The motion of air molecules is a good example to consider with students. When air temperature is constant, no force is applied to keep air molecules moving, yet they do not slow down. If they did, in a matter of minutes the air would condense into a liquid.

**The second law** describes what happens when the forces acting on a body are unbalanced (a resultant force acts). The body changes its velocity, *v*, in the direction of the force, *F*, at a rate proportional to the force and inversely proportional to its mass, *m*. The rate of change of *v* is proportional to *F* / *m*. And rate of change of velocity is acceleration, *a*.

So if the table mentioned above were in an upwardly accelerated lift, an outside observer would see that the two forces acting on the book were unequal. The resultant force would be sufficient to give the book the same upward acceleration as the lift. Put some bathroom scales between the book and the table. If the book is accelerating downwards, its weight would be greater than the reaction force from the table. The book would, however, appear to be weightless.

Mass is measured in kilograms and acceleration in *m* /s^{2}. With an appropriate choice of unit for force, then the constant of proportionality, k, in the equation *F =* k *ma* is 1. This is how the newton is defined, giving *F* = *ma* or *a* = *F* / *m*.

This can also be expressed as *F* = rate of change of momentum or *F* = Δ *p* / Δ *t*.

Newton wanted to understand what moves the planets. He realized that a planet requires no force along its orbit to move at constant speed, but it does require a force at right angles to its motion (gravitational attraction to the Sun) to constantly change direction.

## The third law

Newton’s third law can be stated as ‘interactions involve pairs of forces’. Be careful in talking about third law pairs (often misleadingly called ‘action’ and ‘reaction’). Many students find this law the most difficult one to understand.

Returning to the book on a table, there are three bodies involved: the Earth, the book, and the table. In this example, the interaction pairs of forces are:

- The weight of the book and the pull of the book on the Earth (gravitational forces)
- The push of the book on the table and the push of the table on the book (contact forces)

In general, action and reaction pairs can be characterized as follows:

- They act on two different bodies
- They are equal in magnitude but opposite in direction
- They are the same type of force (e.g. gravitational, magnetic, or contact)