1 of 9 Forces and motion 1 Explaining motion The reason why force is an important idea in physics is because the motion of any object can be explained by the forces acting on the object. The procedure is very simple: 1 identify all the forces acting on the object you are interested in, noting their directions 2 add the forces acting on the object to find the resultant (or total) force acting on it 3 apply the following rules: if there is a resultant force acting on an object, this will cause a change in its motion, in the direction of the force if the resultant force acting on an object is zero, its motion does not change. Both rules also apply in the other direction, i.e. if you know what the motion of an object is, you can deduce what the resultant force acting on it is. These rules are completely general. They apply to all examples of motion, without exception. For that reason they are called (Newton s) Laws of Motion. Although the great value of these laws is that they are absolutely precise and can be used to make exact numerical predictions about the motion of objects, the first target in teaching about forces and motion is a qualitative understanding of these ideas. Because the ideas are so inter-related, it is impossible to teach them in a simple linear manner. To explain what we mean by a force, it is necessary to draw on more basic understandings about pushes and pulls, and how they can be detected. What we are really doing is extending and formalising the kind of everyday understanding that everyone has of motion. The pay-off from these ideas only comes when you have grasped the whole picture (as summarised above). When you understand this, it opens up a completely way of looking at, and explaining, how and why things move the way they do. This set of ideas is one of the great intellectual achievements of humankind that we should try to make accessible to as many pupils as possible. These ideas were not, however, worked out and written down in this form until the 1660s, even though philosophers had studied motion since ancient times. So this way of looking at (and explaining) motion is not obvious and the challenge in understanding it is considerable. 2 Identifying forces The scientific idea of a force grows out of our direct experience of pushes and pulls. Everyone knows that when you pull something hard enough, it comes towards you; if you push it hard enough, it moves away. Most children appear to have little difficulty with the basic idea that a force is a push or a pull. To make progress, however, we need to make this a little more precise. The key idea is that a force always arises from an interaction involving two objects. During an interaction, both objects experience a force in opposite directions. So forces always arise in pairs one on each object involved in the interaction. The most common type of interaction is when two objects touch. Here the force exerted on each object lasts only as long as the contact. Once the objects have moved apart, they can no longer exert any force on the other. So a force is a push or a pull on an object involved in an interaction
2 of 9 with another object. It arises during the interaction. A force is not something which can be put into or stored in an object, and lasts after the interaction has finished. A useful activity for pupils at this stage (KS2, but worth recapping in KS3) is identifying forces acting in everyday situations. As we cannot see forces, we need some indirect ways of identifying when a force is acting, such as: if an object speeds up, or slows down, or changes its direction of motion if the shape of an object changes 1. Pupils should be taught at this stage to think carefully about what is exerting the force, and which object the force is acting on. Arrows are a useful way of showing the forces acting on objects in a given situation, but this exercise is much more valuable if pupils are encouraged to label force arrows precisely as force exerted on X by Y and to use the more precise language of exerted by and acting on when talking about forces. The size of forces The length of the force arrow can be used to give an indication of the size of the force. Pupils know that a push or pull can be strong or weak, and have little difficulty with the idea that a force has a size. You could introduce at this point the idea of measuring the size of forces, using a spring or an elastic string. (Alternatively, you might keep this until you are discussing the force of gravity, see section 3.) Most pupils readily accept the idea that the stretch of a spring gives a measure of the size of the force it is exerting. Forces are measured in units called newtons (N). At this stage, there is no need to explain what 1 newton is, or how it is defined. Direction and point of application of a force The direction of a force arrow is more important than its precise point of application though it is useful to get pupils to think about this and consider what is the best place to show the force acting. Strictly speaking, Newton s Laws of Motion apply to the motion of idealised point masses. But they also apply, completely accurately, to the motion of extended rigid objects which behave as if all their mass was concentrated at the centre of mass. So one option when marking force arrows is to show all the forces as acting at the centre of mass. But often it seems more natural to put a force arrow at the point where the force is actually applied, e.g. where a person pushes or pulls. 3 Invisible forces Some forces are not so immediately obvious as those caused by a person (or an animal, or a motor) pushing or pulling on something else. These are the forces which act at-a-distance, such as gravity, magnetism and electrostatic forces, and forces that are exerted by inanimate objects, such as the reaction of a surface and friction. Pupils will need some time to come to terms with these forces. 3.1 Gravity The most common of the invisible forces is the force exerted by the Earth on every object near it. We call this interaction gravity. Rather than label this force weight or gravity on a diagram, it is better to call it force exerted by the Earth on the object, as this makes clear what is causing the force and what it is acting on. Like all other forces, gravity is also an interaction involving two objects the other force in the pair being the force exerted by the object on the Earth. As the 1 This is not strictly correct, but can be useful at this stage. It takes two forces to make a permanent change in the shape of an object.
3 of 9 Earth is very large, this force has no detectable effect but it is there nonetheless! In other situations involving field forces, such as two magnets near each other, the fact that a pair of forces is involved is much more obvious, and the effects of the two forces are more apparent. Unlike contact interactions, where the force only lasts for the short time that the objects are touching, action-at-a-distance interactions persist and the forces involved act continuously (though they may change in size as the distance between the objects changes). There are some common misconceptions about gravity which it is useful to address directly and try to clear up. These include: the idea that gravity depends on the atmosphere, so there is no gravity, for example, on the Moon the idea that gravity gets stronger as you go further from the Earth (based on the observation that objects that fall from a height land with a bigger bang). If you have not introduced the notion of measuring force earlier (see section 2), this is a good place to bring it in. Most pupils are familiar with the idea of using a spring to weigh something and readily accept the idea that the stretch of the spring gives a measure of the size of the gravity force. They can then extend this to measuring other forces in the same way. 3.2 Reaction (of the floor or other surface) Another type of invisible force is the reaction of a surface. If you set an apple on a table, it doesn't fall. It sits at rest. There is still a force exerted by the Earth on the apple (its weight), pulling it downwards. But it is not moving. There must be a second force, caused by the table, pushing upwards. We call this upwards force the reaction of the table. But how can a table push? For many pupils, this is a difficulty and it is worth taking some time to explain how this reaction force arises. A good way to explain this is to begin with the apple sitting on a less rigid surface, such as a block of foam. The apple makes a depression in the foam. If you set it down gently on the foam, it depresses the foam more and more as you release it gradually until the force exerted upwards on the apple by the foam exactly balances the downward force of gravity on it. There are now two forces on the apple which have the same size but are opposite in direction. These cancel each other out (or we may say they add to zero ). The upwards force of the foam is called the reaction. The size of this reaction force depends on how heavy the apple is. A very light apple won t depress the foam much and so the force exerted back by the foam will also be small. A heavier apple makes a bigger depression and so causes a larger upwards force. The reaction force is a response to whatever causes it. It becomes just big enough to balance whatever is causing it. If we now go back to thinking about a real table top, this does not visibly distort like a foam rubber table would. But, at a microscopic (or molecular) level, it does distort. And this distortion causes a springy reaction force which exactly balances the weight of the apple. It is just the same as the foam, but on a smaller scale. The reaction force is equal in size to the weight of the object. For any given table, of course, there is a maximum limit to the size of reaction force the table can produce. Up to this, the reaction balances the weight of the object. Above it, the table top will break!
4 of 9 3.3 Tension in a string Exactly the same reasoning applies to the tension in a string. If we hang something up by a string, the string exerts an upward force of just the right size to balance the downward force of gravity on the object. 3.4 Friction The other important invisible force is friction. Pupils may think of friction as a resistance, rather than as a force. So they need to be helped to see it as a force. Friction arises when any two surfaces move over one another. Friction always acts to prevent the movement of one object relative to another. If a box slides across a floor, then there is a force exerted by the floor on the box. It is caused by the roughness of the two surfaces and the way they interlock with each other. As with all other forces, friction is an interaction: there is also an equal and opposite force exerted by the moving object on the floor. (Imagine pulling a box across a floor with a carpet and think about the force exerted on the carpet.) Like the reaction of a surface, friction is a responsive force in that its size depends on the size of other forces involved in the following situation. Imagine a large box sitting on a floor. The horizontal force exerted by the floor on the box (the friction force) is zero, because there is no sideways force trying to move the box. Now imagine that someone pushes the box sideways, with a force of 50 N. This is not enough to move the box. The friction force is now equal to 50 N, in the opposite direction to the person's push. The total force acting on the box is zero (the sum of the two forces on the box). 50N not moving 50N For a given box and surface, there will be a maximum limit for the friction force. Let's say it is 70 N for this box and surface. If the person now pushes with a force of 80 N, friction will rise to its maximum limit (70 N). The resultant force (or total force) acting on the box is then 10 N (the sum of 80 N and 70 N in the opposite direction) and so it will start to move to the right. 80N starts moving We can also think of air resistance and water resistance as friction forces, caused by the movement of something through the air or the water. 70N 4 Adding forces In the discussion above, an idea has been introduced which will inevitably come up in any discussion of forces: the idea that we can add together several forces acting on the same object to find the total force (or, to give it its more precise name, the resultant force).
5 of 9 Most pupils have little difficulty with adding forces in a straight line, taking their directions into account. This accords well with common sense. Up to GCSE level they would not be expected to add forces that were not in the same straight line. 5 Two meanings of reaction At the beginning of this discussion, in section 2, the idea that forces arise from an interaction between two objects and so always come in pairs is introduced. The two forces in an interaction pair are equal and opposite (at every moment during an interaction), and act on different objects. This statement is known as Newton s Third Law. It is sometimes stated (rather unhelpfully) as: to every action there is an equal and opposite reaction. It is better to state it more fully as: When two objects interact, each exerts a force on the other. The force exerted by A or B is equal and opposite to the force exerted by B on A. One reason why the briefer statement is unhelpful is that it used the word reaction in a different sense to that used in section 3.2. To help sort out these two different ideas, imagine a box sitting on the floor. The upward force exerted by the floor on the box is equal to the downward force exerted by the Earth on the box (due to gravity). But these forces act on the same object (the box), not on different objects. There are, in fact, two interaction pairs of forces involved here: force exerted by the Earth on the box (A1) force exerted by the box on the floor (B1) force exerted by the floor on the box (B2) force exerted by the box on the Earth (A2) The forces in each interaction pair must be equal at every moment. This is how forces arise. The two forces on the box are also equal here, if the box is stationary (and its motion is not changing). But this is not because of how the forces arise; it is a conclusion we can draw from the observation that the box is stationary. If, however, this box was sitting on the floor of a lift which was just starting to go up or down, then the forces in one pair would no longer be exactly equal to the forces in the other pair though the forces in each pair would still be equal to each other.
6 of 9 6 Forces and motion Having established the above ideas about forces, it is useful to re-state the connection between forces and motion. The basic principle: The motion of any object can be explained by the forces acting on the object. The procedure: 1 Identify the object whose motion you are interested in. 2 Identify all the forces acting on this object, noting their directions. 3 Add the forces acting on the object to find the resultant force acting on it. The rules: 1 If there is a resultant force acting on an object, this will cause a change in its motion, in the direction of the force. 2 If the resultant force acting on an object is zero, its motion does not change. To apply these rules, you have to understand what counts as a change of motion. A change of motion means that the object changes its speed or the direction in which it is moving. So an object at rest (stationary) or one that is moving at a constant speed in a straight line is not changing its motion. In these situations, the resultant force acting on the object is zero. Conversely, an object that is moving in a curved path (e.g. a circle) at a constant speed is experiencing a change in its motion. In this situation, there is a resultant force acting on the object. It is usual, however, when first introducing these ideas, to consider only situations in which the moving object moves in a straight line. In this case, the rules above lead to the following conclusions. When there is a resultant force acting on an object (i.e. the resultant force is not zero): if the object is stationary, it will start to move in the direction of the resultant force, and its speed will steadily increase if the object is already moving in the direction of the resultant force, it will continue moving in that direction with its speed steadily increasing if the object is moving in the direction opposite to the resultant force, it will continue moving in that direction with its speed steadily decreasing until it is zero. If the resultant force continues to act, the object will then start moving in the opposite direction (i.e. in the direction of the resultant force) with its speed steadily increasing. When the resultant force acting on an object is zero: if the object is stationary, it will remain stationary if the object is moving, it will continue moving at a steady speed in the same direction. Reasoning in the other direction, we can say that: if an object is moving in a straight line with increasing speed, there is a resultant force acting on the object, in its direction of motion if an object is moving in a straight line and is slowing down, there is a resultant force acting on the object, in the direction opposite to its motion if an object is stationary, the resultant force acting on it is zero
7 of 9 if an object is moving at a steady speed in a straight line, the resultant force acting on it is zero. Steady motion doesn't require a force The big step in understanding the Newtonian view of forces and motion lies in appreciating that uniform motion does not require a net force to maintain it 2. Almost everyone thinks it does! The reason is that we live in a world where there is a lot of friction. We find that we do have to go on applying a force to keep something moving at a steady speed. If you can imagine a world without friction, then perhaps you can see that, in such a world, moving objects would carry on moving steadily in a straight line, for ever! In the real world, where there is friction, the forces on an object moving at steady speed are balanced they add to zero. The force in the forward direction is not bigger than the friction force. It is not even a little bit bigger. The two forces are exactly the same size. The resultant force (or total force) is zero. This means that, in the Newtonian view, being stationary is just a special case of steady motion. There is no difference between being at rest, and moving uniformly (at a steady speed in a straight line). We do not need to explain uniform motion; it is just as natural as being at rest. Objects that have been kicked or rolled Another situation that pupils find difficult to interpret is the motion of an object that has been set in motion and is now slowing down. Examples include a football that has been kicked and is rolling along the ground, or a ball that has been thrown vertically upwards. In situations like these, many pupils mark a force in the direction of motion. But this force exists only during the interaction that set the object in motion. Once it has left the foot or hand of the person who made it move, there is no force in the direction of motion. The resultant force is in the opposite direction, making the object slow down (and eventually stop, and perhaps start moving in the opposite direction). 7 Applying the rules (in section 6 above) to more complicated situations In many situations the resultant force on an object is in a direction that is not the same as, or exactly opposite to, its direction of motion. The two rules above are valid for all situations but they are not quite so easy to apply to more complicated cases. When there is a resultant force acting on an object, the change of motion of the object is in the direction of the resultant force. If the object is already moving in a different direction to this, then the change of velocity has to be added to the original velocity by vector addition to find the new velocity. Situations like this would not normally be considered in a first treatment of these ideas. 8 A quantitative treatment of forces and motion As with most fundamental ideas in science, it is better to try to develop a qualitative understanding before introducing more quantitative ideas. Once pupils have gained a reasonable understanding of the ideas outlined above, the next stage in developing their understanding is to work towards a more quantitative treatment, which can lead to precise numerical predictions. The first step is to refine the ideas pupils use to describe motion. Then it is relatively easy to restate the rules of section 6 in more precise terms. 2 Newton s First Law is the statement that an object remains at rest, or moves at a steady speed in a straight line, unless a resultant force acts on it.
8 of 9 Describing motion First it is useful to clarify the difference between average speed and instantaneous speed. The latter means the speed of an object at a particular instant. In effect, this is an average speed over a very short time interval around the moment you are interested in. Distance time and speed time graphs are often introduced at this stage, as a way of summarising the information about an example of motion. Pupils should be able to interpret and produce these graphs, and to translate from one to the other. To describe the motion of an object, it is necessary to know not just the size of the speed but also its direction. This is why the idea of velocity is introduced. Imagine an object travelling at 5 m/s when it collides with a wall and rebounds with a speed of 5 m/s in the other direction. Its change of speed is zero but its change of velocity is 10 m/s (from 5 m/s to 5 m/s). It is clear that a force must have acted on the object to cause this change. So a force causes a change of velocity (though not always a change of speed). We can then define acceleration as: acceleration = change of velocity time taken Acceleration is a difficult idea for pupils: it is a rate of change of a rate of change. To develop the idea, a lot of preparatory work is needed on looking at and measuring speeds of things, and changes of speed. Work on data such as the times needed for cars to go from 0 to 60 mph or from 50 to 70 mph is very useful, as the units (miles per hour per second) are much easier to grasp than metres per second per second, or the largely meaningless metres per second squared! Explaining motion using these ideas We can now re-state the laws of motion more precisely using these ideas. If there is a resultant force acting on an object, the velocity of the object will change 3. It will have an acceleration. The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to the mass of the object. This can be summarised in the following equation: force = mass acceleration (newtons, N) (kilograms, kg) (metres per second per second, [m/s]/s) This equation is one way of stating Newton s Second Law. 3 Note that the same cannot be said of speed. It is possible to have a force acting on an object but not changing its speed (e.g. an object tied to a string, moving in a circle; the string is exerting a force pulling it inwards and stopping it flying off, but the speed is not changing).
9 of 9 Some suggestions for further reading For more information and discussion of children s ideas about forces and motion: Driver, R., Squires, A., Rushworth, P. and Wood-Robinson, V. (1994). Making Sense of Secondary Science, chapters 21-23. London: Routledge. Driver, R., Guesne, E. and Tiberghien, A. (1985). Children's Ideas in Science, chapter 5. Milton Keynes: Open University Press. Osborne, R. and Freyberg, P. (1985). Learning in Science, chapter 4 London: Heinemann. For suggestions about teaching sequences and approaches: Kibble, B. (2000). Forces. In Sang, D. (ed), Teaching Secondary Physics (pp. 98-122). London: John Murray. Jerram, A. (2000). Teaching Physics to KS4, chapter 2 (pp. 57-105). London: Hodder & Stoughton. Robin Millar December 2002