Pushing and pulling

I was sitting in a train by the seaside quite recently. We had come to a halt and a steam engine went by pushing a line of four or so carriages. A small child sitting nearby called out excitedly: Engine push wagons, push, push wagons! The child's mother responded: Yes, that's right, the big engine is pushing the wagons.

Ideas of pushing and pulling are common in everyday talk and are used from an early age as this example demonstrates. The word force is used in a whole range of different ways: people refer to force of habit or forcing things open or armed forces. In a tight corner you might argue: you can't force me to do that!

In the sciences the concept of force is used in a more limited way and the good news is that the scientific way of thinking about forces is pretty close to everyday understanding. For example, when young children say: I am lifting the bag or we are pushing the trolley, they are starting to use the language of forces in ways which any scientist would recognise.

From such starting points, pupils need help in developing and applying a scientific description. In one sense this is not difficult: we are not expecting essays. A good starting point is to recognise that in describing situations where forces are acting, it is helpful to focus on three facets:

1. What is the force exerted by?
2. What kind of force is acting?
3. What is the force acting on?

Let's apply these three questions:

1. What is the force exerted by?
2. What kind of force is acting?
3. What is the force acting on?

to the example: The engine pushes the wagons.

1. The force is exerted by the engine.
2. The force is a push.
3. The force acts on the wagons.

This simple statement might be expressed slightly differently:

The push exerted by the engine acts on the wagons.

The term acts on is a good way of linking the force to whatever it is that feels the action of that force. Alternatively you might choose to link to what is providing the force. We suggest the consistent use of the word exerts, in which case: The engine exerts a push on the wagons.

Let's look at a second example: The woman pulls on the rope.

1. What exerts the force? The woman.
2. What kind of force is acting? A pull.
3. What is the force acting on? The rope.

You'll develop the kinds of forces over the next three episodes. But for now expect to find a force wherever something affects an object and you might have the same effect by pushing or pulling. Your push or pull can be identical to the action of the inanimate surroundings (the environment of the object) exerting a force on an object.

You can develop your understanding of the kinds of forces through these next three resources.

• Looking through forces spectacles
• Keeping it simple: modelling
• Force arrows

But for now expect to find a force wherever something affects an object and you might have the same effect by pushing or pulling. Your push or pull can be identical to the action of the inanimate surroundings (the environment of the object) exerting a force on an object.

Recognising forces

Onions don't come from the market with arrows attached labelled: I'm being pulled down by gravity with a force of about 3 newton or I weigh 3 newton.

The fact that forces aren't visible, labelled and ready to be described offers a challenge to the imagination. You must learn to recognise where forces are acting. So change your perspective: moving from the physical (green panes) to a theoretical (blue panes) description.

If you look at things you'd find in the kitchen, you can spot lots of different objects. Each of these has many different facets that you can describe: the materials from which objects are made; the ways in which they move around; the forces acting on these objects; the colours of the objects. In this topic, for one object at a time, we'll be describing the forces – and only the forces.

An everyday scene

So let's take an everyday scene.

This might look like a person carrying some shopping and indeed that is just what it is.

But view the scene through forces spectacles, shifting from the physical to the theoretical, to find out how a physicist might see the situation when looking at this scene through forces spectacles.

The left hand re-description is too complex – there are still several objects: the shopper's head: the bag; the rest of the shopper. Simpler is better – so always focus on just one object. And even then we've only shown a few of the forces acting on the objects. The idea is to avoid hedgehog-like diagrams, with pointy bits heading off in all directions. Like rolled up hedgehogs, they're hard to handle.

The second is better for just this reason, as we have reduced the shopper and his bag to a single object. Why do we say better? Simply because the model (and it is a model) is something that will allow us to make predictions.

An alternative way to make it simpler is by concentrating on some parts of the situation. The rule is always, always to focus on a single object at a time. Just one.

Get those spectacles on

Steps:

1. Look carefully at one object.
2. Put your forces spectacles on to see it in a new way
3. Draw in the forces.

Force spectacles

The world seen through forces spectacles can be very complex. There are many more forces acting in the situation than those shown. (Think of the forces exerted by the muscles in the strained forearm and in the aching fingers.) To help you make sense of the complex world of forces, there is a simple strategy: focus on an object and its interactions with its environment – both local and remote. So first isolate one object from its environment. Here, let's choose the hand. Then identify the forces acting on it by considering the interactions of that object with the environment.

Here's what we do:

1. Identify the object.
2. Isolate it from the environment.
3. Identify the forces acting by thinking about interactions with the environment.

In moving between steps 2 and 3 we're building a model of the situation. How do we know what to include in the model? By paying attention to the situation.

Here two elements of the local environment are both stretched – the forearm and the bag. They're warped, and we'll see that these kinds of distortion lead to a tension or compression force.

Making a model

Now consider the forces acting on the bag.

The process of simplifying a complex situation by concentrating on one part is an example of scientific modelling. An even simpler sketch of the situation might reduce the bag and its contents to a point, as shown in the additional step here.

Let's summarise the three stages in this modelling process:

1. Focus on one object of interest.
2. Isolate this object from its environment, drawing it as simply as possible.
3. Look at the world through forces spectacles, enabling the identification of forces by considering interactions between object and environment.

The key idea is that we're dealing with the world one object at a time – no more.

Using arrows to represent forces

By now you'll have noticed that we use arrows to represent forces. These force arrows (or force vectors as they are referred to in physics books) are very helpful because they can be used to represent the two essential features of any force:

• The direction in which the force acts is shown by the direction of the arrow.
• The size of the force is shown by the length of the arrow (the longer the arrow the bigger the force).

A third convention to be consistent about in drawing force diagrams determines the positioning of force arrows:

• Each arrow is drawn so that it starts from the point where the force acts.

It'll also be helpful to always draw the forces in a particular style (there get to be a lot of arrows on diagrams in physics, not all of them forces). You might also choose colour to show the kind of interaction that the force replaces.

An essential skill is to be able to add the arrows as needed – and not any more than are needed. There are clues in the interactions between the object and its environment that'll help you identify the forces. Later we'll see what those clues are – more on that in episodes 2 and 3.

Adding arrows to a simple situation

Think about the forces acting on a book that is sitting on a table.

The upward push of the table on the book acts on the lower surface of the book and the force arrow is drawn from that lower surface.

The downward pull of the Earth (the gravitational pull of the Earth) on the book is taken as acting through the centre of the book, and the force arrow is drawn from that central point.

Being able to draw arrows to describe forces is an important skill. The activities in the Teaching Approaches section are designed to help pupils practise identifying forces though the use of cut-out card arrows, using these arrows to show forces in a force diagram.

Adding force arrows to a familiar situation

The image shows a situation familiar to most teachers. Think how this will look when seen through forces spectacles. Focus on the forces which act on the hanging masses.

Make a simplifying sketch to model the forces acting on the hanging masses.

Here's what to do:

1. Identify one object.
2. Isolate that object from it's environment.
3. Identify the forces acting by thinking about interactions with the environment.

In episodes 2 and 3 we'll introduce a kind of force-spotter's guide – a series of clues to look for in the environment that allow you to identify the force arrows to add to your description.

Teacher Tip: Don't forget to actually try to do the drawing.

Equilibrium

You saw a situation where the hand was pulled down by a single force, the tension in the shopping bag. It is quite possible for an object to be acted upon by more than one force. A team of nine husky dogs pulling an Arctic sledge or a commuter being squeezed into a busy rush-hour train by a bunch of people pushing on all sides are examples where many forces act on one object. If these forces all push in the same direction the result will be a rapid change – perhaps the Arctic sledge will race away or the commuter will be shoved along the carriage.

However, it could be that all of the forces acting on the object balance each other out. The object is then said to be in equilibrium. All of the forces acting on an object which is in equilibrium add to zero. In other words, one force acting upwards is balanced by another force acting downwards; one force acting to the left is balanced by a similar force acting to the right, and so on. All the forces that are present add up to produce no overall force at all. Here's another way of saying this.

Teacher: Objects in equilibrium have no unbalanced forces acting on them. The resultant force is zero.

Most objects are in equilibrium

Look around you and notice how most things are doing nothing. The coffee cup just sits on the table, the picture hangs from the wall, the shirt lies on the chair. The cup, picture and shirt all have forces acting on them but the result for each one is a balanced or equilibrium state. There are no unbalanced forces acting on each one of these objects. The resultant force is zero.

Two forces on one object

Two forces act on the teapot resting on the tabletop. These two forces add to zero. They appear to be equal and opposite. They are equal in size and they act in opposite directions.

However this is not the same case as described in the commonly quoted Newton's third law of motion: to every action there is an equal and opposite reaction (this is far from the most helpful statement of the law – more on that in the SPT: Force and motion topic).

In our example the two forces both act on the teapot. The forces are the gravitational pull of the Earth and the upward push of the tabletop. The two forces are both acting on the same object, the teapot.

When two forces act on one object to create a balance it is not the same as the action and reaction pairs.

This is often misunderstood, but Newton saw this distinction. His first law of motion describes equilibrium situations where forces add to nothing and act on the same object, just like on the teapot. The second screen of the interactive shows a pair of forces acting on different objects – this is an example of Newton's third law.

Newton's third law

A completely separate law, Newton's third law of motion, describes pairs of forces. These are often called action and reaction, but we don't think that this is helpful.

Newton realised that in every case, forces appear in pairs. If there is a force exerted by A acting on B, then there will be an equivalent force exerted by B acting on A. This is true, even if A and/or B are not in equilibrium. In the case of the teapot, the support force from the table acting on the teapot (one of the pair of forces) is accompanied by an equivalent force from the teapot acting downwards on the table (the second of the pair of forces). A force exerted by one object and acting on another is only half the story of the interaction between the two objects.

In starting out on developing a force description we suggest that you focus on one object at a time. So you'll be working with half the interaction, and so considering only ever one of the pair of forces described. Either describe the forces acting on the teapot, or the forces on the table. Keep it simple: avoid the complexity of trying to describe both objects at once.

If you really, really must work with both: use two diagrams, one for each object.

Some simple cases: a first example – cup on table

The cup is acted on by two forces. Gravity pulls it downwards and the upward contact force from the table pushes upwards. These two forces add to zero and the result is a cup in equilibrium. Episode 01 has considered this type of situation in detail.

At the interface between the table and cup, the cup is in contact with the table. It is this contact which results in the upward force which supports the cup. But the cup also pushes down on the table. So if you are modelling the forces on the table, you need to consider the force exerted by the cup, acting on the table.

So at the interface there is a force exerted by the table acting on the cup and a force exerted by the cup acting on the table. This is the pair of forces representing the interaction.

Note that this pair of forces act on two separate objects, the table and the cup. The two forces, both equal in size but opposite in direction, act on two different objects. You can't claim that these two forces are balanced as they are acting on two separate objects.

A second example: a falling apple

On its way downwards there is only one force acting on the apple (ignoring air resistance). It is the force due to gravity. However if we consider the bigger picture we note that the apple is falling towards the Earth. A gravitational force from the Earth acts on the apple and an equivalent force from the apple acts on the Earth. Here we have a pair of forces representing an interaction. The pair of forces acts even though the Earth and apple are not in contact. One way to think of this is to see the Earth and apple attracting each other. The force of gravity acts always between two objects. In this case the Earth and the apple are the two objects. The apple and Earth are not in equilibrium. Both Earth and apple are accelerating towards each other.

A third example: a deflating balloon

In the third example the pair of forces again act on two different objects, as they must. There is a force exerted by the balloon material on the air. The air is pushed out of the balloon. There is also a force which the air exerts on the inside surface of the balloon, a force acting on the balloon. The result is that the air is being pushed in one direction and the balloon is pushed in the other. In this case there is certainly no equilibrium. The balloon and air will move apart – the balloon is about to whizz around the room. These two forces are equal in size and opposite in direction, but they act on two different objects. The interaction is described by a pair of forces.

Helpful approaches: a summary

When describing a situation using forces, aim to answer these questions:

• What exerts the force?
• What kind of force is acting?
• What is the force acting on?

When drawing force diagrams, a helpful process is to:

• Imagine you are looking through forces spectacles.
• Focus on one object of interest.
• Reduce this object of interest to its simplest representation. This can often be just a point.
• Only then add the force arrows.

In many cases all the forces acting on an object will balance. The net effect is that nothing changes. We describe such objects as being in equilibrium.

What's to follow

Moving on from these key skills of representing forces and recognising that the forces acting on an object can be in equilibrium, we now turn to exploring kinds of forces in episodes 02 and 03. Thinking about these provides the justification for adding arrows to diagrams, so providing a force-spotter's guide. So far how to identify the forces acting on an object has not received sufficient attention. The next two episodes rectify that.

Episode 02 deals with the kinds of forces to look out for when two objects are in contact: kinds of contact forces.

Episode 03 deals with kinds of non-contact forces, sometimes called action at a distance forces.