3.1.3 Contact (and non-contact) Forces

On the Introduction to Forces page there was a picture of a man pushing a trolley and of another man pulling a car; these were both examples of Contact Forces. Without contact, the object couldn't have been moved.

Also on the same page there were pictures of magnets repelling each other and of a ball being pulled by gravity; these were both examples of non-contact forces. No contact was needed in order for the force to act and for the objects to be moved.

Let’s define these clearly:

Contact Force- a force that acts by direct contact.

Non-contact Force- a force that acts without direct contact.

Contact Forces are the forces that we see happening all around us day by day.
Examples include kicking a ball, picking up a bag, pedalling a bike, pushing a skateboard. Sometimes the force is applied continuously, like pedalling the bike, but other times it is just a short impulse, like kicking the ball, but in each case contact is made between two objects.

Sometimes the force is considered to be so special that it is given its own name, for example if we push a book across a table we notice that the force called friction is involved. Friction is just the name we give to a particular contact force that occurs between two objects eg the book and the table, when they move against each other. Other named contact forces include Tension and Compression.

The only non-contact forces are Magnetism, Gravity and Electrostatic Forces, so quite an easy list to learn. More on Gravity in section 3.1.2, but for now we are going to focus on Contact Forces as the title of this AQA section suggests.

Drawing Forces - Force Arrows and the unit for Force

Most of you will be familiar with the way we illustrate the action of a force.

A force is drawn using a Force Arrow.

But it is worth pointing out that a force arrow is a very particular thing! It is a straight line with an arrow head at ONE end.

Here are some typical CORRECT force arrows.

Just a straight line and one arrow head.

And here are examples of INCORRECT force arrows.

I am sure you can now see why they are incorrect; they are either not straight or they have two arrow heads!

So, the single arrow head tells us the DIRECTION of the force and the length of the straight line indicates the SIZE (also known as the MAGNITUDE) of the force.

So, when understood, force arrows are easy to draw and explain.

Now for a little check up.

a) which force arrow represents the smallest force to the left?

b) Which force arrow represents the largest force to the right?

Here are the answers:

The arrow which represents the smallest force to the left is 1; the arrow which represents the largest force to the right is 2.
Notice how the thickness of the arrow is irrelevant.

Most of the time when we draw a force arrow we will put a value beside it rather than just say it is a large or a small force. We can do this because we measure forces in a unit named after one of the most famous scientists of all time; the English Physicist Sir Isaac Newton.

The unit for force is the “newton" and the symbol for it is the capital letter N.

So, our humble little Force Arrow is really important and it conveys a lot of information.

Always take care when you draw them. OK.

Resultant Forces

The term “resultant force” is only relevant in a situation where two or more forces are involved, acting on one object

So, in the first example below, you don't really need to use the term "Resultant force" since there is only one force present. It is enough to say "there is a force of 5N pulling the object to the right."

But in the next diagram there are two forces acting on the one object, so we can now bring in the term “resultant force”,

...but only if we know what we are talking about!

So, what does the term mean?

Time for another definition:

A resultant force is a single force that has the same effect as all the original forces acting together.

To work out this “same effect” is quite simple.

For example in the 2nd diagram, the two forces each pull the object to the right, one with a force of 5N and the other with a force of 3N, so the Resultant Force is simply the “result” of adding these two values;

so the resultant force is 8N to the right. In other words: 5 + 3 = 8

The 3rd diagram shows the single “Resultant force which has the “same effect” as the original two forces.

Easy! But what if the forces acting on the one object act in different directions as shown in the 4th diagram?

If an object is pulled to the right by a force of 6N and to the left by a force of 10N, then the single force that has the “same effect” is a force of 4N to the left. See the 5th diagram.

The Resultant Force, which has the same effect as the original two forces, is a force of 4N acting to the left.

In other words: 10 - 6 = 4

We subtract the 6N force from the 10N because it acts in the opposite direction. (In the previous example, when the forces acted in the same direction, we simply added them.)

Notice in question 4 above that the resultant force became zero when the new member joined Jim’s team; the two teams are still pulling but their forces are now cancelling each other out. If the two teams keep pulling with these forces then they will remain fixed in position forever!

When the resultant force acting on an object is found to be zero, we say that the forces acting on the object are Balanced and that the object is in a state of Equilibrium.

The word “Equilibrium” is a good choice here because it means that everything concerning the motion of the object stays “the same” or “unchanged”.

So if the object WAS :
a) stationary before the pair of balanced forces act on it, then it remains stationary (because the forces have effectively cancelled out and disappeared!),

Here is an illustration:

Here, before any forces are applied, an object is stationary.

Now, forces are applied, but since they are BALANCED, the object remains in its state of EQUILIBRIUM and its motion does NOT change. It remains stationary.

And if the object WAS :
b) already moving before the pair of balanced forces act on it, then it just carries on moving at its previous speed and direction, totally unchanged. (Again, because the pair of forces have effectively cancelled out and disappeared!)

Here is an illustration:

This car is currently moving at a constant speed; it is in a state of EQUILIBRIUM.

Now, the engine produces an extra 7N of forward force, but there is also an additional 7N of air resistance. The resultant of these two forces is zero, so these forces BALANCE and the car remains in EQUILIBRIUM. Its motion does NOT change. It ontinues at its constant speed of 2m/s.

So, just to repeat - if the resultant force on an object is found to be ZERO, then the object is in a state of EQUILIBRIUM and its motion does NOT change. So whatever it WAS doing, it carries on doing.

Have you got it?

Also, a great consequence of this idea of "Equilibrium" is that if you are told that a certain object is stationary, OR is moving at a constant speed, then you can declare with great confidence that the it is in a state of equilibrium and so no matter how many forces are acting on it, they are BALANCED and have a Resultant Force of .....ZERO.

For example: A child slides down a slide due to a downward force of 200N. He slides at a constant speed. What can you say about any other forces acting on the child?

Well, you can say that there is an UPWARD force acting on the child and that it is BALANCING out the downward force, because the child is moving at constant speed (or is in a state of EQUILIBRIUM), and that its size is exactly 200N. Easy!

Notice - you can say all of this only because the child (the object) is in a state of Equilibrium, moving at constant speed; the condition for Equilibrium is to remain at Constant Speed or to be stationary.

The Effect of A Resultant Force

A resultant force ALWAYS causes some change.

We have just been looking at situations where the Resultant Force on an object was Zero and in such cases we said that the object was in a state of Equilibrium, meaning that the forces acting on it were cancelling each other out and so causing no change to the motion of the object. We called such forces, Balanced Forces.

But, when the Resultant Force acting on an object is NOT zero the object will NOT be in a state of Equilibrium and change to its motion will occur.

But what sort of change?

The object might start to move IF it had been stationary.
The object might stop IF it had been moving.
The object might speed up.
The object might slow down.
The object might change direction.
The object might start to rotate.

The object might also be stretched, squashed or twisted, and later we will have to look at some of these in more detail. In other words, all kinds of changes are possible.

The essential point is :

A Resultant Force always brings about some change to the motion or shape (or "form") of an object.

Three Named Contact Forces

Now that we have a fairly good understanding of the general behaviour of forces, we are going to look at 3 examples of well known contact forces. These are: friction, tension and compression.

Friction

Friction is a force which is noticeable whenever two objects or surfaces move over each other.

eg. You notice it when you rub your two hands against each other, one hand one way and the other hand the opposite way.

You don't notice it if:
you only use one hand, or
you don't move your hands, or
your hands are not touching, or
your hands touch but move together in the same direction.

When it occurs, what exactly do you notice?
You notice two things: you notice an opposition to the motion of your hands, and
you notice an increase in the temperature at the point where your hands make contact.

These two things are always noticed whenever friction occurs:
There is an opposition to the motion of the objects, and
There is a rise in their temperature.

Both mean that generally friction is a nuisance!
It causes moving objects to slow down, or it causes fuel to be wasted in keeping objects moving at a steady speed.
And it causes objects, such as engines, to overheat leading to expensive damage or to the need for sophisticated cooling systems to prevent overheating.

Examples of Friction

Here are just two examples. I am sure you can think of many more.

1. A cyclist pedalling, moving forward.

The cyclist must produce a forward force, F, simply to balance the opposing forces of friction due to air resistance (or drag), F_a , and the friction due to the rubbing of the tyres against the road surface, F_f.
If the cyclist stops pedalling, F will decrease but the friction forces will continue to oppose the motion of the bike causing it to slow down and eventually stop.

Can the cyclist get rid of the friction?
NO, the cyclist is an object moving through the air so there will always be some air resistance (drag), and the tyres have to grip the road otherwise the bike will skid, so friction here is inevitable (unavoidable).

What can the cyclist do to minimise the effect of friction?
The cyclist can make himself and bike more "streamlined"; to become more like a sleek racing car than like a double decker bus! This is why racing cyclist crouch down. He or she can also wear closer fitting clothing, but in the end there will always be some friction and the really annoying thing is - the faster you go, the greater the force of friction!

2. A boat or ship moving through the water.

Its engine turns a propeller, to produce a forward force, F ,simply to overcome a water resistance (or drag) force, F_w , which is opposing the motion of the ship.
It has to do this to maintain a constant speed.
If it doesn't do this, it will slow down and stop.
Like the cyclist example, the friction can NOT be eliminated but it can be minimised by streamlining; this is why we see ships with slender, pointy fronts.
Some smaller boats, called catamarans, try to raise themselves out of the water as much as possible in order to reduce friction even further and thus to go faster.

Is friction always a nuisance?

No, not always. For example, when we walk we expect to be able to put our feet/shoes down and step forward without slipping, don't we? In other words we rely on friction between our feet and the ground to "grip" and stop us slipping. Imagine if walking was always like "walking on ice"!

Another example - all vehicles, whether they are cars, buses, trains or bikes rely on friction whenever they use their brakes. In a car braking system a pair of pads get pushed against a steel disc which is attached to a wheel of the car; the car slows down and the disc gets really hot due to friction. But without friction, no vehicle could be driven or ridden safely.

Factors which affect the size of friction forces

From what you have read above, you should be able to state a few factors which have an affect on the size of friction forces.
These would be:

1. The front area of the moving object (or its front cross-sectional area); the larger the area of the moving object, the greater the frictional force felt by the object.
2. The substance/material that the object is moving through (eg there is more friction if the object moves through water than through air)
3. The speed of the moving object; the faster the object, the greater the force of friction eg when you rub your hands together more quickly they produce more friction and get hotter.
4. The smoothness/roughness of the surfaces (eg a smooth surface is slippery and produces little friction compared to a rough surface. This is why ice is very slippery; it is also why oil is used to lubricate in between moving parts especially in engines. Rough surfaces produce a lot of friction when rubbed together.)

Tension and Compression

When we summarised the "Effect of a Resultant Force", we stated that it always causes change.
The change could be to the motion of an object, eg to its speed, or to its shape.
Tension and Compression are examples of resultant forces which cause change to the shape of an object.

Simple Examples of Tension and Compression Forces

Stretching a blob of blu-tac or a rubber band:
Two forces are involved, acting outwards from the object; we call these forces "tension forces".

Squeezing or crushing a drink-can:
Two forces are involved, acting inwards onto the object; we call these forces "compression forces".

By the way, the proper term for a "change of shape" is a deformation.
So when two tension forces stretch an object, making it longer, we can say "it has been deformed".
Or when two compression forces squash an object, making it thinner or shorter, we can say "it has been deformed".

Sometimes the deformation is temporary, such as when we stretch a spring or an elastic band and then release it, it goes back to its original length; we call that type of deformation, an elastic deformation.
But if the deformation is permanent such as when we stretch a piece of blu-tac, then we call that type of deformation, an inelastic deformation.

How the length of a spring varies when the force on it changes

We can apply a tension force to a spring by hanging it from a retort stand and attaching known forces to it, measuring its change of length (or extension) by using a pointer and a metre rule.
The apparatus for doing this is simple and is shown in the diagram below.

The results from such an experiment are shown in the table below.

Force	Extension
(N)	(mm)
2	10
4	20
6	30
8	40
10	50
12	60

You should not be surprised to see that the force is measured in newtons; this was discussed earlier on this page.

If we plot these two quantities against each other (either Force against Extension, or Extension against Force) we get a line such as you can see in the graph below.

As we can see it is a straight line.
What does this tell us?

It tells us that the two quantities have a linear relationship and so are proportional to each other; that as one increases, so does the other and always by a certain amount. So you can see from the graph that every time the Force increases by 2N, the Extension increases by 10mm.

In fact, when a line is straight and it goes through the origin we can add another word to the description of the relationship; we can say that it is directly proportional. So here, because the line goes through the origin, the relationship is directly proportional; this means that if one of the quantities doubles, then so does the other (eg. if the force doubles from 4N to 8N, then the Extension also doubles from 20mm to 40mm).

When an object behaves in this Proportional (or Directly Proportional) way we say that it is behaving "Elastically".
So objects like springs, pieces of rubber and elastic bands tend to behave in this way, or at least they do up to a point !

Eventually even these objects will stop behaving Elastically when the applied force gets too large.

The graph below shows how the "line" is no longer straight once the force is taken beyond 12N.

The "line" becomes a curve; the object stops behaving Elastically. This eventually happens with every spring, elastic band or rubber object.

What about objects or materials such as blu-tac ?
Their graphs never show a straight line at all; they would show a curve right from the start, so for them, Force and Extension are NEVER proportional. They are inelastic materials; sometimes called "plastic" materials.

One final point:
Objects, like springs, that stretch elastically, will also squash (or compress) elastically, so the amount by which they squash is proportional to the compression force applied to them. This is why springs are used in bed mattresses where they compress when a person lies on the mattress and then they return to their original length once the person gets off the mattress.