What are forces?

A force can be a push or a pull. For example, when you push open a door you have to apply a force to the door. You also have to apply a force to pull open a drawer

The unit of force is called the newton, and it has the symbol N. So 100 N is a bigger force than 5 N

We can show the forces acting on an object using a force diagram. In a force diagram, each force is shown as a force arrow. An arrow shows:

• the size of the force (the longer the arrow, the bigger the force)

• the direction in which the force acts.

The arrow is usually labelled with the name of the force and its size in newtons. Text books often show a force with a thick coloured arrow, but it is best if you just use a pencil and ruler to draw an arrow with a single line.

Balanced forces

When two forces acting on an object are equal in size but act in opposite directions, we say that they are balanced forces.

If the forces on an object are balanced (or if there are no forces acting on it) this is what happens:

• an object that is not moving stays still

• an object that is moving continues to move at the same speed and in the same direction

So notice that an object can be moving even if there are no forces acting on it

Examples

Here are some examples of balanced forces.

Floating in water

Objects float in water when their weight is balanced by the upthrust from the water. The object will sink until the weight of the water it pushes out of the way is the same as the weight of the object.

A boat floats because its weight is balanced by the upthrust from the water.

Unbalanced forces

When two forces acting on an object are not equal in size, we say that they are unbalanced forces.

If the forces on an object are unbalanced this is what happens:

• an object that is not moving starts to move

• an object that is moving changes speed or direction

Unbalanced forces make the truck speed up.

Resultant forces

The size of the overall force acting on an object is called the resultant force. If the forces are balanced, this is zero. In the example above, the resultant force is the difference between the two forces, which is 100 - 60 = 40 N.

Moments

Forces can make objects turn if there is a pivot. Think of a playground see-saw. The pivot is the thing in the middle of it. When no-one is on the see-saw it is level, but it tips up if someone gets onto one end. Turning forces around a pivot are called moments.

It is possible to balance the see-saw again if someone else gets onto the other end and sits in the correct place. This is because the turning forces are balanced. We say the moments are equal and opposite.

Working out moments

To work out a moment, we need to know two things,the distance from the pivot that the force is applied.the size of the force applied

This is the equation for working out a moment:

moment = force × distance

Using moments

• A see-saw will balance if the moments on each side of the pivot are equal. This is why you might have to adjust your position on a see-saw if you are a different weight from the person on the other end.

• If a nut is difficult to undo with a short spanner, a longer spanner will help. This is because there will be a bigger moment on the nut, when the same force is applied further from the pivot.

• Using the same principle you can increase the moment applied by a lever or a crowbar, and this can help you move heavy objects more easily.

Moments

A moment is the turning effect of a force around a fixed point called a pivot. For example, this could be a door opening around a fixed hinge or a spanner turning around a fixed nut.

The size of a moment depends on two factors:

• the size of the force applied

• the perpendicular distance from the pivot to the line of action of the force

This explains why less force is needed to open a door by pushing at the side furthest from the hinge than at the side closest to the hinge. To push at the hinge side of the door requires more force to be exerted because the distance is smaller.

A moment can be calculated using this equation:

M = F × d

10 cm= 10 ÷100 = 0.10 m

moment= force × perpendicular distance

moment= 25 × 0.10

= 2.5 Nm

Balancing moments

Where an object is not turning around a pivot, the total clockwise moment must be exactly balanced by the total anti-clockwise moment. We say that the opposing moments are balanced:

sum of the clockwise moments = sum of the anti-clockwise moments

See-saws

A see-saw has a pivot in the middle:

• the person on the right exerts a force downward - which causes a clockwise moment

• the person of the left exerts a force downward - which causes an anti-clockwise moment

If the people are identical weights and sit identical distances from the pivot, the see-saw will balance. This is because the total clockwise moment is balanced by the total anti-clockwise moment.

The see-saw can still be made to balance even if the people are different weights. To do this, the person with the bigger weight must sit closer to the pivot. This reduces the size of the moment so the opposing moments are once again balanced

Levers

A lever is a simple machine that makes work easier to do. Examples of simple levers include cutting with scissors, or lifting the lid on a tin of paint with a screwdriver. Levers reduce the force needed to perform these tasks.

When someone uses a lever, they exert a force (the effort) around a pivot to move an object (the load).

12. principle of momentsA see-saw style lever

Levers rely on the principle of moments to act as ‘force multipliers’ - they reduce the effort needed to move the load by increasing the distance over which it is acting. This means a relatively small effort force has a much greater effect.

A hammer can be used to pull out a nail from a piece of wood.

The effort force acts at a longer perpendicular distance. This is 0.28 m or four times the distance of the load force. As a result, the effort needed is four times less than the load force, or 50 ÷ 4 = 12.5 N.

Note that the moment of the effort is 3.5 (12.5 × 0.28) –the

same as the moment of the load.

In this case an effort force of 12.5 N is sufficient to pull against the load force of 50 N, making it relatively easy to pull the nail out.

Step 1: Work out the moment for which you have been given all of the information

In this case it is the anti-clockwise moment.

moment

= force × perpendicular distance

moment

= 500 × 2

= 1000 Nm

Step 2: Change the subject of the equation to calculate the force

Remember that for the see-saw to be balanced, the total anti-clockwise moment must be equal to the total clockwise moment. Therefore the clockwise moment must be 1000 Nm.force