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LEVERS and PULLEYS can be used to change the magnitude (strength) and direction of a force.

A crowbar is an example of a lever.The effort is less than the load because the load is NEAR to the fulcrum and the effort is a long way from the fulcrum

Notice how the direction of the force can be represented by an arrow.


Other examples for the application of levers are: pliers, scissors, wheel barrow. These are all examples of simple MACHINES.


(The Lever Law)
By using the laws of moments we can calculate an unknown force on a lever

Moment = force x distance
Where distance represents the distance of the force from the fulcrum.The unit of  moment is a newton metre (Nm)
or newton centimetre  (Ncm)Sum of moments on left of fulcrum  = Sum of moments on right of fulcrum(or Anti-clockwise moments = Clockwise moments)
Lever 1
(Forces on opposite side of the fulcrum)
Worked e

Imagine a ruler pivoted at the centre
If the ruler is balanced the lever law states that:

The force on the left x its distance from the pivot = the force on the right x its distance from the pivot
2N x 6cm = 3N x 4cm

Lever 2
Forces on the same side of the fulcrum

Worked example
A spring, attached to a ruler, balances a weight.
What force does the spring exert on the ruler?

The ruler exerts exactly the the same force on the spring, causing it to extend.
If we knew the original length of the spring we could calculate the extension caused by this force.

Interactive lever simulation to try


If some weights are hung from a spring the spring will stretch.

The amount the spring stretches is called the extension.

There will be two forces on the spring:

R = the ceiling pulling on the spring. This direction of this force is up.

W= the weights pulling on the spring. This force is caused by gravity. The direction of this force is down.



Experiment to stretch a spring


A spring is clamped near a metre rule.
The position of the unstretched spring is noted.

1N weights are added to the spring, one at a time, and the total extension for the new load is recorded. A graph is drawn plotting extension against load.

It is noticed that for small loads the extension of the spring is proportional to the load. During this time the spring is obeying Hooke’s Law, and the line on the graph is straight.

Beyond a certain load the spring acquires a permanent stretch. This load is called the elastic limit of the spring. At this point the line on the graph starts to curve as the extension gets longer.


Click on the image below to see a Hooke’s Law simulation

Springs in series

Two springs joined end to end (in series) will have twice as much extension as a single spring.springs_series

Eg if one spring stretches 3cm with a load of 1N then two springs in series will stretch 6 cm. This is because each of the springs stretch 3cm making 6cm all together. If each spring were 10cm long to start (with no load) the total length would be 10cm + 10cm + 6cm = 26cm


Springs in parallel

Two springs joined side by side (in parallel) will have half the extension of a single if one spring stretches 3cm with a load of 1N then two springs in parallel will stretch 1.5cm. This is because the load is shared out between the two springs, so each spring is only receiving 0.5N. Half the load means half the stretch.springs-parallel