Pulleys

In this exhibit, we have equal weights suspending from each of the pulleys. Pull the rope passing over the pulleys down – one at a time. You can feel the difference in the effort that goes into pulling the weight up in each case. The effort reduces with increasing number of pulleys.
A pulley helps lift a weight up by allowing us to change the direction of the force applied. As we increase the number of pulleys, the effort is reduced but at the cost of pulling the rope over a greater distance.


In this model you can see that the same mass is attached to the ends of all the three ropes which run over three different arrangements of pulley systems. You can pull the other end of the ropes to lift up the mass.

When you try to do this, you will realize that difficulty in lifting up the same mass is not the same in all the three cases.

What makes it easier to lift the mass in one arrangement than the others ?
If  it is easier to lift the mass in a particular arrangement, it implies that lesser is the force required in doing the work.

It can be seen that all the three cases, it is the same load that is being lifted up. Then what might be causing a difference in the input force required to them up ?

It actually depends on the number of parts of the rope supporting the load, the direction in which the force is applied and whether the pulley is a fixed or movable one.

In all the three cases, the force is applied in the downward direction and one of the arrangements has a single fixed pulley where as the other two arrangements have fixed as well as movable pulleys.
The variation difference in the force required in these cases depends on the number of parts of the rope supporting the load.

Now let us see how the above factor causes a difference in the required force.

If an object is held by a rope, its weights (w) acts downwards. This downward force causes a tension in the rope which (acts upwards and) is the same all along the rope. If there are x number of parts of the rope that are supporting the load w, then the tension in each of the parts is 
Therefore this implies that the input force is   that is, it is reduced by a factor ‘ x’.
Hence if the load is supported by more number of parts of the rope lesser will be the force required to lift the load making the task easier.

In turn more will be the distance through which the rope is being pulled.

This is because all the three equal loads are being lifted to same heights that is, wok done is equal to force x displacement is the same for all of them since energy is conserved. This should be equal to the mechanical work done by us. Therefore, if lesser is the force required, more will be the distance through which the rope is being pulled.