Lift Yourself Up

We can possibly lift objects weighing more than ourselves. We cannot, however, normally, lift ourselves up. But, the arrangement here allows us to do just that. Stand securely on the platform. Pull the free end of the rope downwards. The platform, along with you, moves up! The situation is similar to drawing water from a well. It is a lot easier to lift the weight when the rope runs over a pulley than when it is directly pulled up. A pulley is a simple machine that allows us to change the direction of application of force thereby reducing our efforts. It becomes increasingly easier to lift as we increase the number of pulleys.

The model here has 3 pulleys fixed to a rigid support and 3 other pulleys are movable.

A long thick rope moves over these pulleys. One end of the rope tied to one of the fixed pulleys and the other end is free. A rigid platform is firmly held by a strong hook connected to a set of movable pulleys as shown in the illustration.
In order to lift oneself up, a person has to stand on the platform and pull the free end of the rope downwards.

We might have seen people lifting up weights which are heavier but not people who lift themselves. Here we can see a person lifting up himself with ease. The credit goes to the pulleys.

A pulley is a simple machine that can be used to lift loads much easily. It is a circular wheel on an axle object with a groove around its circumference.
A rope ( or any other drive element like  cable, belt or chain ) runs over the pulley inside the groove.

Pulleys can be assembled in different kind of arrangements to achieve different mechanical advantages. Mechanical advantage of a machine is a measure of force amplification achieved by it. That is, it is the ratio of the output and input forces. For a machine to have good mechanical advantage, this ratio should be greater than ‘1’. That is, the output force generated should be larger than the input force ( the force applied by the person on the free end of the rope )

How do we achieve a mechanical advantage ?
When an object weighing ‘ W ‘ kg is held by a rope, its weight acts downwards causing a tension in the rope which acts upwards. This tension is the same all along the rope and it gets equally distributed to all the sections of the rope that are supporting the load ‘ W ‘.
Therefore, the input force is reduced by a factor which is equal to the number of sections of rope supporting the load.

  1. Therefore, the input force

Mechanical advantage =

M. A.    x no. Of sections of rope supporting the load. Therefore if the load is supported by more number of sections of rope, higher will be the mechanical advantage.

In this exhibit, the load ( weight of the person + weight of the platform) is supported by 6 sections of the rope. Therefore, there is a mechanical advantage of 6  and the input force is reduced by a factor of 6.

Input work done ( i.e., force x displacement ) by a person in pulling the rope should be equal to the output work done in lifting that person up. The pulley system reduces the input force by some factor but at the cost of pulling the rope over a large distance.