## Friday, December 18, 2015

### Work done against Gravitational Force and Potential Energy

Work has to be done in moving a body against the gravitational force. Once if the work is done, the job is over and body gets displaced. This work done can not disappear all of a sudden. It is against the law of conservation of energy. As per law of conservation of energy, energy is neither created not destroyed. It just converts from one form to other. Work done and energy are just two forms of same expression. If we have energy, we can do work and if we are doing work means, we are using our energy for that.

Here the work done in displacing the body will convert into gravitational potential energy in the body and gets stored in the body. It is also called potential energy.

Let us consider a body of mass m on the surface of the earth. Here surface of  the earth is take like a reference to measure work done and energy. By default, gravitational force is acting on it and it is in the downward direction and towards the centre of the earth always.

To lift the body by body to a certain height, we shall apply some force and that shall be at least equal to the weight of the body acting in the down ward direction so that equilibrium can be disturbed and body can be moved.

Let the displacement is along the same direction of the body and hence the work done is maximum. We can measure the work done as the dot product of force and displacement and here, being they are in the same direction, work done is maximum.

After work is done against the gravitational force, the body acquires a new position and it is at a certain height from the reference point. At that height, the work done is stored in the format of potential energy and that energy is also called gravitational potential energy.

Work done is independent of path in which the body is moved and the important issue is only final point and destination. As it is the dot product of force and displacement. Displacement is a vector and it is the shortest distance between initial and final positions and is independent of path. Hence work done and potential energy are also independent of path.

To calculate the work done by gravitational force, the scenario is little bit different. Here the gravitational force is in the downward direction and the displacement is in the opposite direction and hence work done here is negative and of course the magnitude is same.

This concept  is further explained with a video as show below.

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