Derive an expression for the gravitational potential energy of an object of mass 'm' at a height 'h' above the earth's surface.
Any object on the earth is pulled towards the center of the earth with a force equal to the weight of the object. An object of mass ‘m’ will be pulled towards the earth’s center by a force equal to ‘mg’
So, to lift the object without any acceleration a force equal to its weight must be applied in the opposite direction (away from the center of the earth).
We have, Force = mg, to lift the object. Suppose, h is the height attained by the object due to this force. The work done by this force is stored as gravitational potential energy of the object.
Therefore, potential energy = work done = mgh
We know that every object on the surface of the Earth is attracted by the Earth.So,if an object has a mass'm',it will experience a force that is called the weight of the object which acts vertically downwards.
To move this object upward from 'a' to'b' through a distance 'h', we must apply a force 'f' upward were F=Mg
W=Fh, but as F=Mg,
This work done on the object which changes its position is called the Gravitational Potential Energy. Then:
From (1) & (2), we get:
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