Name: Concept of Energy
Uploaded: 2019-07-19
Duration: 8 min 52 s
Description: Energy can be transformed from one form to another. But how did this conversion occur? What are their units? Let's find out in this video.

Question

Show with the help of an example that gravitational potential energy is independent of the path followed.

Accepted Answer

Consider an object of mass 'm', raised to a certain height 'h' from the ground.
Then the work done on the body against gravity,
$W = F o r c e \times D i s p l a c e m e n t$ .
When a body is lifted against the gravity, a force is required to do so and the minimum
force required to raise the body should be equal to its weight, i.e, $F = m g$ , then $W = m g \times h$ .
The object gains energy equal to the work done on it.
Therefore, energy gained by the object is $m g h$ which is in the form of 'Gravitational Potential Energy'.

Two objects of same mass are raised through a height as shown in the following figures:

case i :

case ii :

In both cases the body reaches point B from bottom which gives the same vertical displacement 'h'.

If you drop both the bodies, they attain the same speed. Since masses are same and they acquire same speed, hence both the bodies have equal energy.

Potential energy is the energy possessed by the body by virtue of its position (i.e height).

Hence, we can say gravitational potential energy is independent on its path followed.

Show with the help of an example that gravitational potential energy is independent of the path followed.

Important Questions on Work and Energy

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