Name: Forces: Conservative and Non-conservative
Uploaded: 2019-07-19
Duration: 4 min 29 s
Description: In this video, let us define the conservative and non-conservative forces and determine which forces are conservative and which are not. Learn more.

Question

Prove that change in gravitational potential energy of a body on earth's field does not depend on the path in which the body has moved but it depends on the vertical displacement.

Accepted Answer

The change in gravitational Potential energy of a body depends only upon the position of the path followed. It is due to the fact that the gravitational force is a conservative force depends only on the position of initial & final points and is independent of path followed.

Let a body of mass $m$ be raised to the height $h$ from the position $A$ to $B$ . The difference in gravitational potential energy between the two points is the work done in raising a body from point $A$ to $B$ is

$E = mgh$ ..........................................................(1)

Now let the body is raised through the path $ACDEB$ . During the horizontal motion $CD and EB$ , the force of gravity is perpendicular to the displacement, so no work is done during these motions

The work done is during this path is again,

$mg (AC + DE) = mgh$ . ..................................................(2)

This shows that the gravitational potential energy depends only on the final and initial points and not dependent on the path followed.

Prove that change in gravitational potential energy of a body on earth's field does not depend on the path in which the body has moved but it depends on the vertical displacement.

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