Work, Energy and Power

Question

A body is dropped from a height h. Plot the potential energy curve versus distance fallen by body.

Answer

Consider the ground as the reference point.
Let at any instant, the body fall by distance d.
Therefore the position of body from ground is,
                        x = h - d

The potential energy of body at that position is,
                U = mgx= mg(h-d)
                   
= mgh - mgd

The graph between potential energy Vs. distance fallen by the body is a straight line as shown in figure below.

            

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