Question

Show how the energy of a freely falling object remains concerned.

Answer 1

Consider a mass  which is falling vertically under the influence of gravity. We already know how to analyze the motion of such a mass. Let us employ this knowledge to search for an expression for the conserved energy during this process. (N.B., This is clearly an example of a closed system, involving only the mass and the gravitational field.) The physics of free-fall under gravity is summarized by the three equations (24)-(26). Let us examine the last of these equations: . Suppose that the mass falls from height  to , its initial velocity is , and its final velocity is . It follows that the net vertical displacement of the mass is . Moreover,  and . Hence, the previous expression can be rearranged to give 
(123)

The above equation clearly represents a conservation law, of some description, since the left-hand side only contains quantities evaluated at the initial height, whereas the right-hand side only contains quantities evaluated at the final height. In order to clarify the meaning of Eq. (123), let us define the kinetic energy of the mass, 
(124)

and the gravitational potential energy of the mass, 
(125)
     
    hope this helps you...