A physics teacher had a bowling ball suspended from a very long rope attached to the high ceiling of a large lecture hall.To illustrate his faith in conservation of energy, he would back up to one side of the stage, pull the ball far to one side until the taut rope brought it just to the end of his nose, and then release it. The massive ball would swing in a mighty arc across the stage and then return to stop momentarily just in front of the nose of the stationary, unflinching teacher. However, one day after the demonstration he looked up just in time to see a student at the other side of the stage push the ball away from his nose as he tried to duplicate the demonstration. Tell the rest of the story, and explain the reason for the potentially tragic outcome.

The work done on a particle by a constant gravitational force can be represented as a change in the gravitational potential energy is given by,

$$\begin{gathered} {\mathit{W}}_{\mathbf{\text{grav}}}\mathbf{=}\mathit{\Delta }{\mathit{U}}_{\mathbf{\text{grav}}} \\ \mathbf{=}{\mathit{U}}_{\mathbf{\text{grav}}\mathbf{,}\mathbf{1}}\mathbf{-}{\mathit{U}}_{\mathbf{\text{grav}}\mathbf{,}\mathbf{2}} \\ \mathbf{=}\mathit{m}\mathit{g}{\mathit{y}}_{\mathbf{1}}\mathbf{-}\mathit{m}\mathit{g}{\mathit{y}}_{\mathbf{2}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\left(1\right) \end{gathered}$$

Here, assume that m is the mass of the egg ${\mathit{y}}_{\mathbf{1}}$and ${\mathit{y}}_{\mathbf{2}}$are the initial and final height of the building,g is the acceleration due to gravity, and ,role="math" localid="1668142150730" ${\mathit{W}}_{\mathbf{\text{grav}}}$ is the change in the gravitational potential energy.

Normally, the gravitational potential energy of the ball will be converted into kinetic energy after releasing the bowling ball right next to the lecture's nose. According to the law of conservation of energy, the bowling ball will have just enough energy to return to the same height.

If the ball were able to reach a higher point, then it will possess negative kinetic energy to conserve impossible energy. If no external forces are acting on the ball then the ball will reach its initial position.

In this case, if the student pushes the ball away at the other end, then the student conveys additional kinetic energy to the bowling ball. So, there is no longer the energy conserved due to the application of an external force. This extra energy increases the ball’s total energy, and the ball can rise to a higher point than when it started.