Question

Prove that the mechanical energy of a free falling object remains constant at every point of motion.

Answer 1

Energy can neither be created nor destroyed, it can only be transformed from one form to another. The total energy before and after transformation remains the same.

A body of mass'm is raised to height b. At A its potential energy is maximum and kinetic energy is 0 as it is stationary.

When body is allowed to free fall and it reaches at B, h is decreasing hence potential energy decreases and V is increasing hence kinetic energy is increasing.

When the body is about to reach the ground level, h = 0, v will be maximum hence kinetic energy > potential energy

$\therefore$ Decrease in potential energy = Increase in kinetic energy

This shows the continual transformation of gravitational potential energy into kinetic energy. Potential energy + Kinetic energy = Constant (Mechanical energy)