Name: Conservation of Mechanical Energy
Uploaded: 2019-07-19
Duration: 5 min 12 s
Description: When a body falls from a height towards the ground, its potential energy decreases but not the total mechanical energy. Let us understand this using data.

Question

State and prove law of conservation of energy in case of a freely falling body.

Accepted Answer

The total mechanical energy of a system is conserved if the forces doing work on it are conservative. The force acting on a freely falling body is the gravitational force, which is a conservative force. Hence, its total mechanical energy is conserved.

Consider a ball of mass $(m)$ , falling from a height $(h)$ above the surface of the earth at point A. As it is dropped from point A, it reaches point B after falling through a distance $x$ . Finally, it reaches point C at the ground.

At point A:

The velocity of the ball $(u_{A}) = 0$

Kinetic energy $(K_{A}) = 0$

Potential energy $(U_{A}) = m g h$

Total mechanical energy $(T_{A}) = m g h + 0 = m g h$ .......(i)

At point B:

The velocity of the ball $(v_{B}) = \sqrt{2 g x}$

Kinetic energy $(K_{B}) = \frac{1}{2} m \times 2 g x = m g x$

Potential energy $(U_{B}) = m g (h - x)$

Total energy $(T_{B}) = m g x + m g (h - x) = m g h$ ......(ii)

At point C:

The velocity $(v_{C}) = \sqrt{2 g h}$

The kinetic energy $(K_{C}) = \frac{1}{2} m \times 2 g h = m g h$

Potential energy $(U_{C}) = 0$

$(T_{C}) = m g h + 0 = m g h$ .....(iii)

From (i), (ii) and(iii), it is clear that total mechanical energy is constant throughout its journey. At the highest point A, it possesses only potential energy and reaching the ground at point C, all its potential energy is converted into kinetic energy.

State and prove law of conservation of energy in case of a freely falling body.

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