Question

Question #10347

Answer 1

The mechanical energy of the ball, which is of course lost, is converted to thermal energy and is dissipated out. But it is still there in the Universe.

Explanation:

Energy Conservation Principle applies to all forms of energy - Mechanical, Electrical, Thermal ... etc.

This is often confused with the Mechanical Energy Conservation condition, which is restricted to only Mechanical energy which is the sum of kinetic energy and potential energy.
`E = K + U`

Forces can be classified into conservative forces and non-conservative forces.

Conservative Forces are those that conserve mechanical energy. Examples of conservative forces are Gravitational Force and Electrostatic Force.
When a force does work, it results in a change in kinetic energy. For conservative forces one can define a potential energy and the work done by these forces can be written as the negative of a change in potential energy.
`W_{con} = \Delta K = -\Delta U;\qquad \rightarrow \DeltaK + \Delta U = 0`

`\Delta E = \Delta K + \Delta U = 0`, which says the net change in mechanical energy is zero (Mechanical energy conservation)

So, mechanical energy is conserved ONLY when all the forces acting on the system are purely conservative forces. When you throw a chalk upwards, its speed decreases and eventually becomes zero. All its kinetic energy appears to have been lost. But it is not lost. It is converted to potential energy. The next instant the chalk starts coming down with ever increasing speed.

Non-Conservative Forces: Non-conservative forces, as their name indicates, do not conserve mechanical energy. We cannot define a potential energy for them. The kinetic energy lost in these cases is lost permanently to the surrounding. There is no way of regaining that, as in the case of conservative forces. Examples of non-conservative forces are friction, drag etc.

In the example you had mentioned, non-conservative forces are involved and so mechanical energy is not conserved. But what is dissipated out as thermal energy stays in the Universe and the total energy of the Universe is still the same.