Question

Explain the work-energy theorem in case of an accelerating conservative force along with a retarding non-conservative force.

Answer 1

1. Consider an object dropped from some point at height h.

2. While coming down its potential energy decreases.

∴ Work done = decrease in P.E of the body.

3. But, in this case, some part of the energy is used in overcoming the air resistance. This part of energy appears in some other forms such as heat, sound, etc. Thus, the work is not entirely converted into kinetic energy.

In this case, the work-energy theorem can mathematically be written as,

∴ ∆ PE = ∆ K.E. + W_{air resistance}

∴ Decrease in the gravitational P.E. = Increase in the kinetic energy + work done against non-conservative forces.