Principle: Decrease in the potential energy due to work done by a conservative force is entirely converted into kinetic energy. Vice versa, for an object moving against a conservative force, its kinetic energy decreases by an amount equal to the work done against the force.
Work-energy theorem in case of a conservative force:
1. Consider an object of mass m moving with velocity u experiencing a constant opposing force F which slows it down to v during displacement s.
2. The equation of motion can be written as, v2 – u2 = -2as (negative acceleration for opposing force.)
Multiplying throughout by \(\frac{m}{2}\), we get,
3. According to Newton’s second law of motion,
F = ma … (2)
4. From equations (1) and (2), we get,
\(\frac{1}{2}\)mu2 – \(\frac{1}{2}\)mv2 = F.s
5. But, \(\frac{1}{2}\)mv2 = Kf = final K.E of the body,
\(\frac{1}{2}\)mu2 = Ki = initial K.E of the body.
and, work done by the force = F.s
∴ work done by the force = kf – ki
= decrease in K.E of the body.
6. Thus, work done on a body by a conservative force is equal to the change in its kinetic energy.
