## The Work Energy Principle

The Work Energy Principle is a version of the Law of Conservation of Energy. It takes into account that energy is not conserved, or at least that useful energy is not conserved. In almost any process in practice, work must be done to overcome friction, and this work that is done cannot be recovered.

The Work Energy Principle states:

Most of the time we want to minimise the work done since this usually represents wasted energy. Sometimes though, we want to maximise the work done, as when a plane lands and needs to decelerate, so undergoes air braking.

Example

In a ski-jump competition, a skier of mass 80 kg moves from rest at a point A on a ski-slope. The skier’s path is an arc AB. The starting point A of the slope is 32.5 m above horizontal ground. The end B of the slope is 8.1 m above the ground. When the skier reaches B, she is travelling at 20 m/s. The distance along the slope from A to B is 60 m. The resistance to motion while she is on the slope is modelled as a force of constant magnitude R newtons. By using the work-energy principle, find the value of R.

is not in fact a constant force. Because the speed and the direction of motion are changing all the time, the normal reactionis always changing, hence the frictional forceis always changing too.