The bicycle and the hill

Neither kind of mechanical energy is trapped where it is. A cyclist freewheeling over a hill turns one into the other and then back again, without pedalling once.

Figure to be added

Figure 18.8 — a cyclist shown at three points on a small hill: approaching the foot on the level road, at the summit, and rolling down the far side.

Going up

A bicycle is ridden quickly along a level road and then reaches the foot of a small hill. The rider stops pedalling. The speed the bicycle already had may still carry it to the top — but as it climbs, its speed falls away steadily.

What is happening to the energy

Kinetic falls → Height rises → Potential rises

At the summit the kinetic energy has fallen to a minimum and the potential energy has risen to a maximum.

Coming down

If the bicycle has managed to pass the summit, the rider can travel down the far slope without pedalling at all — and as it descends, its speed steadily increases again.

What is happening to the energy

Height falls → Potential falls → Kinetic rises

By the bottom the bicycle is moving quickly again, and most of the potential energy is gone.

The conversion runs both ways

E_k → E_p → E_k

Kinetic energy can be converted into potential energy, and potential energy back into kinetic energy. Nothing is being created or destroyed on that hill — the same energy is simply changing which of the two forms it is held in.