A motor drags the roller-coaster car to the top of the first hill. The car runs down the other side, picking up speed as it goes (see Figure 5.11). It is moving just fast enough to reach the top of the second hill, slightly lower than the first. It accelerates downhill again. Everybody screams!

The motor provides a force to pull the roller-coaster car to the top of the hill. It transfers energy to the car. But where is this energy when the car is waiting at the top of the hill? The car now has gravitational potential energy; as soon as it is given a small push to set it moving, it accelerates. It gains kinetic energy and at the same time it loses g.p.e.

As the car runs along the roller-coaster track (Figure 5.12), its energy changes.
1) At the top of the first hill, it has the most g.p.e.
2) As it runs downhill, its g.p.e. decreases and its k.e. increases.
3) At the bottom of the hill, all of its g.p.e. has been changed to k.e. and heat and sound energy.
4) As it runs back uphill, the force of gravity slows it down. k.e. is being changed to g.p.e.
Inevitably, some energy is lost by the car. There is friction with the track and air resistance. So, the car cannot return to its original height. That is why the second hill must be slightly lower than the first. It is fun if the car runs through a trough of water, but that takes even more energy, and the car cannot rise so high. There are many situations where an object’s energy changes between gravitational potential energy and kinetic energy. For example:
- a high diver falling towards the water – g.p.e. changes to k.e.
- a ball is thrown upwards – k.e. changes to g.p.e.
- a child on a swing – energy changes back and forth between g.p.e. and k.e.