Great question!
Most roller coasters work by lifting the train of cars up a tall
hill using a metal cog or chain mechanism which isn't very fast. It
gets the cars up to the top, and the speed of the cars is very small
during the lifting process and at the top.
The total energy of the cars at the top then is just the
gravitational potential energy, which is proportional to the mass of
the cars and the height of the hill. The constant of proportionality is
the local gravitaitonal acceleration g, which is 9.81 meters per second
per second.
This potential energy can be exchanged for kinetic energy at the
bottom of the hill. The kinetic energy can be traded again for
gravitational potential energy when climbing the next hill. The total
energy never goes up, only down, due to frictional losses, and so the
maximum hill the cars can climb gets smaller and smaller. Putting a
bigger hill later on will only make the roller coaster cars roll back
down the way it came.
Some roller coasters actually do have hills the cars go up and
roll backwards along the track (I don't know if any like that are still
in operation). The one I rode once launched the cars very quickly out
of a horizontal station on the ground, sent them through a vertical
loop, and then up a steep hill. The cars then rolled backwards from the
hill, around the vertical loop backwards (!) then backwards through the
station (with passengers screaming, scaring the people waiting in
line), up another steep hill on the other side, and then back down to
the station where the brakes were applied. It was a lot of fun, but a
very short ride.
Tom J.
(published on 10/22/2007)
