3.6 Problem Solving

Conservation of Energy

Roller Coaster

roller_coaster

A roller coaster ride is a thrilling experience which involves a lot of physics. A great tool for the analysis of a roller coaster is the conservation of energy.

Once the cars are lifted to the top of the hill, gravity takes over and the remainder of the ride is an experience in energy transformation.

As the cars descend they lose much of this initial potential energy (as they lose height). While losing potential energy, the cars subsequently gain kinetic energy. 

roller_coaster

Test your knowledge by trying the problem below (assume no heat loss).

A. The initial build-up of energy in a typically a result of:

A. Kinetic energy due to falling down a hill.
B. Work done to pull the coaster to the top of a hill.
C. Gravitational potential energy in a loop.

B. Once at the top of a hill, a roller coaster has:

A. Gravitational potential energy.
B. Work done by a hill.
C. Kinetic energy.

C. Rolling down the first hill allows:

A. Kinetic energy to convert to potential energy.
B. Work done to the coaster.
C. Potential energy to convert to kinetic energy.

D. The maximum kinetic energy is experienced at:

A. Half-way down the first drop.
B. At the bottom of the first drop.
C. At the top of the first loop.

E. At the top of the first loop, the coaster has:

A. Only kinetic energy.
B. Only potential energy.
C. Both kinetic and potential energy.

F. At the top of the smaller loop (as compared to bigger one):

A. Same energies.
B. More potential energy and less kinetic.
C. More kinetic energy and less potential.

Energy Reality
The above questions give a good sense on how energy conversions make for a fun ride on a roller coaster.  On a real roller coaster, energy is continuously being lost to heat so that they total energy at the end is less than that at the beginning.