roller coaster energy problem

Question

A roller coaster starts from rest at the top of a hill with 1000J of potential
energy. How much kinetic energy does it have?

• How much total mechanical energy?

 (KE + PEg + PEs)

• How much total, kinetic, and potential energy does the cart have after it has travelled halfway down the hill?
• How much total, kinetic, and potential energy does the cart have after it has travelled all of the way down the hill?

Answer 1

Kinetic energy is the energy of motion, and governed by the equation KE = 1/2 mv²

Potential energy is the energy stored in an object due to its having counteracted a force such as gravity. Gravitational potential energy is defined by the equation PE_g = mgh

 

At the beginning of this ride, the roller coaster is at rest, and no motion means KE = 0.

There are no springs or elastic objects described here, so PE_s will always be 0 for this problem.

 

The total mechanical energy is: KE + PE_g + PE_s = 0 + 1000 + 0 = 1000 J

 

If there is no friction or other non-conservative force, then the total energy will always be 1000 J. As the coaster moves down the hill, kinetic energy will increase, and potential will decrease, but the total will stay 1000 J.