1. A roller coaster car starts from rest and rolls down a frictionless track, reaching speed fv at

Question

the bottom.
a. If you want the car to go two times as fast at the bottom, by what factor must you
increase the height of the track?
b. Does your answer to part (a) depend on whether the track is straight or not? Explain.

2. You release a frictionless cart at the top of each of the 2 ramps. On Ramp B, the cart is
released from rest, but on Ramp A the cart is pushed at the top so that it has some initial
velocity. The ramps have the same height as each other at start and finish. One has a small
bump up then down just before the end. The other has a small bump down then up. Which cart has the larger speed at the finish? Why?

Answer 1

1. Twice the speed requires 4 times the kinetic energy. What does that tell you about the height or the top of the track?

2. Forget about the bumps. The car that starts out with kinetic energy (from the push) has more kinetic energy at the bottom.