True or false

Question

Consider a simple frictionless roller-coaster. It begins at x = 0, at a height of y = H. Then it drops into a dip, reaching a minimum at x = 100, with zero height (y = 0). Finally, it goes back up at x = 200, but only reaches a height of y = H/2. Assume the roller-coaster car starts from rest at x = 0. Which of the following statements are true?

1)At the end, at x = 200, the car has only gravitational potential energy

2)The car's maximum kinetic energy occurs in the dip, at x = 100

3)Mechanical energy of the roller-coaster is conserved because the normal force does not do work

4)In the middle of the dip, at x = 100, the car has only kinetic energy

5)At the end, at x = 200, the car has more total energy than it began with

Answer 1

1) true if stopped

2) yes max Ke at min height

3) Huh? It is true the normal force does not do work, but the friction force does so mechanical energy is LOST to heat. That is why it ends up lower and has to be towed back up to the start.

4) Well, this is true only if you define zero potential level at the dip, at y = 0

5) of course not.