Please help... What are the main energy transfers that happen as a roller coaster cart travels along the track from the start of the ride to the end?

Answer 1

We start with the fundamental tenet that all closed system objects have some total energy TE that can be neither created nor destroyed. Which is to say TE = constant as long as we are not adding energy to it like through work or taking energy out of it like through friction.

So all objects can have a TE = PE + KE + QE = constant; where PE is potential energy, KE is kinetic energy, and QE is all other energies, like friction heat or work done on the object. So let's see what happens to the RC cart at its various waypoints along the tracks.

1. While it's picking up passengers, TE = PE + KE = 0, the cart has no energy. It's just sitting there not moving, waiting for you to climb aboard. And it's at the lowest point on the tracks; so there is no potential energy.

2. Now, as you are safely aboard, the cart is pulled up by the force F of some motor pulling it up to the (gasp) highest peak H on the track. So work energy QE is added to TE and we now have TE = QE = PE because all that work was transformed into potential energy TE = PE = mgH where m is the mass of the cart and you at the height H.

3. And over you go. At the peak H you and the cart have TE = PE = mgH potential energy, but for a moment no kinetic energy KE. But discounting friction losses, now that H is getting smaller as you plunge toward a low point h < H in the track the potential energy drops from PE = mgH to pe = mgh < mgH = PE. And there you are, since TE = constant = PE + ke if the PE is getting smaller, pe < PE, the kinetic energy ke must be getting bigger KE > ke to keep TE constant. That means the cart's speed is increasing as you fall to the bottom of the track's height. To use your term, the PE has been transferred to KE by the drop from that height H.

4. But you survive that breath taking plunge and because the cart has lots of KE at the bottom, it continues on past the h point and starts to climb back up to yet another high point. And because TE = KE + pe = constant as the cart and you go back up you are converting that kinetic energy into a new potential energy level; so at the second high point you have TE = PE and virtually no kinetic energy at the new peak. All this repeats for every plunge along the way.

In sum, the conversions (transfers) go something like:

TE = 0 + QE = PE + ke = pe + KE = PE + ke = ... = constant. Where we see the potential energy at each high point is traded off for kinetic energy at each low point. But, overall, the total energy stays constant when friction is discounted.