Theme Park Rides - Roller Coaster and Free fall - can anyone explain the detailed physics that can be applied

Question

I am looking for energy changes and Newton's Laws

Answer 1

Assuming a frictionless track (and no air friction, too) the energy is perfectly conserved, and any question you encounter will deal with potential energy or kinetic energy.
PE = mgh
KE = .5mv^2
If you have a roller coaster at height h, and it falls x meters, it will have a potential energy of PE = mgx and a simultaneous kinetic energy of KE = mg(h-x) plus whatever it started out with.
Think of the energy as a pie chart - the chart isn't going to get any bigger without outside forces, so the distribution of the energy within the chart will be balance.
Free fall on a roller coaster track involves the same concepts of energy, no matter what the angle or the time, it just depends how much energy the thing started out with and how far away from the ground it is. I guess free fall helps reinforce the idea that the track is frictionless.

I'm not sure what you mean by Netwon's laws, other than that the energy conservation is supported by 'any object in motion will remain in motion unless a force acts upon it'...
...and of course the sum of the forces equals ma. That's always a useful one.
Basically, there are no outside forces acting on most roller coasters. After the energy put INTO the roller coaster by WORKING to raise the coaster to a desired height (PE = mgh) at that point, it will continue to transfer that to kinetic energy until all the PE has been turned into KE at ground level.