sample problem for the law of conservation of energy?

Question

I dont understand

Answer 1

Energy cannot be Created or Destroyed (Current level of understanding of Physics)

Assume a Simple System (Fake, ideal world situation, aka Cartoon)

When a Body takes in a source of Energy to do work.
Assume the Energy is used up completely
- Some of the Energy is used to do the Work,
- Some to over come the various friction/resistance in and outside the Body, while the work is been carried out. This Energy can manifest itself as either Heat/Sound and even Light.

Sum all the small bits of Energy (Work Done), Friction,/Resistance (Heat/Sound, Light) the Total is Equal ti the Energy Taken In.

Back to the Real World.
While it is easy to measure Work done. Measuring the various small bits Friction,/Resistance, is difficult. Thus it is common to get a figure less that the amount put in.

Answer 2

I'm not sure what the question is but think roller coaster and ignore friction.

At the top, the train is barely moving so it has no kinetic energy but does have potential energy. As it rolls down the hill, it gains speed and hence kinetic energy, but it loses potential energy because it is lower.

At the bottom, it has converted all (assuming no friction) of its potential energy to kinetic energy and is going at its maximum speed.

Now as it climbs the next hill, it converts that kinetic energy back to potential energy, losing speed as it does so. If there were no friction, it would convert all the kinetic energy to potential energy and end up at exactly the same height as it started.

So, if you want a sample problem, how about this:

"The roller coaster hill is 100 feet high. Assume the wheels have no mass; there is no friction; you're at the surface of the Earth; etc. How fast is the train moving at the bottom? How fast is the train moving half way (50 feet) up or down?