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A) The least Kinetic Energy (KE), and the Greatest Potential Energy (GPE), is at point X based on the the Law of Conservation of Energy as the GPE is the greatest at the highest point.
B ) Comparison of PE and KE of points V and Y.
Assumptions:
- First we must assume that the mass of any riders on the carriage is constant all the way around.
- We do not know the radius of the wheel nor the height of points V and Y and thus are making the assumption that the difference in height between V and Y is material (Y be materially higher than V).
Answers:
PE = mgh (mass * gravity * height) where height is distance through which the mass will fall. Thus by definition the PE at point Y is greater than the PE at point V. The inverse is true for KE - the KE is greater at point V.
Using KE to answer ....
We can also answer this question using the KE = (1/2)mv^2 formula which requires us to make an additional assumption.
Assumption: We assume that to start the carriage there is significant work (electrical) done to drive the carriage up to point X. However, at point Y, we assume the carriage is already decreasing in speed. Coming down, we assume the carriage has a high speed at point V, or at least greater speed at point V.
Based on the above assumption, ie the carriage has higher speed at point V, therefore the KE is greater at point V.
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