Question

A person is riding on a Ferris wheel of radius R. He starts at the lowest point of the wheel. When the wheel makes one complete revolution, is the net work done by the gravitational force positive, zero, or negative?
Do you need to know how the speed of the person changed before you can answer the question?

Suppose he started at the highest point of the wheel. What is the net work done by the gravitational force when he reaches the lowest point?

Answer 1

zero. potential energy in gravity is m g h
If you come back to the same h, no net work was done.
(you had to put work in going up, you took it out coming down.)

In the second part it is m g htop -mghbottom
= m g (2R)