(This is a high school–level problem, so no air resistance, etc.)
A person is sitting on a Ferris wheel of radius $r$ moving at a constant speed. What is the force from the seat acting on the person when the person is at the bottom of the ride? When the person is at the top?
My attempt at a solution:
When the person is at the top, the forces acting on the person are his weight and an equally large normal force from the seat pushing him upwards. Since the problem involves uniform circular motion, at the top of the ride, there must be some force pulling the person towards the center of the circle with magnitude $\frac{mv^2}{r}$.
The cause of this centripetal force must be the seat belt on the person, pulling him downwards?
When the ride is at the bottom, the normal force from the seat both counteracts the weight of the person and applies a centripetal force of $\frac{mv^2}{r}$ upwards.
Centripetal force kind of confuses me since my professor says a proof of it is beyond the scope of the course.
Best Answer
Assuming that you mean a "ferris" wheel:
In a ferris wheel, $\frac{m*v^2}{r}$ is very small, because ferris wheels move slowly.
Also, on the wheel, all of the cars with people remain upright. This means that the force of gravity is always pulling downwards on people as they ride.
So, there are three cases that you can look at to explain this:
In this case, the centripetal force (which is required to keep you moving within the circle is provided by gravity. Gravity pulls you down towards the center of the wheel.
In this case, the force provided is an upward force provided by the metal structure of the wheel. The metal beams that support the car as it travels along at this point.
In this case, the force towards the center of the wheel is provided by a combination of the structure of the wheel (if you are on the bottom/side, and gravity if you are more on the top)