# Centripetal Force of an amusement park ride

## Homework Statement

In an amusement park ride, passengers stand inside an 8m radius cylinder. Initially, the cylinder rotates with its axis oriented along the vertical. After the cylinder has acquired sufficient speed, it tilts into a vertical plane, that is, the axis tilts into the horizontal. Suppose that, once the axis has tilted into the horizontal, the ring rotates once every 4.5 seconds. If a rider's mass is 40kg, with how much force does the ring push on her at the top of the ride?

## Homework Equations

F = ma, W = mg, Centripetal Force = mvv/r

## The Attempt at a Solution

Since it's asking for the force that the wall of the ride is pushing on the person, shouldn't it just be mvv/r? So the answer is about 620N? Yet the correct answer is mvv/r - mg, which is 230N.
Why is that? Why does gravity matter if the question is asking "how much force does the ring push on her at the top of the ride?

Simon Bridge
Homework Helper
It's a question of semantics - how hard the ring pushes on the person is the force felt by the person is what they are after. In general, "how hard you get pushed" refers to the net force - what you get pushed by is whatever is in the direction the net force appears to come from.

So, the correct answer should be mvv/r? Not the net force, since the question is asking how hard the ring pushes on her, not how hard does the person get pushed? Do you get 620N if you do mvv/r?

also, v = wr

Simon Bridge
Homework Helper
That's what I mean - it's semantics: you have to be able to tell when the question is using sloppy everyday language and when it is using careful physics jargon. In this case it was sloppy everyday ... they wanted the net force.

It's very borderline though.
If I were you I'd complain: it is not clear from the wording if the question wants the effective force from the ring or if it wants the contribution to the effective force from the ring. i.e. is the question to be answered from an inertial or a non-inertial POV?

If you look at it when the person is on the other side of the ring, then they feel the ring exert a stronger force - part of the stronger force comes from gravity.

I think the writer was relying on the shift to talking about the force that the person feels would clue the reader to realizing that the persons POV was needed.

haruspex
Homework Helper
Gold Member
So, the correct answer should be mvv/r?
No. How hard the ring pushes on the person is the same as how hard the person pushes on the ring - action and reaction are equal and opposite. Pace Simon, but I see no sloppiness here.
If the ring pushes on the person with force F, what is the sum of the vertical forces on the person? What is the person's vertical acceleration? What equation does that give you?

Simon Bridge