# Circular Motion -> amusement park ride

1. ### the_EVIL

4
Circular Motion --> amusement park ride

1. The problem statement, all variables and given/known data
A gravitron ride at a fair consists of a large 15m cylinder, which rotates about a vertically oriented axis of symmetry. The rider is held to the inner cylinder wall by static friction as the bottom of the cylinder is lowered. If the coefficient of static friction between the rider and the wall is 0.8, then how many revolutions per minute must the cylinder execute?

2. Relevant equations
Fc= m vsquared/r
Fg= mg

3. The attempt at a solution
I don't really know where to start on this one. all i know is that i have to set up an equivalency, and that mass will somehow end up canceling out. Please help me out here, it would be greatly appreciated! Thanks in advance!!!

2. ### silentwf

37
Re: Circular Motion --> amusement park ride

You should always start with a free-body diagram with all the forces on it.
Here's a free body diagram (sorry about the suck-ish quality)

You've basically got all the forces, you're just missing the friction equation, which would be
$$F_{f} = \mu N$$

So you'd set your equations like this:
$$\stackrel{+}{\rightarrow}\Sigma F_{x} = 0 \Rightarrow N - F_c = 0 \Rightarrow N - \frac {mv^2}{r} = 0 \Rightarrow N=\frac {mv^2}{r}$$
$$\stackrel{+}{\uparrow}\Sigma F_{y} = 0 \Rightarrow F_{f} - F_{g} = 0 \Rightarrow \mu N - mg = 0 \Rightarrow \mu N = mg$$

Now solve the two equations, substituting N into the second equation
$$\mu \frac {mv^2}{r} = mg \Rightarrow v = \sqrt{\frac {gr}{\mu}}$$

And so now you've got "v". The rest shouldn't be hard, try it first.

Last edited: Nov 7, 2009
3. ### the_EVIL

4
Re: Circular Motion --> amusement park ride

Thanks for the reply! I guess that problem wasn't all that bad at all!

4. ### silentwf

37
Re: Circular Motion --> amusement park ride

No prob. Just remember to start with free body diagrams with each physics equation, they're pretty much a must.