# Circular Motion -> amusement park ride

by the_EVIL
Tags: circular motion, friction, gravity
 P: 37 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.