# Test review

1. Dec 13, 2013

### Panphobia

1. The problem statement, all variables and given/known data

A man starts riding on a frictionless roller coaster track at initial velocity v$_{o}$. At point A the radius of the bend is r.

a) What is the maximum v$_{o}$ such that when the cart gets at point A it stays on the track?
b) Using you answer in a) what should h' be such that the cart only just makes it to point B?

2. Relevant equations

Ei = Ef
mv^2/r

3. The attempt at a solution
So this question was kind of bugging me, and I want to know if I got it right so for the a) part this is what I did firstly

mgh + (1/2)mv$_{o}$$^{2}$ = mg(2/3)h+1/2mv$^{2}$
v = $\sqrt{2gh/3 + Vo^2}$

and then since at point be its a circle and its looking for the max velocity until the normal force = 0 I did
mv^2/r = mg
v = $\sqrt{rg}$
then
rg = 2gh/3 + v$_{o}$$^{2}$
v$_{o}$ = $\sqrt{g*(r-(2/3)h)}$

THEN for b) I just used Energy again.
so
v = $\sqrt{rg}$
Ei = (1/2)mrg + mg(2/3)h
Ef = mgh'
h' = r/2 + 2h/3

2. Dec 13, 2013

### TSny

Looks good to me. :thumbs:

3. Dec 13, 2013

### Panphobia

Oh thank you so much!!!!!!!!!This was one of two questions I was unsure of so I just went with my gut on it.