# Homework Help: Rotational motion roller coaster problem

1. Oct 21, 2012

### joe426

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

2. Relevant equations
ƩF = ma = (mv2) / r

3. The attempt at a solution

For part A:
Fn - Fg = (mv2) / r
Fn = ((mv2) / r ) + mg
Fn = (500x20^2) / 10 + 500x9.8
Fn = 24900

This seems too high to be true. But I'm unsure of what I did wrong. I know the normal force is the force of which the track is acting on the car.

For part B:
I think it is just 20m/s but I'm not sure. I know an object traveling in a circle has the most speed when it's at the bottom of the circle.

Thanks for the help in advance!

2. Oct 21, 2012

### TSny

Part A looks correct.

For part B, set up equations similar to part A and think about what happens to the value of Fn when the vehicle leaves the track.

3. Oct 21, 2012

### joe426

Hmm...

I think Fn would equal 0 when the vehicle leaves the track. So I use the same equation as part A except I set Fn to 0 and solve for v?

4. Oct 21, 2012

### TSny

Yes Fn will be zero. Good. But if you use the same equation you will end up taking the square root of a negative number (oops). Set up a correct similar equation using a new free body diagram for point B

5. Oct 21, 2012

### joe426

Fg - Fn = (mv2) / r
(mgr / m)1/2 = v
(500x9.8x15 / 500)1/2 = 12.1

V = 12.1

6. Oct 21, 2012

### TSny

Good! (minus 1 point for not including units )

7. Oct 21, 2012

### joe426

Haha thank you so much! I got the units on my paper :P