Rotational motion roller coaster problem

[joe426]

Homework Statement

Homework Equations

ƩF = ma = (mv²) / r

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!

 

[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.

 

[joe426]

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.

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?

 

[TSny]

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?

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

 

[joe426]

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

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

V = 12.1

 

[TSny]

Good! (minus 1 point for not including units )

 

[joe426]

Good! (minus 1 point for not including units )

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