Maximum velocity at the top of a roller coaster?

[pcandrepair]

Homework Statement

A roller-coaster car has a mass of 509 kg when fully loaded with passengers.
-The radius of the circle is 15m. (See picture below)

What is the maximum speed the vehicle can have at point B and still remain on the track?
_________m/s

Homework Equations

Sum of forces in the radial direction = -m(v^2)/R

The Attempt at a Solution

There would be a normal force pointing up and mg pointing down

 

[Doc Al]

There would be a normal force pointing up and mg pointing down

Right. And what will the normal force become just before the car leaves the track? Use that to calculate the maximum speed. (You already know the radius of the curve at point B.)

 

[pcandrepair]

So I set the normal force equal to zero just before it would leave the track and use..

normal - mg = m(v^2)/r masses would cancel.
0 + g = (v^2)/r
gr = (v^2)
sqrt(gr) = v

when i take the sqare root of 9.8*15 I'm getting 12.1244m/s which sounds reasonable.

 

[Doc Al]

Sounds good to me.