Rotational motion and tangential speed?

[yramos9]

Homework Statement

A 919 kg rollercoaster is about to go up a hill that acts as the top of a circle 16.21m in diameter. What is the fastest that car can move (in m/s) without leaving a track?
known:
mass: 919 kg
diameter: 16.21
radius: 8.105

Homework Equations

Vt=r\omega
\omega=\theta/time

The Attempt at a Solution

i have no idea how to work this out without knowing the time or speed or somekind of time measurement. Is there another way to solve this?

 

[Pythagorean]

centrifugal force

force balance

free body diagram

 

[yramos9]

huh??

 

[Pythagorean]

Draw a free-body diagram of the cart with centrifugal force pulling it up and gravity pulling it down. The sum of the forces on the cart should be zero in the radial direction (since that's the direction for which you don't want motion). Centrifugal force should be a function of tangential velocity, which is the velocity in question.

What level of physics is this? Gravity would realistically be a function of the angle about the center of the circle and only be exactly g when the cart is exactly on the tip of the half-circle. But you could probably neglect this if it's an introductory physics course.

 

[yramos9]

this is 11th grage physics pre-ap.. i don't think I've learned what youre trying to teach me.

 

[ideasrule]

When gravity can provide the centripetal acceleration required to keep the roller coaster on the track, the coaster doesn't fly off. Otherwise, it does. When does gravity exactly equal the required centripetal force? (Hint: F=ma)