- #1

Anne Armstrong

- 11

- 1

## Homework Statement

In a loop-the-loop ride a car goes around a vertical, circular loop at a

__constant__speed. The car has a mass m = 260 kg and moves with speed v = 15 m/s. The loop-the-loop has a radius of R = 10 m. What is the minimum speed of the car so that it stays in contact with the track at the top of the loop?

## Homework Equations

a

_{c}=v

^{2}/r

F=ma

## The Attempt at a Solution

At the top of the loop, the forces acting on the car are F

_{gravity}, F

_{Normal}, and F

_{centrifugal}(I think). So I think the minimum speed would be one that made all the forces cancel to zero (aka, F

_{c}is just strong enough to counteract F

_{gravity}and F

_{Normal}). If that's true, then F

_{c}=F

_{N}+F

_{g}. Since F

_{c}=m*a

_{c}=v

^{2}/r , so far I have: m*a

_{c}=v

^{2}/r = m*g+m*g.

..but I don't think that makes sense... Is F

_{N}in this case equal and opposite to F

_{c}?