# Centripetal force motorcycle problem

1. Aug 24, 2011

### bulbasaur88

A motorcycle is traveling up one side of a hill and down the other side. The crest of the hill is a circular arc with a radius of 45.0 meters. Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road.

Will somebody sound this problem out with me please? I think I am missing an important concept that I am missing...

Given
r = 45 m
Vmax = ____ m/s

What I Gather
We do not want the motorcycle to lose contact with the road, especially at the zenith.

At the very top of the hill, we have mg pointing down towards the center of the circle. We also have FN, which points up and away from the center of the circle.

***I hope the above forces have been set up correctly in my free body diagram.***

My question is: Doesn't FN = mg ?

That would give me: FC = mv2 / r = mg - FN = 0

????? I get lost here...I am sure there is something wrong with either my FBD or my reasoning. Can I get a hint please?

2. Aug 24, 2011

### Staff: Mentor

Looks good.

No. If FN = mg, then the net force on the motorcycle would be zero--no acceleration at all.

Hint: What must FN be when the motorcycle just loses contact with the road?

3. Aug 24, 2011

### bulbasaur88

Zero!!! - thank you ))