Centripetal force motorcycle problem

[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
V_max = ____ 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 F_N, 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 F_N = mg ?

That would give me: F_C = mv² / r = mg - F_N = 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?

 

[Doc Al]

At the very top of the hill, we have mg pointing down towards the center of the circle. We also have F_N, 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.***

Looks good.

My question is: Doesn't F_N = mg ?

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

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

 

[bulbasaur88]

Zero! - thank you ))