Normal Force at the bottom of a Ferris Wheel

[AnkhUNC]

Homework Statement

A student of weight 678 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force N on the student from the seat is 565 N. (a) What is the magnitude of N at the lowest point? If the wheel's speed is doubled, what is the magnitude FN at the (b) highest and (c) lowest point?

Homework Equations

The Attempt at a Solution

So M = 678N, NTop = 565N. Fc = mg - Ntop = 6079.4
So Nbottom = Nbottom - mg = 6079.4 which leads Nbottom to = 12723.8 but this is incorrect. Where am I going wrong?

 

[Doc Al]

At the top, normal force, weight, and acceleration all point down:
N + mg = mv^2/r; so N = mv^2/r - mg

At the bottom, normal force and acceleration point up, but weight points down:
N - mg = mv^2/r; so N = mv^2/r + mg

 

[AnkhUNC]

I really don't need all that though do I? If I do how am I going to solved for v^2 or r? I only have one equation and two unknowns. At best I'd have Ntop+Nbottom = mv^2/r.

 

[Doc Al]

I really don't need all that though do I?

Yep. It's the easy way!

If I do how am I going to solved for v^2 or r?

No need to solve for those.

Examining those expressions for N, how does Nbottom compare to Ntop? (Hint: What's Nbottom - Ntop?)