Find an expression for the power developed at the given rotation rate

[hi im nimdA]

Homework Statement

A Prony brake is a device that measures the horsepower of engines. The engine rotates a shaft of radius R at N rev/sec. The rotation is opposed by a belt which is attached to two tension measuring devices, such as springs. (a) What is the force of friction acting on the engine? (b) Obtain an expression for the power developed at the given rotation rate.

Relevant Equations

T=(2 pi R)/v , F=(m v^2)/R, P=Fvcos(theta)

So for part (a), I used the fact that 1/N = the period = T. I solved for the velocity, where i got v=2πRN. I plugged that v into F=(m v^2)/R, which is the centripetal force, but also the force of friction. My answer to part (a) is 4(π^2)mR(N^2).

I'm a bit confused on part (b). I know that P=Fvcos(theta), but since v acts at a tangent and F acts towards the center, my theta will be 90, and
cos 90 = 0, so I'm getting 0 for the power (this doesn't make sense). What am I doing wrong?

 

[haruspex]

into F=(m v^2)/R, which is the centripetal force, but also the force of friction.

The belt is not moving, and the drum is rigid, so I'm not sure what mass your m is, but centripetal force cannot be of interest. And it certainly does not equal the force of friction.
What torques are being exerted on the drum?