Thermal Energy from Friction on a Rope?

Question

A capstan is a rotating drum or cylinder over which a rope or cord slides to provide a great amplification of the rope's tension while keeping both ends free
http://session.masteringphysics.com/problemAsset/1006856/15/36898.jpg
Since the added tension in the rope is due to friction, the capstan generates thermal energy.

A)
If the difference in tension (T_0-T') between the two ends of the rope is 520 N and the capstan has a diameter of 10.0 cm and turns once in 0.90 seconds, find the rate P_thermal at which thermal energy is being generated.
Give a numerical answer, in watts, rounded to the nearest 10 W.

B)
If the capstan is made of iron (with a specific heat capacity C=470 J/(kg C) and has a mass of 6.00 kg, at what rate dTheta/dt does its temperature rise? Assume that the temperature in the capstan is uniform and that all the thermal energy generated flows into it.

Note that Theta is a temperature.
Give answer in degrees Celsius.

Answer 1

A) Power P is a product of force F applied to a speed v. We have
P=Fv
F=T=540N
v= piD/t
P=F pi D/t= 540 pi 0.1/0.9
P=190 W

B) Q=mC(T2-T1)
Heat rise per second
Q/t=P=mC(T2-T1)/t

(T2-T1)/t= P/(mC)=190/(6.00 x 470)=
(T2-T1)/t=0.0674 degC/sec

Answer 2

Rope Capstan

Answer 3

181.51424220741027600006