Question

What is the biggest and smallest M can be and have the system remain motionless? (Diagram/work to follow)

Coefficient of static friction between the rope and the pulley is 0.2

Answer 1

My friend and I are working on this problem.

We are using the capstan equation: http://en.wikipedia.org/wiki/Capstan_equation
First we solved for T1 and T2 (T1 being tension on the left side; T2 being tension on the right)
T1 - 100 = 0, T1 = 100
Mg - T2 = 0

First case we considered: T2 is the pulling side
T2 = 100e^(0.2*pi) = 187.45, Upper bound for M = 18.745 kg

Second case: T1 is the pulling side
100 = T2e^(0.2*pi); T2 = 53.35, Lower bound for M = 5.335 kg

Any help would be greatly appreciated. Thank you! :)