Belts & Friction: 25 ld-ft Torque, 6 in. Drum, 0.30 µ

[GSXR1000]

Homework Statement

A flat belt is used to transmit the 25 ld-ft torque developed by an electric motor. the drum in contact with the belt has a diameter of 6 in., and the coefficient of static friction between the belt and the drum is 0.30. Determine the minimum allowable value of the tension in each pert of the belt if the belt is not to slip.

Homework Equations

T1=T2e^(µß)
ß=2.79 rad
µ=0.30

The Attempt at a Solution

please see attached for attempts at solution

 

[GSXR1000]

I think that my assumption that force of friction (Ff ) is equal to µdN is wrong. I am not sure how to determine what dN is in this problem. If anybody has suggestions it would be greatly appreciated.

 

[GSXR1000]

Ok I have realized that the motor produces torque M and ΣM about G =0, T2*r-T1*r=0 (See attachment in post #1 for FB)

If you set M=T2*r-T2*r this will be when incipient slipping of the belt is about to occur. Using this with T1=T2*e^(µß) we have two equations and two unknowns. Solve for the unkowns!