Find out the largest torque:

A flat belt is taken in use to transmit torque from pulley A to pulley B as shown in figure given below. The radius of each pulley is 50mm and coefficient of friction is 0.3. Find out the largest torque that can be transmitted if the allowable belt tension is 3KN.

Sol: Radius of each pulley = 50mm, R1 = R2  = 50mm

R₁ = Radius of driver = 50mm

R₂ = Radius of driven = 50mm

θ = Angle of contact= 1800 = p,

µ = Coefficient of friction = 0.3

T₁ = Allowable tension = 3KN 

T₁  greater than T₂

Using relation T₁/T₂  = e^µθ

By putting all the value,

3/T₂  = e(0.3)(p)

On solving T₂  = 1.169KN                                                                       .......ANS

Since Radius of both pulley is same;

So, Torque exerted on both the pulley is same and

= (T₁-T₂).R₁  = (T₁-T₂).R₂

By putting all the value we get,

(3 - 1.169) X 50 = 91.55 KN-mm                                                    .......ANS