Question

Two pulleys are joined together and share a common rotation point, the 4” diameter pulley has a 80 lb load on it. To be at equilibrium how much force needs to be applied to the 2 foot in diameter pulley?

Answer 1

Since both pulleys are joined together and shares a common rotation point, So to be at equilibrium, same torque should be applied on both pulley

Torque = r*F

r = lever arm = distance from rotation axis

F = perpendicular force applied

So,

r1*F1 = r2*F2

F2 = F1*(r1/r2)

r1 = distance of tension force from rotation axis on larger pulley = radius of pulley = 4''/2 = 2 inch

r2 = distance of tension force from rotation axis on smaller pulley = radius of pulley = 2 foot/2 = 1 foot = 12 inch

F1 = 80 lb, So

F2 = 80*(2/12)

F2 = 13.33 lb = force required for equilibrium