Find the minimum weight to keep equilibrium:

A belt supports the two weights W₁ and W₂ over a pulley as shown in the figure given below. If W₁ = 1000N, find the minimum weight W₂  to keep W₁  in equilibrium. Assume that pulley is locked and µ

= 0.25.

Sol: Let the tensions in belt be T₁ and T₂ as shown, since weight W₂ checks the tendency of weight W1 to move down, tension on the side of W₁ is bigger.

That is, T₁>T₂

µ = 0.25, q = P, W₁  = 1000N

By using the relation Ratio of belt tension

=     T₁/T₂  = e^µθ

W₁/T₂  = e(0.25)(P)

By solving,         T₂  = W₂  = 456N                                                                           .......ANS