Find the minimum weight to keep equilibrium:
A belt supports the two weights W_{1} and W_{2} over a pulley as shown in the figure given below. If W_{1} = 1000N, find the minimum weight W_{2} to keep W_{1} in equilibrium. Assume that pulley is locked and µ
= 0.25.
Sol: Let the tensions in belt be T_{1} and T_{2} as shown, since weight W_{2} checks the tendency of weight W1 to move down, tension on the side of W_{1} is bigger.
That is, T_{1}>T_{2}
µ = 0.25, q = P, W_{1 } = 1000N
By using the relation Ratio of belt tension
= T_{1}/T_{2} = e^{µθ}
W_{1}/T_{2} = e(0.25)(P)
By solving, T_{2} = W_{2} = 456N .......ANS