Find the minimum weight to keep equilibrium, Mechanical Engineering

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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.

 

1016_Find the minimum weight to keep equilibrium.png

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  = eµθ

W1/T2  = e(0.25)(P)

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


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