A tension Q is maintained in the cord shown as it passes over pulleys of diamete

Question

A tension Q is maintained in the cord shown as it passes over pulleys of diameter d. (a.) Neglecting the weight of the rod and pulleys, express the magnitude of the force P corresponding to equilibrium in terms of Q, a, d, and theta. (b) Knowing that Q = 10 lb, a = 5 in, d = 0.8 in, and , theta=30 degrees, determine the magnitude P.

A tension Q is maintained in the cord shown as it passes over pulleys of diameter d. (a.) Neglecting the weight of the rod and pulleys, express the magnitude of the force P corresponding to equilibrium in terms of Q, a, d, and theta. (b) Knowing that Q = 10 lb, a = 5 in, d = 0.8 in, and , theta=30 degrees, determine the magnitude P.

Explanation / Answer

To be in equilibrium the moment about A as to be zero (taking anticlockise moment as positive)

Net moment

-Q*a*cos(theta)+2Q*a*cos(theta)-P*3asin(theta) = 0

Qacos(theta) = 3Pa*sin(theta)

P = Q cot(theta)/3 = 10 *cot(30) = 17.32 lb

=

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