Please help A light, inextensible cord passes over a frictionless pulley as show

Question

Please help

A light, inextensible cord passes over a frictionless pulley as shown in figure below. One end of the rope is attached to a block, and a force P is applied to the other end. Block A weighs 600 lb and block B weighs 1000 lb. The coefficient of friction between the blocks 0.33, and the coefficient of friction between block B and the floor is 0.25. Determine if the system would be in equilibrium for P = 400 lb. Determine the maximum P for which the system is in equilibrium. (Answer: P = 800 lb)

Explanation / Answer

Horizontal force due to 500 lb= 300 lb

Vertical force due to 500 lb= 300 lb

Net horizontal force=P-300

For equilibrium,

N=600+1000+400=2000 lb

maximum frictional force=0.25*2000=500 lb

P-300=frictional force

For P=400 lb

frictional force=100 lb < 500 lb

Hence,system is stationary

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For maximum P friction should be maximum

P-300=frictional force

P-300=500

P=800 lb

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