Please help A 20-lb homogeneous box has tipped and is resting against a 40-lb ho
ID: 1862307 • Letter: P
Question
Please help
A 20-lb homogeneous box has tipped and is resting against a 40-lb homogeneous box as in figure shown below. The coefficient of friction between box A and the floor is 0.7, and between box B and the floor is 0.4. Consider the contact surface between the two boxes as smooth and determine if the boxes are in equilibrium. 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
1.
Consider box B,
For equilibrium,
N(from floor)=40 lb
max f= 0.4*40=16 lb
N(from box A)=f
Consider box A,
For eqilibrium,
N(from floor)=20 lb
max f= 0.7* 20=14 lb
N(from box B) = f
Taking moment about the point of contact with floor,
20*12*cos 30 =f* 24* sin 30
required f=10*cot 30=17 lb
Since required f=17 lb > 14 lb(max frictional force)
The boxes cannot be in equilibrium.
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2.
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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