Two 8-kg blocks A and B resting on shelves are connected by a rod of negligible mass. Knowing that the magnitude of a horizontal force P applied at C is slowly increased from zero, determine the value of P for which motion occurs, and what that motion is, when the coefficient of static friction between all surfaces is (a) µs = 0.40, (b) µs = 0.50.

Step: 1

Draw the free body diagram of the system.

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Step: 2

a)

Calculate the friction force at block A,

Here, coefficient of static friction is, normal reaction at block A is

Substitute, 0.4 for

Calculate the friction force at block B,

Here, normal reaction at block B is Substitute, 0.4 for

Calculate the weight of the block,

Step: 3

The equilibrium condition of forces in y-direction

Take the condition of equilibrium

Substitute, for W

Step: 4

The equilibrium condition of forces in x-direction

Substitute for

Step: 5

Take the moment about the point B

Assume that the moment in the anticlockwise direction is positive.

So,

Therefore, the system slides

The load P,

b)

Calculate the friction force at block A,

Here, coefficient of static friction is, normal reaction at block A is

Substitute, 0.5 for

Calculate the friction force at block B,

Here, normal reaction at block B is Substitute, 0.5 for

Step: 6

The equilibrium condition of forces in x-direction

Substitute for

Step: 7

Take the moment about the point B

Assume that the moment in the anticlockwise direction is positive.

, there will be uplift and rotation about B.

Step: 8

For, calculate the value of P.

Take the moment about the point B

Assume that the moment in the anticlockwise direction is positive.

Therefore, the system rotates about B and the load, P is