The coefficients of friction are µs = 0.40 and µk = 0.30 between all surfaces of contact. Determine the smallest force P required to start the 30-kg block moving if cable AB(a) is attached as shown, (b) is removed.

Step: 1

Given

Coefficient of static friction,

Coefficient of kinetic friction,

Step: 2

Let us draw the free-body diagram of the system.

Step: 3

a)

First apply the equilibrium condition,

Now,

Apply the equilibrium condition,

Step: 4

Let us draw the free-body diagram of the second block.

Step: 5

Apply the equilibrium condition,

Now,

Step: 6

Apply the equilibrium condition,

Therefore, the force is

Step: 7

b)

Without the cable, both blocks will stay together and motion will impend only at the floor.

Now, apply the equilibrium condition,

Now,

Step: 8

Apply the equilibrium condition,

Therefore, the force is

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