**Example 5:** If the block weighs 100 lb
and μ_{s} = 0.3, determine the force P
needed for impending sliding. Use

b. θ = 0°

c. θ = -30°

d. Find P

**Solution:**

We begin by drawing the free-body diagram of the block and writing the two force equilibrium equations.

Since the condition is impending slipping, the friction force is related to the normal force as

Substituting for F and eliminating N gives

For the three specified angles, we get

a. θ = 30°, P= 41.9 lb.b. θ = 0°, P= 30.0 lb.

c. θ = -30°, P= 29.5 lb.

To find the minimum P, we need to first find the corresponding θ as

Substituting this value into the function P gives