Example 5: A 100-lb. block is in contact with an inclined plane as shown. Assuming the pulley is frictionless and that the coefficient of static friction between the block and the surface is 0.3, determine:

a. the minimum value of W to keep the block stationary,
b. the maximum value of W to keep the block stationary.
figure 1 figure 2
Free-Body Diagram of Weight

figure
Free-Body Diagram (Part a)
figure
Free-Body Diagram (Part b)

Solution:

Part a:

Equilibrium Equations:

equation (1)
equation (2)

From Eqn. (2), N=50 lb, and from Eqn. (1), T=71.6 lb.

Therefore, Wmin=71.6 lb to prevent the block from sliding down.


Part b:

Equilibrium Equations:

equation (3)
equation (4)

From Eqn. (4), N=50 lb, and from Eqn. (3), T=101.60 lb.

Therefore, Wmax=101.60 lb to prevent the block from sliding up.