13. The coefficient of static friction between all the surfaces is, A random force P ~ N(15, 1²) N is applied to the wedge, and the weight of the block is W ~ N(10, 0.5²) N due to the manufacturing uncertainty. If P and W are independent, what is the probability that the block will be lifted.

Solution

System:

(1)

(2)

Wedge:

(3)

(4)

From Eqns. (3) and (4), we obtain

(5)

From Eqns. (1) and (2)

(6)

Combining Eqns. (5) and (6), we have

Therefore, we have

Thus, we have P ~ N(13.46, 0.673²) N.

Since the actual random force P_s follows ~ N(15, 1²) N, we construct . Therefore, the probability that the block will be lifted is :

Ans.