15. A normally distributed force P~ N(30,2²) N is applied perpendicularly to a beam which weights m ~ N(5, 0.2²) kg, where P and m are independent. Determine the probability of slipping if the coefficient of static friction between the beam and the ground at A is.

Solution

According to the force equilibrium, we have

Then, we have

Where, the frictional force is

The probability of slipping is that, where

Thus, we obtain

Finally, the probability of slipping is

Ans.