9. Blocks A and B are connected by two links as shown. The force P and coefficient of friction are independently and normally distributed with P ~ N(75, 2²) N and μ_s ~ N(0.5, 0.002²), respectively. Determine the probability that two blocks will start to move if A and B both have mass of 5 kg.

Solution

And

Then, we have

f ~ N(17.34, 0.0694²) N.

Also, we have

Therefore, we can obtain

T ~ N(52.02, 0.0694²) N

The probability that two blocks start to move is P ≥ 2Tcos45° or Y ≥ 0, where

Y ~ N(1.425, 2²) N

Consequently, the probability that two blocks will start to move is

Ans.