2-2. The motor draws in the cable at a rate of , where follows a normal distribution and is in seconds. The crate has a mass of 50 kg, and the coefficient of the kinetic friction between the crate and the ground is . If the maximum tension that the cable can stand is . Assume that and are independent. Determine the time when the probability that the cable does not beak is 0.95.

Solution

Referring to the free-body diagram of the crate, we have

Thus

Solving the above equation

Ans.