1. The weight of the crate follows a normal distribution , and the crate is hoisted using the ropes AB and AC with a constant speed. AB always remains horizontal, and  is . If the strength (maximum tension) of the ropes also follows a normal distribution  and S is independent of W, determine the probability that rope AB and AC will break, respectively.

Solution

For  and

So the distributions of F_AC and F_AB are  and , respectively.

We know the maximum tension of each rope is before it breaks, suppose

Thus

So the distributions of Y and Z are and , respectively.

The probability of the break of rope AC is  and the probability of the break of rope AB is,

Ans.

Ans.

Thus, we conclude that the probability of the break of rope AC is 0.205 and the probability of the break of rope AB is 0.098.