1-21.  A normally distributed Weight  kN is being pulled up an incline by a ramp and pulley system as shown.  If the yield stress of the cable also follows a normal distribution  MPa, and the cable has a diameter of 25 mm, what is the probability that the cable will break? Assume  and  are independent. 

Solution

Sum the forces: The forces N and T can be found by summing the forces in the x and y directions.

Since T represents the force applied to the cable, we use it to show:

      (1)

Since  kN, and  MPa are independent,  also follows a normal distribution.  .  Also,  mm².

 MPa                                             (2)

MPa                                (3)

Equation (1) can be written as

Ans.