6. A random force T ~ N(0.95, 0.015²) lb is applied to pull a bookmark with a width of 1 in. The weight of the book is W ~ N(12, 0.15²) lb, and the coefficient of static friction between the bookmark and the paper is µ_s=0.6. If the pages are 8 in. by 10 in., determine the probability that the bookmark will start to move out. Assume the pressure on each page and the bookmark is uniform.

Solution

Pressure on book mark is:

Then, with W ~ N(12, 0.15²) lb, we could have the distribution of pressure P:

Normal force on bookmark:

Then, we have:

Thus, we can obtain the distribution of friction force F with :

Finally, we can calculate the distribution of the drag force T_s which is required to pull the bookmark out:

Then, we can construct

Finally the probability the bookmark can be moved out is

Ans.