Photo via : fourthandfifteen  In this "dissecting" series of posts we discuss every problem in the NCEES "Sample Questions + Solutions" book. The afternoon section problems in this book are numbered 501 through 540. This post is about problem 504 for the Mechanical Systems Depth (PM) exam. Description of Problem 504: The problem statement shows a sketch of a rope wrapped around a cylindrical surface. You are asked to calculate the minimum force to be applied on one end of the rope in order to lift a body of known weight at the other end of the rope. 
Analysis of Problem 504 This kind of problem is straightforward as long as you are aware of the relationship describing the variation of the tension in a cord or rope wrapped around a cylindrical surface due to friction. What makes this problem complicated is that, chances are, the last time you saw this relationship was in your sophomore year in engineering school when taking engineering statics. Here's a similar problem dealing with friction that is a little more challenging than Problem 504, yet it is not harder than anything you did in school: Mechanical Systems and Materials Depth (PM) Exam Sample Problem #4 The following experiment has been devised to determine the coefficient of friction between a cord and a steel cylinder of 0.2 m in diameter: The steel cylinder is fixed and does not rotate. A small force is applied at end of the cord. This force is slowly increased until the block is set in motion (sliding horizontally). The experiment was performed maintaining a constant angle of contact, ϕ=90°, between the cord and the cylinder. The force required to initiate movement of the block was measured to be 65 N. The mass of the block is 20 kg, and the static coefficient of friction between the block and the horizontal surface on which it slides is 0.25... 
The coefficient of friction between the rope and the cylinder is nearest: (A) 0.003 (B) 0.180 (C) 0.750 (D) Cannot be calculated with the information provided. You may download the solution via the link below. Have any questions? Need help? Leave a comment!
