Most textbook problems (including the problems in this book) have “weightless” cables and ropes. There are two reasons for this:
Here, though, the weight of the rope is essential to the solution of the problem. Because the rope weighs 1 lb/ft, the weight on the left side of the pulley is 10 + x + y (when x and y are measured in feet), and the weight on the right side of the pulley is 20 + x. These weights must be equal to one another for moment equilibrium about the center of the pulley.
Notice that the semicircle of rope around the top of the pulley contributes no net moment about the center of the pulley because the left and right quarter-circles balance each other out.
The x terms cancel and we are left with y = 10\,\rm{ft}. We can now find x from the length of the rope
Plugging in our value for y and solving, we get x = 5 - \pi/4 = 4.21\,\rm{ft}.
Last modified: January 22, 2009 at 8:32 PM.