 #1
 15
 1
1. A rope wraps an angle θ around a pole. You grab one end and pull with a tension T0. The other end is attached to a large object, say, a boat. If the coefficient of static friction between the rope and the pole is µ, what is the largest force the rope can exert on the boat, if the rope is to not slip around the pole?
The question I have is really just about the diagram. Here it shows the two tension forces at both ends, my question is how did he get the angle there to be sin(d(theta)/2)? Well, more importantly the d(theta)/2, I understand why its sin. I was unable to derive that myself, so I looked at the solution to see what angle I needed to use, and from there I was able to do the problem, but I still need to know how he got that angle.
My thoughts are that the angles on both sides of those tension forces contribute an angle of theta/2 and so that add up to being a total of theta. but I guess I still don't know why geometrically.
The question I have is really just about the diagram. Here it shows the two tension forces at both ends, my question is how did he get the angle there to be sin(d(theta)/2)? Well, more importantly the d(theta)/2, I understand why its sin. I was unable to derive that myself, so I looked at the solution to see what angle I needed to use, and from there I was able to do the problem, but I still need to know how he got that angle.
My thoughts are that the angles on both sides of those tension forces contribute an angle of theta/2 and so that add up to being a total of theta. but I guess I still don't know why geometrically.
Attachments

3.6 KB Views: 405
Last edited by a moderator: