welcome to electron line in this example we're going to wrap the rope around the post once twice and four times so in essence each time doubling the number turns a number of loops around the post we're going to keep your coefficient of static-friction the same and what we want to do is calculate what the tension will be over here in order to keep the rope from slipping if we apply a force of a thousand Newton's on the other side so again we use the same equation as before we solve the 41 and I'll calculate it for each of these three cases he 1 is going to be equal to a thousand Newton's apply it on one side divided by e to the coefficient of static-friction 0.4 times only one turn which is 2pi radians and now we could see what that is equal to inverse times 1,000 equals that gives us 81 Newton's t 1 is equal to 81 Newtons ok what we're going to do now is we're going to do it again but now we take two turns around the post and see what happens all right so it gives us T 1 is equal to 1,000 Newtons 1/4 times 4 PI again we take point four times four times out high equals and it gives us six point five six Newtons so what's interesting here is even though we simply doubled the number turns from one to two demand the tension required to keep the rope from slipping drop dramatically from 81 Newtons down to less than 10% of the original amount so now let's do it four turns and see what happens now we get teeth 1 is equal to 1,000 Newton's the coefficient of static ratify times 8 pi which is 4 times around see what we get point four times eight thousand equals and now t1 is just a very tiny 0.04 3 Newtons notice that if you compare this to the previous example that doubling and quadrupling the coefficient of static friction had the same effect as doubling and quadrupling the number turns around the post because both of them are part of the exponent of T of the number E and because of that the tension dramatically or the tension required to keep your rope from slipping dramatically decreases and that's how you can see the relationship between the tension the coefficient of friction and the number of turns in the rope and that's how it's done