welcome to our lecture line our next example deals with a belt drive we have two pulleys pulley a and pulley B and pulley B is driving pulley a by causing attention to exists on this drive belt right here the tension of course is created by pulley D turning and so what we can say is that the tangent here let's call that T 2 and T 2 is going to be at maximum 800 Newtons there's a limit as to how much force we can apply and how much tension we can put on this belt so we don't want that belt to break what we're trying to calculate is the maximum moment we can apply on a using this belt drive system like this so what that means is we're going to have to find the tension over here and the tension on the other side of the belt t1 and of course that will depend upon what happens on pulley B right here once we calculate t2 and t1 we could then calculate the moments on pulley a alright let's go ahead and use our equations we know that t2 divided by t1 is equal to e2 the coefficient static friction times the angle of contact now notice if this is a 20 degree angle with the horizontal we have a similar situation here this must be a 20 degree angle here and a 20 degree angle there which means that the angle of contact beta here on pulley B is going to be 180 degrees which would be half a turn minus 2 times 20 degrees which is 140 degrees which of course we're going to have to convert to radians we're given the coefficient of static-friction and we're trying to find t1 that means that t1 is equal to t2 divided by e to the U sub F times beta so in this case we have a maximum tension of 800 Newton's divided by e to the 0.3 and data will be a hundred and 40 degrees but we'll have to convert that to radians which is pi divided by 180 as the conversion factor alright now we're ready to 91 so we have 0.3 times 140 times pi divided by 180 and that becomes the exponent of e to the X take the inverse of that times 800 equals 384 Newtons so T 1 is equal to 384 Newtons now we're ready to calculate the moment we can apply to a notice that the tension here is equal to 800 Newtons and the tension here is equal to Newtons and over here is 384 Newtons so the moment on a is equal to the net tension on that which would be 800 minus 384 800 minus 384 Newton's times the moment arm or in this case the radius of the polling which is 15 centimeters converted to meters which is 0.15 meters and that will be the moment the maximum moment we can apply to a so the maximum moment on a is going to be equal to 800 minus 384 multiplied times 0.15 and that gives us 16 2.4 Newton meters quick check 800 I've minus 5 equals yes oh yeah 62 points for new 10 years so again the way we do that is there's a polar that's driving the belt we have an angle of contact which is 180 minus 40 we have a coefficient of static friction and then using the equation that we found we can then calculate the tension on the other side of the belt if this tension here is a maximum of 800 Newtons notice that this pulley will be turning in a clockwise direction pulling on this belt and will be less tension on this side because of the difference in tension on both sides of the pulley that differs in tension then applies to this pulley and then we can find a moment by taking the difference in the time's the moment art that's how it's done