Stress on a Mountaineer's Rope. A nylon rope used by mountaineers elongates 1.10 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for nylon?

Video transcript

Welcome back everybody during a firefighter rescue mission, There is a cable being used and we are told that this cable has a diameter of 11 mm or .011 m. We are told that it is lifting a person with a mass of kg and that the initial length of the cable is 50 m during the rescue two. It also makes a A change in length of 0.35 m. And we are tasked with finding what the young's module. This is of the polyester that makes up the cable. Well we know that the ratio between the change in length and the initial length is equal to the maximum tension of the cable over the area of the cross section of the cable. Times the young's module asse rearranging this, we get that the Young small Angeles is equal to that tension in the cable which is just going to be equal to the weight of the person or mass times the acceleration due to gravity all over the area of the cross section, Times that ratio between the change in length over the initial length. So we actually have all those values. So let's just go ahead and plug those in. We have that the mass of the person is 70 times the acceleration due to gravity which is 9.81, all divided by the area of the cross section of the cable. Well, assuming that the cable circular, we're gonna have pi times the radius which is just half of the diameter squared. Then this is going to be times this ratio right here. So we have 0.35 divided by 50. Which when you plug all of this in your calculator, you get that the young small a jealous of polyester is one point oh three times 10 to the ninth pascal's corresponding to our answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.