For safety in climbing, a mountaineer uses a nylon rope that is 5.0m long and 1.0cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6m. Find its Young's modulus. Science deformation?
in this problem, we have been given that there's a rope hose. Initial length is five m, and the diameter of this rope is one centimetre. So that means the radius would be .5 into 10 race to -2 m. And here we need to figure out the young smugglers so that A 90 kg Climber will climb using this rope. So the mass of the climber is 90 Kg. And the rope in this process elongates too one point six m. So that's the change in length. And we need to determine the young smugglers. So we know that young smugglers is the ratio of stress of our strength. So to compute the stress, it is the force applied per unit area of cross section. And we divide this by the change in length with respect to the original length. So that will be f by delta L. Into L. By a So forth. Here will be the weight of this climb, but which is supported by this rope. So that will be 90 times 9.81 Times the length which is five m divided by the change in length, which 1.6 m times the area area will be pie our square. So are we have already figured out so we have to do square off this. So here we simplify to get the young smugglers. So first we multiply the numerator together And we get the numerator as 44, And we divide by The product of the denominators. So 1.6 times 3.14 times .5 sq Off Back. So that becomes one 256 into 10, raise to four. That comes to the top here, So we take 4, 4, 10 and divided by 1.256. And Wicked, the young smugglers as 3.5 into 10 ways to seven newton per meter square. So this is the young smugglers out this wire.