Answer to Question #172545 in Physics for Diocos

Question #172545

By how much does a 54-kg mountain climber stretch her 0.871-cm diameter nylon rope when she hangs 49 m below a rock outcropping? (For nylon, Y=1.35 × 109Pa.) 


1
Expert's answer
2021-03-26T11:41:18-0400

We can find the Young's modulus as follows:


"E=\\dfrac{FL_0}{A\\Delta L},""\\Delta L=\\dfrac{FL_0}{AE}=\\dfrac{mgL_0}{\\dfrac{\\pi d^2}{4}E},""\\Delta L=\\dfrac{54\\ kg\\cdot9.8\\ \\dfrac{m}{s^2}\\cdot49\\ m}{\\dfrac{\\pi (0.871\\cdot10^{-2}\\ m)^2}{4}\\cdot1.35\\cdot10^9\\ Pa}=0.32\\ m."

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