Question

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.) 

Answer 1

We can find the Young's modulus as follows:

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