Answer to Question #165111 in Mechanics | Relativity for Sage Topaz

Question

A 2.5 m long steel wire has a diameter of 0.30 mm is hanging vertically. A lamp shade whose mass is 1.7 kg is attached to the wire and released. How much does the wire stretch (in mm)? (refer to Young’s Modulus of Elasticity)

Answer 1

By the definition of the Young's Modulus of Elasticity, we get:

$$E=\dfrac{FL_0}{A\Delta L},$$ $$\Delta L=\dfrac{FL_0}{AE},$$ $$\Delta L=\dfrac{1.7\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot2.5\ m}{\dfrac{\pi (0.3\cdot10^{-3}\ m)^2}{4}\cdot2\cdot10^{11}\ Pa}=2.95\cdot10^{-3}\ m.$$