Question

A bolt is needed to attach an actor's harness to a wire across a stage. The bolt is 5.0cm long with a 0.25cm^2 ross sectional area, and must extend by no more than 0.020mm when supporting a 900kg mass. Calculate the minimum value of Young's Modulus of a material if it is to be suitable.

Answer 1

For the extension of the bolt the force is proportional to the extension and to the cross section, so

$F = ES\dfrac{\Delta l}{l},$ so $E = \dfrac{F}{S \Delta l/ l} = \dfrac{mg}{S \Delta l/ l}= \dfrac{900\,\mathrm{kg}\cdot9.8\,\mathrm{N/kg}}{2.5\cdot10^{-5}\,\mathrm{m^2}\cdot2\cdot10^{-5}\,\mathrm{m}/0.05\,\mathrm{m}} = 8.8\cdot10^{11}\,\mathrm{Pa}.$ It is quite big value, but there exist some types of material with such a big Young's Modulus.