A lift cable which is 50m long ,is made from high tensile steel of Young Modulus 2.0x 10^11 Pa. the cable is made from 100 wires each of radius 2.0mm . Calculate the extra extension in the cable when 10 passengers pile into the lift ,the total mass of the passenger is 500kg .

Question

A lift cable  which is 50m long ,is made from high tensile steel of Young Modulus 2.0x 10^11 Pa. the cable is made from 100 wires each of radius 2.0mm . Calculate the extra extension in the cable when 10 passengers pile into the lift ,the total mass of the passenger is 500kg .

bobpursley · Answer

I think I would use Hooke's law here. Note the wires are in parallel, so the effective

Modulus is 100*2*E11 Nt/m^2, so

deltaL=FL/AE where F is force, L is length, A is area of each wire, and E is the modulus of Elasticity.

deltaL=500kg*9.8N/kg*50m/PI*(2E-3)^2*200E11N/m^2

check that.