Question

A mineshaft has an elevator hung from a single steel-wire cable of diameter 2.5 cm. Young's modulus of the cable is 10×1010N/m2. When the cable is fully extended, the end of the cable is 600 m below the support. How much does the fully extended cable stretch when 1000 kg of ore is loaded into the elevator?

Answer 1

stress = F/A

= m*g/(pi*d^2/4)

= 1000*9.8/(pi*0.025^2/4)

= 1.996*10^7 N/m^2

we know, young's modulus, Y = stress/strain

strain = streess/Y

delta_L/L = stress/Y

delta_L = L*stress/Y

= 600*1.996*10^7/(10*10^10)

= 0.12 m or 12 cm <<<<<<--------Answer