Question

A tow truck is pulling a car out of a ditch by means of a steel cable that is 9.3 m long and has a radius of 0.50 cm. When the car just begins to move, the tension in the cable is 1070 N. How much has the cable stretched?

Answer in m

Answer 1

Multiply the length L of the cable by the strain, (deltaL)/L

You can get the strain from Hooke's law and Young's modulus of steel, E.

Young's Modulus for steel is
E = 2.0 x10^11 N/m2

Stress = Strain/E

Stress = 1070 N/(cable area)
Cable area = pi*r^2 = 0.7854 cm^2
= 7.854*10^-5 m^2
Stress = 1.362*10^7 N/m^2
Strain = 6.8*10^-5

Cable Length increase = 6.3*10^-4 m