Question

A tow truck is pulling a car out of a ditch by means of a steel cable (y = 2.0 x 1011 n/m2) that is 9.55 m long and has a radius of 0.437 cm. when the car just begins to move, the tension in the cable is 803 n. how much has the cable stretched?

Answer 1

If you know the real modulus of the cable (Y), the length, and the area (based on the radius), you can compute the spring constant, k = AE/L. Then, if you know the force used, you can compute the displacement, using F = kd, or d = F / k = FL/(AE). Our answer should work out to units of length. So,
d = 803 N * 9.06 m / [pi*(0.574 cm)^2 * 2.0 x 10^11 N/m^2]
d = 3.5 x 10^-8 Nm^3 / (cm^2 * N)
d = 3.5 x 10^-8 m^3 / cm^2 * (100 cm / 1 m)^2
d = 3.5 x 10^-4 m