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?

Question

Physics

Cecelia Donaldson

27 November, 15:01

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?

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Answers (1)

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Ruby Mcintosh · 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