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A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm-2.)

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Given:

Steel cable’s length, I = 9.1 m

Radius, r = 5mm = 5 × 10-3 m.

Tension in cable, F = 800 N

Young’s modulus = 2 × 1011 N/m2

Young’s modulus,

Y = \(\frac{F}{A}\) × \(\frac{l}{∆l}\)

Or ∆l = \(\frac{F}{πr^2}\) × \(\frac{l}{Y}\)

\(\frac{800×9.1}{3.14×(5×10^{−3})^2×2×10^{11}}\)

= 4.64 × 10-4 m

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