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Question
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.)
Solution
According to the problem,
Length of steel cable l = 9.1 m
Radius r = 5 mm = 5 × 10–3 m
Tension in the cable F = 800 N
Young’s modulus for steel Y = 2 × 1011 N/m2
Change in length ∆L = ?
Young’s modulus If given by `Y = (F/A)/((∆L)/L)`
⇒ `∆L = (FL)/(Y(pir^2)`
`∆L = (800 xx 9.1)/((2 xx 10^11)(3.14 xx 25 xx 10^-6)) = 4.64 xx 10^-4 m`
⇒ ∆L = 5 × 10–4 m = 0.5 × 10–3 m
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