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A truck is pulling a car out of a ditch ...

A truck is pulling a car out of a ditch by means fo a steel cable that is `9.1m` long and has a radius of `5mm`. When the car just beings to move, the tension in the cable is `800 N`. If Young's modulus for steel is `2xx10^(11) N//m^(2)` then the strecth in the cable is (neraly)

Text Solution

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Length of steel cable l = 9.1 m
Radius r = 5 mm = `5 xx 10^(-3)m`
Tension in the cable F = 800 N
Young's modulus for steel `Y=2xx 10^(11) N//m^(2)`
Change in length `Deltal = ?`
Young's modulus `(Y) = (F)/(A) xx (l)/(Deltal) implies Deltal = (F)/(pir^(2))xx(l)/(Y)`
`" "=(800)/(3.14xx(5xx10^(-3)) ^(2))xx(9.1)/(2xx10^(11))`
`=4.64 xx 10^(-4)m`
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