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 \times 10^{11}\,Nm^{-2}$)
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 \times 10^{11}\,Nm^{-2}$)
$\mathrm{Y}=\frac{\mathrm{F} l}{\mathrm{~A} \Delta l}$
$\Delta l =\frac{\mathrm{F} l}{\mathrm{AY}}=\frac{\mathrm{F} l}{\pi r^{2} \mathrm{Y}}$
$\Delta l =\frac{800 \times 9.1}{3.14 \times\left(5 \times 10^{-3}\right)^{2} \times 2 \times 10^{11}}$
$=46.369 \times 10^{-5}$ $\approx 4.64 \times 10^{-4} \mathrm{~m}$
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