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A truck is pulling a car out of a ditch by means of a steel cable that is $9.1 \mathrm{~m}$ long and has a radius of $5 \mathrm{~mm}$. When the car just begins to move, the tension in the cable is $800 \mathrm{~N}$. How much has the cable stretched? (Young's modulus for steel is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )
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As given that,
Length of cable $l=9.1 \mathrm{~m}$
Radius $r=5 \mathrm{~mm}=5 \times 10^{-3} \mathrm{~m}$
Tension in the cable $F=800 \mathrm{~N}$
Young's modulus for steel $Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$,
Change in length $\Delta l=$ ?
We know that,
Young's modulus $(Y)=\frac{F}{A} \times \frac{l}{\Delta l} \Rightarrow \Delta l=\frac{F}{\pi r^2} \times \frac{l}{Y}$ $=\left[\frac{800}{3.14 \times\left(5 \times 10^{-3}\right)^2}\right] \times\left[\frac{9.1}{2 \times 10^{11}}\right]=\frac{728}{157} \times 10^{-5} \mathrm{~m}$
$\Rightarrow \Delta L=4.64 \times 10^{-4} \mathrm{~m}$
Length of cable $l=9.1 \mathrm{~m}$
Radius $r=5 \mathrm{~mm}=5 \times 10^{-3} \mathrm{~m}$
Tension in the cable $F=800 \mathrm{~N}$
Young's modulus for steel $Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$,
Change in length $\Delta l=$ ?
We know that,
Young's modulus $(Y)=\frac{F}{A} \times \frac{l}{\Delta l} \Rightarrow \Delta l=\frac{F}{\pi r^2} \times \frac{l}{Y}$ $=\left[\frac{800}{3.14 \times\left(5 \times 10^{-3}\right)^2}\right] \times\left[\frac{9.1}{2 \times 10^{11}}\right]=\frac{728}{157} \times 10^{-5} \mathrm{~m}$
$\Rightarrow \Delta L=4.64 \times 10^{-4} \mathrm{~m}$
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