A wire elongates by l , mm when a load W is h | vedclass

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(C) From Hooke's Law,the elongation $\Delta L$ of a wire of length $L$,cross-sectional area $A$,and Young's modulus $Y$ under a tension $T$ is given b

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$l$

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(C) From Hooke's Law,the elongation $\Delta L$ of a wire of length $L$,cross-sectional area $A$,and Young's modulus $Y$ under a tension $T$ is given by $\Delta L = \frac{TL}{AY}$.In the first case,a load $W$ is hung from the wire. The tension in the wire is $T_1 = W$. Therefore,the elongation is $\Delta L_1 = \frac{WL}{AY} = l$.In the second case,the wire passes over a pulley and a weight $W$ is hung at each end. The tension $T_2$ in the wire is equal to the weight $W$ because the system is in equilibrium. Thus,$T_2 = W$.The elongation in the second case is $\Delta L_2 = \frac{T_2 L}{AY} = \frac{WL}{AY} = l$.Therefore,the elongation remains $l \, mm$.

$A$ wire elongates by $l \, mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$):

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