Question

Two wires diameter $0.25cm$. One made of steel and the other made of brass are loaded as shown in figure. The unloaded length of steel wire is $1.5m$ and that of brass wire is $1.0m$. Compute the elongations of the steel and the brass wires.

Answer 1

Given,

Length of the steel wire, $L_1=1.5m$,

Length of the brass wire, $L_2=2.0m$

Diameter of the wires, d =0.25m

Hence, the radius of the wires, $r=\frac{d}{2}=0.125cm$

Total force exerted on the steel wire:

$F_1=(4+6)\times 9.8=10\times 9.8=98N$

Young's modulus for steel,

$Y_1=\frac{\frac{F_1}{A_1}}{\frac{\Delta L_1}{L_1}}$

$\Delta L_1=\frac{98\times 1.5}{\pi (0.125\times {10}^{-2}{)}^2\times 2\times {10}^{11}}=1.49\times {10}^{-4}m$

Total force on the brass wire:

$F_2=6\times 9.8=10\times 9.8=58.8N$

Young's modulus for brass,

$Y_2=\frac{\frac{F_2}{A_2}}{\frac{\Delta L_2}{L_2}}$

$\Delta L_2=\frac{58.8\times 1.0}{\pi (0.125\times {10}^{-2}{)}^2\times 0.91\times {10}^{11}}=1.3\times {10}^{-4}m$.