A very light 1.00-m wire consists of two segments of equal length,one of steel (Young's modulus is 2.00 × 10¹¹ N/m²)and one of brass (Young's modulus is .The steel segment is 1.50 mm in diameter,and the brass segment has twice this diameter.When a weight w is hung from the ceiling by this wire,the steel segment stretches by 1.10 mm.By what distance does the brass segment stretch? A) 0.50 mm B) 0.61 mm C) 1.2 mm D) 2.4 mm E) 9.8 mm

Question

Quizplus · Accepted Answer

Let the tension in both segments be T and the stretching in brass segment be x.

From the given data, we have:

$T=\frac{w}{2}$ (since the wire is supporting the weight at the middle)

$F_{steel} = AE_{steel}\frac{\Delta L_{steel}}{L_{steel}} = \frac{\pi}{4}(1.5	imes 10^{-3})^2 E_{steel}\frac{\Delta L_{steel}}{L_{steel}}$

$F_{brass}=AE_{brass}\frac{\Delta L_{brass}}{L_{brass}}=\frac{\pi}{4}(3	imes 10^{-3})^2E_{brass}\frac{\Delta L_{brass}}{L_{brass}}$

Since the wire is in equilibrium, we have:

$T=F_{steel}=F_{brass}$

Substituting the values and simplifying, we get:

$x=\frac{4\Delta L_{steel}E_{brass}}{E_{steel}(1.5^2-3^2)}=\boxed{	extbf{(B) }0.61	ext{ mm}}$

A Very Light 1