Answer
A hanging mass of 55 kg will stretch the wire by 1%
Work Step by Step
We can use Young's modulus to solve this question:
$Y = \frac{F/A}{\Delta~L/L}$
For aluminum, $Y = 69\times 10^9~N/m^2$
If the wire stretches by 1%, then $\Delta L / L = 0.01$
We can find the force required to stretch the wire by 1% as:
$Y = \frac{F/A}{\Delta~L/L}$
$F = Y~A~(\frac{\Delta L}{L})$
$F = (69\times 10^9~N/m^2)(\pi)(5.0\times 10^{-4}~m)^2~(0.01)$
$F = 541.9~N$
If this is the weight of the hanging mass, we can find the mass as:
$M = \frac{weight}{g}$
$M = \frac{541.9~N}{9.80~m/s^2}$
$M = 55~kg$
A hanging mass of 55 kg will stretch the wire by 1%.
