Question

A hanging wire made of an alloy of aluminum with diameter 0.12 cm is initially 2.4 m long. When a 37 kg mass is hung from it, the wire stretches an amount 1.24 cm. A mole of aluminum has a mass of 27 grams, and its density is 2.7 g/cm3. Based on these experimental measurements, what is Young's modulus for this alloy of aluminum?

Answer 1

Answer:

The Young's modulus for this alloy of aluminum is $6.21\times10^{10}\ N/m^2$

Explanation:

Given that,

Diameter = 0.12 cm

Length = 2.4 m

Mass = 37 kg

Stretch length = 1.24 cm

Density = 2.7 g/cm³

We need to calculate the area

Using formula of area

$A=\pi\times r^2$

Put the value into the formula

$A=\pi\times(\dfrac{0.12\times10^{-2}}{2})^2$

$A=0.000001130\ m^2$

$A=1.13\times10^{-6}\ m^2$

We need to calculate the Young's modulus

Using formula of Young's modulus

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$

$Y=\dfrac{Fl}{A\Delta l}$

Put the value into the formula

$Y=\dfrac{37\times9.8\times2.4}{1.13\times10^{-6}\times1.24\times10^{-2}}$

$Y=6.21\times10^{10}\ N/m^2$

Hence, The Young's modulus for this alloy of aluminum is $6.21\times10^{10}\ N/m^2$