Question

A force of 16,000 will cause a 1 1 bar of magnesium to stretch from 10 to 10.036 . Calculate the modulus of elasticity in . (Enter your answer to three significant figures.)

Answer 1

The modulus of elasticity is 44.4GPa

Explanation:

Given

original length L1=10cm

New length L2=10.036 cm

Force F=16000N

$dimensions\ of\ the\ bar\ is\ 1 cm\times1cm\\Area=1cm\times1cm=1cm^2=0.0001m^2$

Stress of the bar σ=Force/Area

$=16000/0.0001=16\times 10^7N/m^2$

Change in length ΔL=L2-L1=10.036-10=0.036 cm

Strain is obtained by dividing the change in length by original length

Strain ε=ΔL/L1

=0.036/10=0.0036

Modulus of elasticity=stress/strain

=σ/ε

$=16\times10^7/0.0036\\=4.44\times10^\ 10$Pa

$=44.4GPa$