The goal of the lab is to find the modulus of elasticity for

The goal of the lab is to find the modulus of elasticity for aluminum:(69GPA)

A tensile test was used.

E=stress/strain

The data is:

500g 14microstrains

1000g 25 microstrains

1500g 33 microstrains

The cross sectional area is 0.0000818m^2 from t=3.21mm and w=25.49mm

I keep getting 4.8GPA-6.0GPA for the modulus, which is a factor of 10 off from the accepted value. Please show me where I\'m making the error. Thank you!

Solution

Given data

load P1 500g =4.9N elongation ,14 microstrains =14*10^-6mm

P2 1000g=9.8N 25 microstrains=25*10^-6mm

P3=1500g=14.7N 33microstrains=33*10^-6mm

cross sectional area =0.0000818m² ,thoickness t=3.21mm ,w=25.49mm

Modulus of Elasticity E=stress/strain

stress=P/A

from the above data load with elongation was given

at load P1 is converted into newtons

stress=P1/A=4.9N/0.0000818m² =59.9KN/m²

at P2

stress=P2/A=9.8N/0.0000818m² =119.8KN/m²

=P3/A=14.7N/0.0000818m² =179.8KN/m²

Strain e1=change in length/original length

e1=14*10^-6mm/25.49=0.549*10^-6

e2=25*10^-6mm/25.49=0.98*10^-6

e3=33*10^-6mm/25.49=1.29*10^-6

therefore E1=stress/strain

E1=59.9KN/m²/0.549*10^-6=109GPA

E2=119.8/0.98*10^-6=122GPA

E3=179.8/1.29*10^-6=139GPA