Youngs Modulus of copper wire experiment

jokiemay

1. The problem statement, all variables and given/known data
I’m doing some basic young’s modulus homework and I think I’ve solved it but I want other people to give their answers to see if the match my own. Its young are of copper wire.



2. Relevant equations
E = stress over strain
Stress = applied force (F) over Cross sectional area (A)
Strain = Extension (e) over Original length (Lo)
A = 0.27mm
F = mxg
Lo = 1.788m
e = variable

My table of results are:
M / kg e / mm
0.100 0.45
0.200 0.94
0.300 1.40
0.400 1.97
0.500 2.46
0.600 3.29
0.700 4.12
0.800 5.00
0.900 6.36
1.000 8.22


3. The attempt at a solution

I’ve worked it out with 0.100kg

M (0.100) x g (9.81) = 0.981 so F = 0.981
Pi x 0.27 squared over 4 = 0.05725566 so A = 0.05725566

So stress = 17.13371733038794867967

e = 0.45
Lo = 1.788

So strain = 0.25167785234899

Young’s Modulus = 68.0779701927423389726993185

I know I’m going wrong somewhere so any help would be appreciated

LawrenceC

You have an error in your strain computation. You seem to be dividing mm/m.

jokiemay

Ohh yes i see that - i know im going wrong somehwere and i cant get my head fully around that.

Why would the strain be such a low figure but the stress be so high

Im sure 00025167785235 is to low for strain

jokiemay

Ohh yes i see that - i know im going wrong somewhere and i cant get my head fully around that.

Why would the strain be such a low figure but the stress be so high

Im sure 00025167785235 is to low for strain

jokiemay

im getting 68077.97019246913753978559011651

couldnt be right

LawrenceC

Because

sigma = e * E

where E is Young's Modulus, a large number. Strain, e, is small. For steel, the modulus is 30X10^6 psi. sigma is stress. So as an example, for a strain of 0.00025, the stress is 7500 psi. Reasonable stress example.

jokiemay

so would be answer of 68077.97019246913753978559011651 be right ?

LawrenceC

Units would be N/mm^2. Watch your significant figures. Based on your first set of data, you did it correctly but consider the comment below.

You say A is area and its value is 0.27 mm. Is that a typo? Should 0.27 be the diameter? That is how you used it.

I looked up the modulus for Cu. It's somewhat higher than what you calculate.

jokiemay

Yes the 0.27 is the diameter which is the cross sectional area (A)

I calculated that as Pi x 0.27squared / 4

Thanks very much for your help so far.

jokiemay

can anybody else hint to me where im going wrong as i see Cu is suppost to be 117GPa

LawrenceC

If you plot your data, the curve looks ok. Are you certain you measured the diameter and wire length correctly?

jokiemay

Hi there - My mistake was the diameter - it should have been calculated as 0.000573mm or 5.73x10-3

so the result in getting now is 6.03 x 10(10) Pa as the youngs modulus.

Im also working out the percentage error;

ive worked out the length as 1.788m +/- 0.01m so 0.01/1.788 x 100 = +/- 0.56%

does this look correct?

My next task is to work out the percentage uncertainty of the cross section area and the gradient of the graph.