Youngs Modulus. Copper wire experiment

[Gregg]

Homework Statement

Calculate Youngs Modulus for the copper wire

We have done the experiment today, here is the data:

(KG)/F(N)/x(M)

0.1/0.1g/0.0
0.2/0.2g/0.0
0.3/0.3g/0.001
0.4/0.4g/0.001
0.5/0.5g/0.002
0.6/0.6g/0.003
0.7/0.7g/0.004
0.8/0.8g/0.005
0.9/0.9g/0.006
1.0/1.0g/0.009
1.1/1.1g/0.029
1.2/1.2g/0.053
1.3/1.3g/0.089
1.4/1.4g/0.160

Diameter = 0.27mm = 2.7x10^-4Natural Length = 1m

Homework Equations

E = FL/AX

gradient = F/X

E = gradient x L/A

The Attempt at a Solution

Radius = 1.4x10^-4

A = (pi)(1.4x10^-4)²

So i take the elastic region to be up to the 1kg load. The gradient of the line is (1g/0.009) = 1090.

The beginning length of the copper wire was 1mE = 1090 x 1 / AA = (pi)(1.4x10^-4)^2 E = 1090/(pi)(1.4x10^-4)^2E = 1.77x10^10 Pa = 17.7 GPa

According to the internet the young modulus is about 10 times larger than this. Have i gone wrong somewhere?

 

[LowlyPion]

Here is an online lecture that performs that very experiment.

https://www.youtube.com/watch?v=YrRP-oGPjvk

 

[Gregg]

Ah, brilliant.

 

[LowlyPion]

I would have chosen another point further back because you might notice that the 1 kg point is already into the elastic region as the slope of the curve has changed.

 

[Gregg]

Yeah I have drawn a graph and can see this, also. Still strange to be out by a factor of 10, though.

 

[LowlyPion]

It's not that bad.

Using the .8/.005 point I get F/A as 1.371*10⁸

divide by .005 and that yields 27.4 GPa

Copper looks like 110 to 130.

Do an error propagation analysis of the measurements. You're only a factor of 3 to 4 off. And a small measurement uncertainty in A or in ΔL can be pretty substantial.

 

[queend4eva22]

you need to convert your mass to (N) Newtons

 

[queend4eva22]

oh n your lengths should be in meters (m) too stick with the metric measurements