What is the Young's Modulus of Aluminum, Steel, and Brass?

[Edward Trail]

Homework Statement

hi guys

I am conducting an experiment for my coursework in physics and i have come across a bit of a problem. i am trying to calculate the youngs modulus of 3 different metals Aluminium steel and brass. To calculate the modulus of the material i am using a chart of Mass k/g against the deflection thus giving me the gradient.

i am going wrong somwhere as i am getting a result of double the normal GPa for each item i.e 320Gpa instead of 140. see below data and charts that i have created.

Homework Equations

S=L³/WT³ which is 1796850000 for all metal strips
E=4Sg x gradient of graph

The Attempt at a Solution

Here is a printscreen of my results, have i graphed them correctly?

 

[Chestermiller]

Can you please define the variables in your equations, and also tell us the type of supports and the location of the load in your beam deflection experiments.

 

[Edward Trail]

Hi chestermiller
Thanks for getting back to me so quickly.
The variables are
L=o.33
W=0.025
T=0.001
All are in metres. We used a simple g clamp and measured from the point of suspension.

Hope this clears it up a bit.

 

[Chestermiller]

So, it is a cantilevered beam, right? What does g stand for in your equation?

 

[Edward Trail]

Yes it is.it is for gravity

 

[Chestermiller]

I get a different value than you for S. And, those deflections can't be in meters. At most, they are in cm.

I confirm your equation for the modulus.

 

[Edward Trail]

hi chestermiller

ah i seee i rounded 0.025 to 0.02, not sure why, it should be 1437480000. the Deflection is in metres i think the table results are unclear. the deflections are on the left. as i have done P0 -P50 etc so with 50 grams on the beam gives a deflection of 1cm or 0.01 mtrs. the only problem is that the GPa for steel is arround 200GPa. given my gradient is 5.4457 then my GPa for steel is 5.4457x9.81x4x1437480000=3.07x10^11 to 2 dp. which is 307GPa, even factoring in my error percentage which is arround 12 percent which is 36.86 GPa it is no where near the known value. should i be worried about this?

Many Thanks

Edward Trail

 

[Chestermiller]

How accurate is Rhee thickness? Could it be 1.1 mm?

 

[Edward Trail]

i used a pair of verniers which measures to a thousanth of a mm but the only problem was the angle at which the verniers gripped the beams. as it did vary from 1mm to 1.3 dependant on the agnle, do you think this could be the issue?

 

[Chestermiller]

i used a pair of verniers which measures to a thousanth of a mm but the only problem was the angle at which the verniers gripped the beams. as it did vary from 1mm to 1.3 dependant on the agnle, do you think this could be the issue?

What is 1.3 to the 3rd power?

 

[Edward Trail]

oh i think that is what the problem is i have just calculated it for 1.3mm thickness and found out that my GPa is now 1.398x10^11 which is pretty close when considering my error percentage. i think I am going to have to measure the thickness again for each one

 

[Chestermiller]

oh i think that is what the problem is i have just calculated it for 1.3mm thickness and found out that my GPa is now 1.398x10^11 which is pretty close when considering my error percentage. i think I am going to have to measure the thickness again for each one

It looks like you've got it figured out.

 

[Edward Trail]

okay so I've just re measured them now its only a slight difference but noted down more decimal points does it check out for you. its now within the range of the recomended GPA of each material.

sorry if the image is blurry i can zoom in if needed

 

[Chestermiller]

I can't read it too well. But, in my judgment, you've pretty well analyzed this as much as it will permit.

 

[Edward Trail]

Thanks very much ill mark this as resolved

cheers