Why is My Young's Modulus Calculation Giving a Different Result?

AI Thread Summary
The discussion centers on a calculation of Young's modulus for two wires made of the same material, with the expectation that their modulus values should be identical. The calculations reveal discrepancies due to differences in wire thickness and the corresponding force required to achieve the same elongation. It is clarified that the area does not reduce linearly, affecting the force needed for each wire. The conclusion emphasizes that without knowing the change in force, one cannot obtain the same Young's modulus value for both wires. The problem is conceptual rather than numerical, focusing on the principles behind the calculations.
toforfiltum
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Homework Statement


upload_2015-7-8_22-54-55.png


Homework Equations


E= (F/A) x (L/ΔL)

The Attempt at a Solution


I know that since the material is the same, the Young modulus should be the same. However, when I try to find the ratio of the second wire to the first, I get the answer C. For the first wire, E= 4FL / d2Δl, since A = d2/4.
For the second wire, the value of E I obtain is F x ½L / (d2/16) x Δl , which is twice the first value. I can't see what's wrong with my working. Can someone point it out?
 
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This is a conceptual question, so we know for a particular material at a certain temperature Young's modulus will be a constant. Using the above equation we see that area does not reduce linearly so you're probably wondering how do I compare a thicker wire to a thinner one. Remember that to get the same ratio of change in length from original length in the thinner wire will require less force. So while your area is a quarter of the size of the original wire, the force needed is also reduced.
 
vanoccupanther said:
This is a conceptual question, so we know for a particular material at a certain temperature Young's modulus will be a constant. Using the above equation we see that area does not reduce linearly so you're probably wondering how do I compare a thicker wire to a thinner one. Remember that to get the same ratio of change in length from original length in the thinner wire will require less force. So while your area is a quarter of the size of the original wire, the force needed is also reduced.
Oh I see, so from the information given in the question above, there's no way of obtaining the same value of E as the first wire without knowing the change in the value of F is it?
 
toforfiltum said:
Oh I see, so from the information given in the question above, there's no way of obtaining the same value of E as the first wire without knowing the change in the value of F is it?

Yes, its not meant to be solved numerically.
 
vanoccupanther said:
Yes, its not meant to be solved numerically.
Ok, thanks.
 

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