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

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Homework Help Overview

The discussion revolves around the calculation of Young's modulus for two different wires made of the same material. Participants explore the implications of varying wire diameters on the modulus and the relationship between force, area, and elongation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants examine the formula for Young's modulus and question the assumptions regarding force and area in relation to different wire thicknesses. There is a focus on understanding how to compare the properties of the two wires and the implications of their dimensions on the calculated values.

Discussion Status

Some participants have provided insights into the conceptual aspects of Young's modulus, noting that the relationship between force and area is not straightforward. There is recognition that without additional information about the force applied, the comparison of the two wires' Young's modulus values remains incomplete.

Contextual Notes

Participants acknowledge that the problem is not intended to be solved numerically, which may limit the ability to derive a definitive conclusion regarding the modulus values for the two wires.

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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