What is the elastic modulus of the wire?

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Homework Help Overview

The discussion revolves around calculating the elastic modulus of a wire based on its diameter, the force applied, and the resulting stretch. The problem involves understanding the relationship between force, area, length, and change in length.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the formula for elastic modulus and question the calculations related to area and the change in length ratio. There is confusion regarding the correct values to use for these calculations.

Discussion Status

Participants are actively engaging with the problem, with some offering corrections to the original poster's calculations. There is a recognition of potential errors in the area calculation and the ratio of change in length to original length, but no consensus has been reached on the correct approach yet.

Contextual Notes

There is a mention of specific values for diameter and force, as well as the percentage stretch of the wire, which are critical to the calculations but may not have been applied correctly by the original poster.

joseg707
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Homework Statement


A wire of diameter 0.2mm stretches by 0.20% when a 6.28-N force is applied. What is the elastic modulus of the wire?


Homework Equations


Elastic Modulus=F/A/L/[tex]\Delta[/tex]L


The Attempt at a Solution


r=.1mm=1x10-4m

6.28N/(2[tex]\pi[/tex]1x10-8/.02=5x109N/m2

The right answer is 1.0x1011.

What am I doing wrong?
 
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joseg707 said:

Homework Equations


Elastic Modulus=F/A/L/[tex]\Delta[/tex]L
That should be (F/A)/(ΔL/L).
 
Oh, yeah. Well how do I calculate that? I know that the change is .2% if I use .002 or .2 as a value for [tex]\Delta[/tex]L/L I don't get the right answer. What is wrong with my calculation?
 
joseg707 said:
6.28N/(2[tex]\pi[/tex]1x10-8/.02=5x109N/m2
Area = pi*r². Looks like you have an extra factor of two in there. And ΔL/L = 0.002.
 
Ah! Thank you so much! I don't know why I was thinking are was 2*pi*r^2. Thanks a lot!
 

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