# What is the elastic modulus of the wire?

## 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/$$\Delta$$L

## The Attempt at a Solution

r=.1mm=1x10-4m

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

What am I doing wrong?

Doc Al
Mentor

## Homework Equations

Elastic Modulus=F/A/L/$$\Delta$$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 $$\Delta$$L/L I don't get the right answer. What is wrong with my calculation?

Doc Al
Mentor
6.28N/(2$$\pi$$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!