Units for Strain? | Learn About Strain & Hooke's Law

[Baumer8993]

Homework Statement

Here is a picture of the problem: http://imgur.com/Ldw1fUF
Make sure to click on the picture to make it bigger!

Homework Equations

The strain/hooke's law equations.

The Attempt at a Solution

I have this for two parts. The second part is the deformation which I got right. I am confused on what the units for strain. I got 4 x 10^-4 for my answer which is wrong. How would I put the units into micrometers per meter? I think it should be a simple conversion, but let me know if I am wrong.

 

[Chestermiller]

If 4 x 10^-4 is the strain in m/m, and there are 10⁶ microns in a meter, what is the strain in μm/m?

 

[Baumer8993]

Ah thank you. Things online told me strain is dimensionless, but it was in m/m. Thank you!

 

[Chestermiller]

Ah thank you. Things online told me strain is dimensionless, but it was in m/m. Thank you!

Well... It really is dimensionless: length per length. Anyway, I think of it as being dimensionless.

 

[PeterO]

Ah thank you. Things online told me strain is dimensionless, but it was in m/m. Thank you!

It is dimensionless in the sense that all the units "cancel out" metres divided by metres gives no units / dimensions.

Another example of this is the rating of Yachts. The Americas Cup used to be contested using what were known as 12 metre class boats.
The formula for rating a yacht is extremely complex involving the overall length, sail area, length on the waterline, mass of the hull, mass of the keel, the area of the triangle formed by the deck, mast and imaginary line from bow to mast top, and many other measurements.

When all the units are put through the formula, all except 1 metre unit cancel out so we get a 12 metre yacht: the value 12 pops out the end of the calculation, and the unit metre also results.

Strain is dimensionless because a number pops out of the calculation - the value, but the units used cancel, so the answer has no unit associated - it is dimensionless.