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

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    Strain Units
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Strain is dimensionless, meaning it represents a ratio of length to length, such as meters per meter (m/m), where the units effectively cancel out. Although it can be expressed in terms of micrometers per meter (μm/m), the fundamental nature of strain remains dimensionless. The discussion clarifies that while strain can be numerically represented, it does not carry a unit in the traditional sense. This concept is similar to yacht rating systems, where complex measurements ultimately yield a dimensionless value. Understanding strain as dimensionless is crucial for correctly applying Hooke's Law and related equations.
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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.
 
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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?
 
Ah thank you. Things online told me strain is dimensionless, but it was in m/m. Thank you!
 
Baumer8993 said:
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.
 
Baumer8993 said:
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.
 
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