How to calculate extension using hooke’s law?
Hello, I am given a load (N) and a corresponding length (mm). For example, a load of 1N results in a length of 58mm. I need to calculate the extension using Hooke’s Law. My understanding is that the relationship can be expressed as ( F = k \cdot l ), where ( l ) is the extension. This leads to the equation ( l = \frac{F}{k} ). However, my data provides the force (F) but not the spring constant (k). What should I do in this situation? Just to clarify, in this context, ( F ) represents the force, ( k ) is the spring constant (expressed in N/m), and ( l ) is the extension or length (measured in meters, centimeters, or millimeters). Thank you very much!
2 Answers
Jan 23, 2025
Load “is” the force. They are just simply two names for the same thing.
As for the k constant of stiffness, this is ultimately your goal to calculate.
You are given the total length of the member, at any given tension load. Subtract the initial length of the member, to get the extension distance. That is the x in the formula F=k*x.
If your material is somehow a perfect linear elastic material, and your measurements are also perfect, then you should be able to take any given load divided by any given extension distance, and get the spring constant.
However, most of the time, this isn’t the case. You have deviations from the linear elastic trendline, that can fool you. It is best to get a good plot on a graph, and see the overall picture. Heck, even do some trendline analysis, to get what the slope of the linear elastic trendline actually is.
Also, after reaching a certain point in the material’s loading, it will no longer be linear elastic. It will be in the realm of irreversible deformation, due to exceeding the yield strength. It still can hold the load, but on release, it will not restore to the initial length.
To avoid including the irreversible deformation in your trendline, it is important that you look at your load vs extension plot, and seek the exact point, where the graph ceases to be close to a straight line. Do not include anything more extended than that, in it.
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