Stiffness
Stiffness is the property of a specimen, e.g. a piece of wire. It is not a "material property". In other words we can talk about the stiffness of a copper wire but not the stiffness of copper.
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If we apply a tensile load, F, to a copper wire it extends
by a certain amount x.
If we plot F against x we get a graph which is initially straight. Take a pair of values from this straight line section and then stiffness k = F / x (N/m) Knowing the stiffness of the wire we can calculate by how much it would extend under any load (as long as we do not go beyond the limit of proportionality). |
How stiff a wire is depends on the material it is made from but it also depends on its dimensions, i.e. its length and how thick it is.
Consider the stiffness of a combination of springs.
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If we put springs in series the tension in them is the same
as if there were just one spring. Each extends by the original amount so
the total extension is double. The stiffness is therefore halved.
Increasing the length of a wire decreases its stiffness for the same reason. If we put springs in parallel then the tension is shared between them. The extension is halved. This is equivalent to increasing the cross sectional area of a wire. The force is spread out over a bigger area. Increasing the c.s.a. of a wire increases its stiffness. |
Is there any way we can take the dimensions of a wire into account and produce a quantity that describes the material itself?
