Metallic strings exist in different kinds but I would like to measure for a metallic string:
the section/geometry along its length, to a precision of 1/100 mm
its elongation when a tension is exerted on it on a measuring system I would construct to apply forces of the order of 1 to 100 daN. I have no clear idea of the order of magnitude of the elongation, so it might be too small to measure with reasonable equipement.
Any ideas, suggestions, theoretical and practical remarks welcome.
In a physics laboratory session at university we measured the extension of copper wire with different weights attached. To do so requires two wires hung vertically, one has the weights attached and is stretched, the other acts a sort of control. Between them a device is attached, this contains an adjustable spirit level.
Before the weight is applied the spirit level is set to horizontal, after the weights have stretched one string the device can be re-levelled and this 'correction angle' implies a certain extension.
To predict the sort of stretch you might achieve I would suggest looking up Youngs Modulus: http://en.wikipedia.org/wiki/Young%27s_modulus. (For metal wires and 'safe' loads don't expect very much!).
To accurately measure the cross section, assuming you know the material's density, just measure the length, mass and use $$\sigma = \frac{M}{\rho\;L}$$
If you're interested in the answer (rather than having to measure it), and you know the material's Young's modulus, it's easy to calculate the extension. But I'll assume you don't know this (which strength of a material is a lot harder to predict than its density).
If you're having trouble measuring the extension due to its small amount, then use the following fixture:
The idea is to use leverage so you can measure a smaller change in string length. There are two strings, one with no weight applied, the other stretches slightly. The result is that the blue stick moves quite a lot. (Probably it would be better to have the blue stick set up so that it has equal lengths on either sides of where you attach the strings. I'd use balsa for the stick.)
Ah. Hobby engineering. You have strayed into an area of intense interest. Here is a simple Rube Goldberg device which may give you other ideas:
build a short teeter-totter ("TT") with a laser pointer clamped to it, so that the laser points at a wall. Make sure the TT is fairly level, the fulcrum of the TT is firmly supported and that it is fairly balanced (so as to not add weight to your string). Attach one end of the TT near the free end of the string. Turn on the laser, make a pencil mark on the wall where it hits, load the string, and make your second mark.
Call the length from the TT fulcrum to the string = TS. Call the length from the string to the wall = SW. Call the length from your first to second wall mark = WW Call the length of stretch of the string = SS
Then: SS/TS = WW/(TS+SW) ---> SS = (WW)(TS/(TS+SW))
If you build a TT with a 2 inch half-arm (TS), and your wall is 9 feet away, you will get a movement magnification of 110/2 = 55. This might not be enough.
Another idea would be to mount a small mirror on the TT and hit it with a fixed laser, so that it bounces back to the wall. This would double your sensitivity (movement magnification of 110). If you made TT for the mirror = 1 inch, you could get approximately double that (218). If you wanted to add another mirror at the target spot on the wall and make your pencil marks on the opposite wall... well... you do the math. :-) As long as you keep the angles small (less than 5 degrees) you can dispense with any trig and just use simple geometry.
string-theory... $\endgroup$