Monday, July 30, 2012

M and I: Young's Modulus

After looking at the relatively involved apparatus used by the authors and the $1100 Pasco apparatus, I was pretty worried about measuring the Young's modulus for materials. After a very fun meet-up dinner with M and I adopters (seriously - when's the last time that you, Halliday, Resnick, and 20 excited adopters had dinner?) last night, I got three different methods to measure it from folks there:
  •  First, from Mark Hammond, the idea of just hanging a wire from an I beam in the ceiling, putting a pointer on it, and measuring.  I hadn't gotten around to trying this, but I was thinking that it'd be a good last-ditch substitute. 
  • Second, from Aaron Titus (do you have a blog Aaron?), the idea of doing that but with a motion detector underneath the mass hanger.  If the wire stretches enough, this will measure the distance more accurately than the first method (which is apparently possible - I thought that the stretch wouldn't be much relative to the motion detector's resolution, but I guess that I'm underestimating one of the two).
  • Third, also from Aaron, attach one end of the wire to a clamp, run it horizontally (I ran it a little more than 6 meters to maximize the stretch amount) over a Pasco rotary motion sensor.  Have a short length of wire hanging over the pulley and wrapped around a mass hanger.  It only took about 500 g of mass to get a nice range of stretch.  Even a 50 gram difference caused an easily measurable stretch for the sensor (around .05 radians/50 grams).
For the third method:
  • No knots: wrap the wire around both connection points - you don't want kinks and knots slipping.
  • I measured the tension force with a force probe as well as calculating it from mg.  They were pretty equivalent in practice (as well as in theory, of course), so I'll just use mg.
  • I used thin enameled magnet wire (.17 mm diameter - don't know the gauge); I'd like to get aluminum wire as well, so that I can predict resonant frequencies for the singing rods.
  • Edit: put a catch box underneath.  As I was writing this, the wire gave way with 500 g hanging from it.
  • Here's the data - 118.9 GPa (117 on Wikipedia). I'll surely take that. I'll use this to predict v for a transverse wave, too, and see if I can get agreement there, but this is seriously encouraging.

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