# Gas station without pumps

## 2011 December 16

### Young’s modulus lab in physics

Filed under: home school — gasstationwithoutpumps @ 16:36
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In Physics homework (Chapter 4) I proposed 3 labs to do with Chapter 4 of Matter and Interactions.  Last week we did the Slinky Lab (though students have not done the computational simulation of the Slinky yet and have not tried measuring the speed of compression waves from the video).

This week we did Measurement of Young’s modulus using a wire.

The session started out with us comparing answers on homework that we had all done (which finished up the homework for Chapter 3).  Then we looked up Young’s modulus, the yield strength, and the ultimate tensile strength for copper on the web.  We found 110-128 GPa for Young’s modulus, 20MPa for the yield limit, and 220MPa for the ultimate tensile strength.

Our goal was to figure out how long a wire we needed to measure a stretch of about 1cm, and how much force we would need to apply to get that much stretch.

We had three spools of magnet wire (AWG 30, 26, and 22).  For each wire we measured the diameter of the wire and looked up what it was supposed to be for that gauge (surprisingly, the numbers agreed to within the measurement accuracy of our micrometer).  We allowed ourselves a stress of 60MPa (staying below the yield limit) and independently computed how much strain this would cause (about 5.5E-4).  For a stretch of 1cm we would need a 20m wire at this stress.

We also independently computed cross-sectional areas of the wires and how much force would be needed to achieve that stress, getting 19.6N, 7.7N, and 3.0N for the 3 wire gauges. We chose the middle wire (26 gauge) as requiring forces in a reasonable range for pulling by hand. Since the forces are small and the wire long, we decided not to use hanging weights, but to use a hand-held force gauge, and stretch the wire horizontally.

We hammered a nail into a crack in the sidewalk and attached one end of the wire there.  We measured 20m of wire and attached the force gauge to the wire.

Here are our measurements of force and stretch:

force (kgf) stretch (cm)
0.29  1.2
0.445  1.1
0.90  3.1
0.64  2.7
0.765  3.2
0.995  2.5
0.84  1.5
1.11  2.2
1.285  3.6

We plotted these points and did a one-parameter fit, getting that the stretch was about 2.79 cm/kgf, but the scatter was rather large.

Of course, we abhor the “kilogram-force” fake unit (but that is what the \$5 force gauge is calibrated in), so this can be converted to a spring constant of 350 N/m. Our estimate for the spring constant of the 26-gauge wire based on published Young’s modulus was about 770N/m, so we seem to be off by a factor of 2.  Given the sloppiness of measuring with the force gauge we used, this is not really so bad.  The setup was certainly quite cheap—much simpler than Young’s modulus apparatus suggested by Chabay and Sherwood.

## 1 Comment »

1. […] we did then was to make a big loop of wire (26 gauge magnet wire—the same wire we used for our Young’s modulus experiment) from the floor to the ceiling beams, holding it to the floor with a couple of books, so that we […]

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