This is a way to determine the Young Modulus as an individual, rather than group practical. For years I thought that you needed a pulley for the wire, but it turns out you don’t. Without that limiting factor, it becomes a pfaff reducing exercise.
Summary
Get a plank of “whatever you can find” width, about 1.2m long, drive a screw in about 5cm from one end. Photocopy a normal ruler at 100% then at 90%. Check the reduction is accurate! Use the 90% to make a vernier scale. Get about 2m of 32swg copper wire and tape the vernier scale to the wire at 1m from the nail. Line the vernier up with the 100% scale and gently hang 1N weights to the end of the wire that hangs off the end of the plank, measuring each extension. The diameter of the wire is done traditionally by using a micrometer or looking up the diameter of swg wire in mm.
Steps and Photos
This is one of our dynamics ramps, but any old plank could be used. It needs to be more than 1m long and should stick out over the desk to give the weights room to hang. This is 32swg copper wire, diameter 0.27mm90% photocopy of the ruler. Do check that 10.0cm in the copy is 9.0cm on the real ruler (some photocopiers reduce by a few percent as a matter of course). It may take some trial and error (keep notes for next time…). In the experiment I took photos of, I used a real ruler for the 100%, but realise a photocopy would be better.The vernier scale at 1m from the screw. It is sellotaped on. ± 2mm is fine (± 0.2% uncertainty is negligible compared to the extension and area)Wear goggles, but you also need some protection from flying wires (not such an issue with copper, but other alloys can store a lot of energy). These cardboard pieces help prevent the wire from flying around. e.g. with 32swg copper you 1-10N is fine and prety safe if it breaks, but with nichrome you might want 1-40N in 4N steps which is altogether more interesting if it snaps.)I use a 10g hanger to tension the wire so that there is a nice talking point about the ice hockey stick shape of the graph (a false extension on the first weight because it is taking up the slack and pulling out kinks). Note the hanger is near the floor and there is a sandbag in case the weights fall: it stops you putting your foot there more than protecting the floor.
For those of you who assess against CPAC, this is a good experiment for 3a (Identifying Risks) and 3b (Working Safely). I use the Hazard | Risk | Control approach to a risk assessment. e.g.
Hazard
Risk
Control
Wire breaking.
Flailing wire causing damage to exposed skin/eyes. Weight falling on feet.
Eye protection. Weights over wire for kinetic energy transfer. Sandbag on floor.
I realise that the weights on foot issue is not a massive one, and using copper wire makes the flailing wire unlikely too, but they do need practise thinking about these things for bigger challenges ahead.
The main pfaff is getting the top ruler (the scale) parallel with the wire. The bottom ruler is just raising the vernier to the height of the top scale. I now realise I could dispense with both rulers and use a 100% photocopy (or thinner ruler!) for the scale. This reading would be 828.8mm.Normal micrometer screw gauge practice for the diameter (three times). Check the micrometer for zero error. I would do a whole lesson on micrometers well before attempting Young modulus, and would give a few a nice zero error using the little adjustment spanner that comes with them. Area is πd²/4 (rather than finding r, which just introduces another opportunity for mistakes). Uncertainty here (assuming a perfect zero) is ± 0.005mm (it is a reading) or 1.9% for the diameter so 3.7% for the area, which I would round up to 4% (I always err on the side of caution).My lab book, but before I stuck in a screw instead of using a G clamp! With 1m of 32swg copper you get about 1 mm extension per 4 N weight on the wire. The wire starts to slip at around 10-13N, and the general guidance is 5 < number of readings < 10 so the whole experiment can comfortably be done with one hanger with ten 1N weights on it. Assuming we discount the first couple of readings, making 2N our “zero” the uncertainty in the first real extension (2 to 3N) is ± 0.1mm on 0.3mm or 33%, but this reduces so by the fourth point (2 to 6N) the uncertainty is ± 0.1mm on 0.9mm or 11%.
With the pulley
Very similar to pulley but over the edge of the plank, honest!
Hooke’s Law using this apparatus – this was the wire hung over the end of the plank
Three graphs of real data showing how the pulley (middle) makes no difference, the first and third are with the wire simply hanging over the edge of the plank. The final one (green dots) is Hooke’s Law.
I also made a video.
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