How can I work out the Young’s Modulus of Copper?
List of apparatus:
Physics:
Variables:
Method:
Safety:
Sources of uncertainty:
Total percentage error = 0.24%+11%+1.8% = 13%
Largest source of uncertainty:
The largest of these uncertainties is most definitely the breaking of the loop. Not having a strong enough loop caused the wire to unravel at the end and the weights to drop off. This does not give an accurate representation of the yield point of the material by any means, as it doesn’t show the material itself snapping, just the loop unraveling. This will therefore not show the point at which the material starts to undergo plastic deformation, and will hence make the graph look completely different, ...
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Total percentage error = 0.24%+11%+1.8% = 13%
Largest source of uncertainty:
The largest of these uncertainties is most definitely the breaking of the loop. Not having a strong enough loop caused the wire to unravel at the end and the weights to drop off. This does not give an accurate representation of the yield point of the material by any means, as it doesn’t show the material itself snapping, just the loop unraveling. This will therefore not show the point at which the material starts to undergo plastic deformation, and will hence make the graph look completely different, meaning that an accurate Young’s Modulus cannot be determined. To fix this, the loop was strengthened by being doubled over upon itself, and not being twisted as much, as the twisting would also weaken the wire. This allows more weights to be hung onto the end, and so allows the Young’s Modulus to be calculated properly.
Possible sources of systematic error:
Evaluation of improvements:
Results:
Results with a white background above indicate the results I used to calculate the gradient – The rest are the results once the material has undergone plastic deformation, and are therefore impossible to determine properly.
Results with a black background are anomalies. These are ones that did not fit with the general pattern of the data. They were discounted, as they would make the final result inaccurate.
The gradient of the above graphs (y=mx + c) will give an overall average of the force/extension. This allows me to work out the Young’s Modulus of the material, in comparison to its recognised value of 117GPa (according to Wikipedia).
Here are the results for the first two runs:
As you can see, these two results are both wildly inaccurate in comparison to the actual measured result of 117 GPa. This shows me that strengthening the loop does not improve the accuracy of the measurement. My prediction was wrong – in actual fact, a different yield point should not change the elastic properties of the material, and therefore would not change the gradient.
After this, the same experiment was tried but with increments of 5N weights as opposed to 10N weights, hoping to achieve a more accurate result:
Results with a white background above indicate the results I used to calculate the gradient – The rest are the results once the material has undergone plastic deformation, and are therefore impossible to determine properly.
Results with a black background are anomalies. These are ones that did not fit with the general pattern of the data. They were discounted, as they would make the final result inaccurate.
As you can see above, the result has increased, becoming around 8GPa closer to the expected value, presumably showing that this is indeed a more accurate way of finding the Young’s Modulus. Having said this, it is still very far off the actual expected result (even regarding the percentage boundaries of 13%), certainly showing that this inaccuracy was not the result of instrumental uncertainty errors, but instead a large procedural error.
Conclusion:
In conclusion, this was not the best way to find out the Young’s Modulus of Copper, as there were too many ways in which the experiment could have gone wrong. A Vernier scale would have been a much more efficient way of recording the extension, and would have more easily resulted in the correct value for the Young’s Modulus.
