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How can I work out the Young's Modulus of copper wire?

Extracts from this document...

Introduction

How can I work out the Young’s Modulus of Copper?

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List of apparatus:

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Physics:

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Variables:

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Method:

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Safety:

Risk

How was this reduced?

Wire snapping and injuring eyes

Safety goggles were worn while undertaking the experiment

Weights dropping and injuring feet

Moved away from weights once plastic deformation took place, visibly obvious by the wire stretching and not stopping.

Weights dropping and marking floor

Carpet tile was placed underneath the weights, protecting the floor from being scratched.

Sources of uncertainty:

Source

How can the experiment be improved to combat this?

Measurement of total wire length (±0.24%)

A tape measure could be used to measure the length of the wire, as it would allow me to be make measurements in more awkward places, such as up the side of the wooden block. Numerous measurements could be taken and then an average could be found to give the total wire length.

Measurement of extension length (±11%)

I could’ve placed the

...read more.

Middle

Taking more readings at further points down the wire and then finding an average will give a more certain result for this. The micrometer must also be calibrated.

Values of extension between 10N increments

Using 5N weights instead of the 10N ones should make this experiment more precise, as more values will be used to determine the average, making my result more accurate.

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:

Source

How can the experiment be improved to combat this?

Zero error – measuring extension

The marker to measure the extension could have not been properly aligned with the zero on the ruler, meaning that all the rest of the measurements are invalid. The only remedy of this was to take extra care in aligning the two.

Placement of weights on hook

While placing the weights on the hook, extra pressure may have been applied by accident, causing the wire to stretch more. Once again, the only way to fix this problem was to take more care while placing the weights on, and to place them on quickly, without applying extra force to the end of the wire.

Evaluation of improvements:

 Improvement

Did it work?

Doubling over of loops

Although the experiment was able to go on for longer, this made no difference to the value of the gradient– as despite the loop breaking, the elastic region’s gradient did not change – only the yield point.

Use 5N weights instead of 10N ones, to improve precision.

This did work, as can be seen in Run 3 – The result is much closer to the expected value, a result of the experiment being more precise, and a more accurate line being able to be drawn.

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Conclusion

±0.005mm

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.

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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.

...read more.

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