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Young’s Modulus of Copper Abstract:
I did an experiment to find the young’s modulus of a copper wire, which was resulted to be 27.6 GPa for my first experiment, and for my second experiment it was 74.4GPa. I did this by finding the length of the copper wire I used for the experiment I was doing and adding 1 Newton each time to the Newton hanger and seeing how much the copper wire extends by each time. At the end of all three of my experiments I calculated an average extension of the copper wire. Then I drew my graphs to show how the copper wire extension is affected by force. From my graphs I could find the young’s modulus of copper wire, by taking the gradient and multiplying it by length over area.
Introduction:
During my experiment, I am hoping to find out the young’s modulus of the copper wire. The results that I am expecting to achieve is that, as I carry on adding the same amount of Newton’s on the copper wire, I am expecting to see that the extension of the copper will gradually increase. The key equations that would be effective to use in my experiment is, the young’s modulus is a measure of elasticity and stiffness of a specific material. Strain is the proportional percentage of extension in comparison to the original length. Stress is the pressure of force that is applied to a material to change its shape. The young’s modulus is also used by engineers in today’s time, to make sure that the material that they are using can withstand sufficient forces.
Young’s Modulus (Nm¯²) = Stress/ strain
Stress (Nm¯²) = force (N)/ area (m²)
Strain= extension length (m) Original length (m)
This can be written as:
E= F*L/ A*X
E= Young’s Modulus
F= Force
L= Original length
A= Area
X= Extension length
This can also be written
as:
2 | P a g e Equipment List: • G- Clamp • Vernier caliphers • Tape • 1 Metre ruler • Bench pulley • 2 wood pieces
• Thin copper wire of 0.375 • Safety spectacles
• Hanger with slotted weights for Newton’s.
Method:
The method I that I used to find the different extension lengths and the young’s modulus of copper was quite simple. Firstly I gathered up all my equipment that I would be using for the experiment, (which I have listed above), I measured the length of my copper wire to my desired measurement where I used the average length for all three of my tests. Then I got that piece of copper wire and put it on a piece of wood and I then covered the piece of wood with another piece and clamped it together with a G- clamp. Thirdly, I attached the vertical pulley to the table, where I positioned it opposite to the clamped pieces of wood and at quite a distance too, I then laid the copper on the vertical pulley so that it hangs off. Then I place the 1 metre ruler in between the g- clamp and the vertical pulley, and put it so that it touches the vertical pulley, to get accurate readings, I then put a piece of tape on the copper and where the start of the tape was is where I read the measure, I did this to get my first reading of 0 Newton’s (without any force). I then, got the Newton hanger and tied the copper wire to it and again let it dangle off the vertical pulley this gave me a reading for 1 Newton. I then slotted in the 1 Newton every time into the Newton hanger and then see how much the copper wire has extended by. During my first test I found it quite hard to read the measurement of how much the copper wire was extending by, so I got a ruler and places it at where the tape starts and read the read the measurement, this gave me a more precise reading. However when I used the ruler, the ruler may have been in contact with the copper causing movement to the wire, this may have disrupted my results.
Safety:
The first thing I used to ensure that I took precautions in doing my experiment is that I used safety goggle just in case the wire rapidly becomes loose from the g clamp or the Newton’s. Another precaution that I took is that I stood at a reasonable distance from the Newton hanger, and when I was adding on the Newton on the hanger a I made sure that my feet weren’t below it, otherwise if the copper wire snapped it would of fell on my feet and may of have caused severe injuries.
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Results (1st experiment):
To get my results I performed three tests that were all very similar, the only that may have been different is the length of the wire, as this may have affected the displacement of the wire and would therefore affect the extension of the copper wire. I did three tests to ensure that my results are reasonable and sensible and don’t looks like a random set of results.
Table 1: Thickness of copper wire (on vernier calliper) = 0.4± 0.1mm Length of copper wire= 1.85 m ± 1mm
Force (N) (0.4±0.01N) Displacement (mm) (±2 mm) Extension (mm) (±2mm)
0 801 0 1 803 2 2 805 4 3 806 5 4 806 5 5 807 6 6 807 6 7 809 8 8 809 8 9 809 8 10 810 9 11 810 9 12 811 10 13 812 10 14 812 10 15 813 12 16 814 13 17 815 14 18 816 15
In this table of results, the original length of the copper wire that I measured was 1.85m. As you can see from my table that I started to measure my copper wire at 801mm, also my displacement measurement were quite consistent as I kept adding 1 Newton each time. To work out how much the copper wire was being extended by, I simply took a cumulative of the displacement results; I did this for the following tables also.
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Table 2: Thickness of copper wire on vernier calliper= 0.4± 0.1mm Length of copper wire= 1.87m ± 1mm
In this table of results, the original length of the copper wire that I measured was 1.87m. As you can see from my table that I started to measure my copper wire at 796mm rather than starting to measure at 801mm so the difference would be 5mm. However, in my results of displacement, we could see that it is quite different to table 1 results as there are more duplicates in millimetres as I kept adding 1 Newton each time.
Force (N) (0.4±0.01N) Displacement (mm) (±1.5 mm) Extension (mm) (±1.5 mm) 0 796 0 1 797 1 2 798 2 3 798 2 4 798 2 5 799 3 6 800 4 7 800 4 8 801 5 9 801 5 10 802 6 11 802 6 12 803 7 13 804 8 14 804 8 15 804 8 16 806 10 17 807 11 18 810 14
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Table 3: Thickness of copper wire (on vernier calliper) = 0.4± 0.1mm Length of copper wire= 1.90m ± 1mm
In this table of results, the original length of the copper wire that I measured was 1.90 m. As you can see from my table that I started to measure my copper wire at a much lower
measurement of 785mm than the other to tables. Similar to table 2 the measurements of
displacement kept on duplicating each other after 2- 3 Newton’s were added.
Uncertainties (1):
During my experiment there were quite of few uncertainties that have made an effect on my results. One of these uncertainties is measuring the thickness of the copper wire, which has an uncertainty of 0.03%, this uncertainty may have come from the Vernier caliphers which are not very accurate in their readings, whereas in my second experiment I have used a micrometer which would reduce the uncertainty to a minimum and would give me a more accurate reading. Another uncertainty in my experiment is my actual results, this is because systematic errors may have affected the results, as I may have read the metre rule wrongly and not accurately, I may have read this incorrectly by the angle I was looking and
measuring the metre rule under the copper wire. Also during my first experiment I kept touching the metre rule by accident which may have changed my readings and results. To improve, I sell taped the meter ruler to the table to ensure that it doesn’t move. The length
Force (N) (0.4±0.01N) Displacement (mm) (±0.5mm) Extension (mm) (±0.5mm)
0 785 0 1 787 2 2 788 3 3 788 4 4 788 4 5 789 5 6 789 5 7 790 6 8 790 6 9 790 6 10 791 7 11 791 7 12 792 8 13 792 8 14 792 8 15 792 8 16 793 9 17 794 10 18 795 10
6 | P a g e of my copper wire also had uncertainties within as it had 0.05%, which is very little; this may be due to dents and bends within the copper wire as I unwrapped the wire. Another
uncertainty is my extension, as it has 0.02% uncertainty. This could have been made by my readings of the meter rule; I may have been off by half an mm. I think the main factor that causes my largest uncertainty would be the length of my copper wire due to systematic errors. In addition, there are various ways in which I could have reduced the uncertainties, one of my best ways would be to tape my ruler to the table and probably mark the copper wire from where I am measuring, and this would give me much clearer readings.
Results (2nd experiment):
Table 1: Thickness of copper wire (on micrometre) = 0.19± 0.05mm Length of copper wire= 1.800 m ±1mm
Force (N) (0.4±0.01N) Displacement (mm) (±0.5 mm) Extension (mm) (±2 mm)
0 709 0 1 710 1 2 711 2 3 711 2 4 712 3 5 713 4 6 730 21 7 771 62
Force (N) (0.4±0.01N) Displacement (mm) (±0.5 mm) Extension (mm) (±1.5 mm) 0 700 0 1 700 0 2 701 1 3 701 1 4 702 2 5 709 9 6 718 18 7 792 92
Table 2: Thickness of copper wire (on micrometre) = 0.19± 0.05mm
Length of copper wire= 1.700m ± 1mm
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Table 3: Thickness of copper wire (on micrometre) = 0.19± 0.05mm Length of copper wire= 1.710m ±1mm
ANOMOLOUS RESULTS!
These results are spurious results as the copper wire snapped at just 3 Newton when all my other results show that the copper wire started to behave elastically at around 7 Newton’s. I ignored these anomalous results, and done test 3 again as you can see below which gave me a more sensible and reasonable set of results.
Table 3: Thickness of copper wire (on micrometre) = 0.19± 0.05mm Length of copper wire= 1.770m ±1mm
Uncertainties (2):
As you can see from my results from my second experiment my uncertainties in my
displacement and extensions are very much better, as before they were around 1.5 to 1.0. Whereas in my second experiment I reduced my uncertainties to around 0.5, this would have a great significance on my results. In my length of the copper wire I had a uncertainty of 0.05% which is very similar to my uncertainty in my 1st experiment, this tells us that nothing has really changed in measuring my length, but it does however have a really low uncertainty which is good. I also had an uncertainty of 0.01% which is exceptional as it has made a great difference in my results and is much better from my uncertainty in my
extension in my 1st experiment; this tells us that my improvement worked. The thickness of my copper wire which I had measured with a micrometre had an uncertainty of 0.021%, so this result was much better.
Force (N) (0.4±0.01N) Displacement (mm) (±1.0 mm) Extension (mm) (±0.5 mm)
0 696 0
1 700 4
2 700 4
3 701 5
Force (N) (0.4±0.01N) Displacement (mm) (±0.5 mm) Extension (mm) (±0.5 mm)
0 700 0 1 701 1 2 702 2 3 702 2 4 703 3 5 706 6 6 710 10 7 727 27
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Analysis:
As you can see from my results tables above that they show that as I add Newton’s on the Newton hanger, the displacement increases by small amounts, this may be because of the thickness of the copper wire that I was using and the length of the copper wire. When I performed my second experiment, I used a much thinner thickness of copper wire of 0.19 ± 0.05mm when I used the micrometre (another factor/equipment that I used to improve the results from my first experiment). My results also show that they are also uncertainties in my displacement as I may have measure an mm to short or too much. Within my results I had to perform calculations to reach my extensions result, which I simply just did a
cumulative of the displacement. I also had to calculate my young’s modulus of the copper wire as this was my main focus and target to reach, I got the young’s modulus by, plotting a graph (force on x axis and extensions on y axis) for both my experiments, then drew line of best fit to get a gradient then with the gradient I multiplied it with L/A, I found L by reaching an overall average, and found the area by doing ² to the thickness of my copper wire, but first I had to divide it by 2 to find the radius. The anomalies in my experiment was in my 2nd experiment where one of my result tables just went up to 3 Newton’s, this is because it plastically deformed very quickly, this may have occurred by me putting more weight on the Newton hanger or by making the length of the copper wire to short so there would be more stress on the wire as I add weight, I dealt with my anomalies by ignoring those results and fully repeating that specific experiment.
