Calculating the Young's Modulus of Copper and Constantan Wire
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Calculating the Young's Modulus of Copper and Constantan Wire
Aim === The aim of the investigation is to calculate the young's modulus of copper and constantan wire, using five different diameters. Prediction ========== I predict that the stress Vs strain graph for copper and constantan will look like:  * E  the elastic limit, above this point Hooke`s law (where stress and strain are proportional to each other) can now longer be applied. * P  the plastic limit, above this point the material no longer returns to its original shape once the force is removed. e.g. the point a will contract online the dotted line parallel to the original slope. * D  the breaking stress, where the wire finally snaps. [IMAGE] I predict that the copper and constantan wires will follow the same pattern, as constantan is an alloy of copper, it is normally 60% copper and 40% nickel. Background information ====================== Young's modulus is given by tensile stress divided by tensile (the direction it is in tension) strain. E = tensile stress / tensile strain Young's modulus E is a constant for the same range over which Hooke`s law can be applied. Stress is the force per unit cross sectional area on a wire, and hence has units of N m2 or Pascal's, it is a measure of the strength of the material. Strain is the extension divided by the original length, and hence has nounits, it measures the length at which the material will stretch. Young's modulus (E) measures a material's elastic response in tension; it is normally measured from the stress/strain curve. It establishes the strength of a material. In metals and ceramics E is constant for the material, which doesn't change much with alloying. Method ====== Ceiling support Apparatus  · Micrometer screw gauge · Searles apparatus. · 100g masses · 1m rulers · Wire clippers · Sand tray · Stop watch · Pliers [IMAGE]Diagram ============== [IMAGE] [IMAGE] Test weight [IMAGE][IMAGE][IMAGE] Method ====== Firstly the wire that was being tested was cut out to a length of just over 1m, two wires of the length were cut out. The reason why they are cut just over 1m is because the wire has to be attached to the equipment and this takes up some of the wire. Before the wires are attached to the equipment the diameter of the wire was measured, measurements were taken at three different points of the wire and an average was taken, this was to make sure that throughout the wire was the same diameter. It is important to take the diameter of the wire as it is needed to work out the area of the wire. The area of the wire needs to be calculated to work out the stress of the wire (Force/area). The reference wire and the test wire was then hung on the bracket attached to the ceiling, this is where the wire was measured to 1m, it was important that the test wire was the same length throughout the experiment, so that the extension of the wires could be compared to one another and it would also be better for working out the strain of the wire. As the wires were not entirely straight test weights were added to the reference wire and the test wire to help straighten out the wire, the test weights that was added was 500g (approximately 5N). The test weights were added for 2 minutes and this was timed using a stopwatch. After these 2 minutes was up the spirit level was level and the reading on the vernier scale was recorded. Then 200g were added to the test wire and not the reference wire, as the reference wire was there to show how much the test wire had stretched. The 200g was added for 2 minutes, the reason this was done as the wire may not have reacted to the weight being added straight away, therefore decided to time the amount of time the weights were added so that the experiment was kept fair and accurate. After the 2 minutes were up the spirit level was levelled up again and then new reading on the vernier scale was recorded and this then gave us the extension of the wire. This was repeated with the adding of weights 400g, 600g, 800g and 1000g. To eliminate any inaccuracy each wire was tested 3 times, this is so any errors where averaged out. The extension of the wire is needed to calculate the strain of the wire (extension of wire/original length) This experiment was repeated with all the different thickness for copper and constantan wires. As we are using weights and the wires could snap at any time it is important to take into considerations the safety aspects. In case the wire does snap goggles should be worn and also a trap of sand should be place underneath the weights so that if the weights do fall they fall into the tray of sand instead of on our toes or on the floor. Fair Test ========= To make the experiment as fair and accurate as possible only one variable should be used. The variables in this experiment:  Thickness of wire: the thicker the wire the more force needed to extend the wire and vice versa Temperature: the temperature affects the wire as if the wire is warm it will extend further where as a colder wire will not make the same extension and is likely to snap quicker than a warm wire. Load: the more weights that are added to the wire the more extension that occurs In the experiment I am testing how much the wire extends by varying the weights, but I am also changing the thickness of the wire. To make it a fair test I changed one variable at a time. To make the experiment accurate I am using searles apparatus. This is where the scale for measuring extensions is on the reference wire. If the test wire extends as weights are being added to it the scale moves with it therefore measuring the extension. The extension of the wire is measured using a vernier scale and this is used to measure tiny extensions accurately and is accurate to 0.1mm. If the temperature changes and makes the test wire expand or contract the reference wire changes in the same way. The constantan and copper wires diameters can be measured using a micrometer screw gauge. This is accurate to 0.001mm. Analysis ======== Graph 1: This line graph of stress & strain for copper after a load of 1.96N shows that after a load of 1.96N the plastic limit hasn't been reached, this region is the point where the material no longer returns to its original shape once the force is removed. This means that if the force of 1.96N were to be removed the copper wire would return to its original length of 1m. The reason that the wire can return back to its original length is because the no dislocations in the ploystalline structure have occurred. Also after a load of 3.92N (graph 2) and 5.88N (graph 3) the plastic region hasn't been reached. As the plastic limit hasn't been reached it shows that Hooke's law can be applied, this is where stress and strain are proportional to each other. Graph 4 & 5: These line graphs of stress & strain for copper after a load of 7.84N & 9.8N shows both the elastic (above his point Hooke's law can no longer be applied) and a plastic region. We can tell that the elastic limit of the copper wire was at 81MP on both graphs, this is found from reading of the graph where the straight line ends and the curve begins to start. This also shows the yield stress for copper. The yield point is a point just after the elastic limit this is where there is a big change in the material and this is due to a distorting force. The bonds between molecular layers break and layers flow over each other. After this point the material starts to become plastic, as it has reached and exceeded its elastic limit. The reason that the material can no longer move back to its original shape once the force is lifter is due to dislocations in the polycrystalline structure of the metal moving, the dislocations move along by a process called slip. All the atoms are in a crystalline arrangement and during the elastic area they are stretched and elongated until they reach their elastic limit when they will begin to slip against each other and permanently deform. As the wire extends the crystalline structure stretches and begins to dislocate and the dislocations slip until the structure is perfect and there are no dislocations left. The young's modulus of copper can be seen in table 7. It would have been expected to find the young's modulus of the copper wire of different wires to be the same however looking at the table it can be seen that it does not. This therefore shows some errors in the experiment. By taking an average of the results the I have found the young's modulus of copper to be 20917.09 Mpa. Graph 6, 7 & 8: This line graph of stress & strain for constantan after a load of 1.96N, 3.92N & 5.88N shows that after a load of 1.96N, 3.92N and 5.88N the plastic limit hasn't been reached. As the plastic limit hasn't been reached it shows that Hooke's law can be applied, this is where stress and strain are proportional to each other. Graph 9 & 10: This line graph of stress & strain for constantan after a load of 7.84N & 9.8N like graph 1 shows both the elastic and a plastic region We can tell that the elastic limit of the constantan wire was at 85MP, this is found from reading of the graph where the straight line ends and the curve begins to start. This also shows the yield stress for constantan. It can be seen that the young's modulus varies quite a lot this shows that there have been some errors in the experiment, which will be discussed later. The young's modulus of constantan can be seen in table 14. The young's modulus has been calculated for each wire separately, the reason for this is because in theory the young's modulus for copper whatever the diameter of the wire should be the same, however looking at the table it can be seen that the youngs' modulus is not the same throughout the table. Looking at part of the table:  Young's modulus (Mpa) 1.96 3.92 5.88 7.84 9.8 7699.798978 7699.798978 8662.273851 9726.061867 10043.21606 21276.94528 10638.47264 9118.690836 9118.690836 9386.887625 21460.61282 30402.53483 36483.04179 32429.37048 36483.04179 84181.12692 59421.97195 47351.8839 41231.57237 43541.9622 41917.35127 44383.07781 43529.55708 42210.4796 41917.35127 Taking an average of the young's modulus for constantan we get 30012.63 Mpa. Looking at the graphs and the elastic limit and young's modulus of the two wires it can be seen that they are quite similar. This is to be expected, as constantan is an alloy, which usually mainly consists of about 60% copper, this would therefore mean that it would have similar properties. It will not have the same properties as copper as it is also usually contains 40% nickel, it would then also have some of nickel properties. Also as mentioned above the young's modulus of a metal doesn't really change much with alloying. By comparing the two graphs it can be seen that constantan has a steeper graph and the steeper the graph to stiffer the material, therefore constantan is slightly stiffer that copper. Also by looking at the young's modulus that has been worked out it can be seen that constantan has a bigger young's modulus then copper. In physics "modulus" means a measure of the extent that a substance processes some property. Young's modulus describes how well an abject retains its length when stretched or compressed. It is also a measure of stiffness. Therefore as copper has the smaller value of young's modulus it means that copper is more easily stretched then constantan, since less stress is needed to achieve a given strain. On the graphs I have included error bars. The reason that I have included error bars is because the metre ruler has an error of 0.1mm and also an error of 0.01mm on the veriner scale and the micrometer screw gauge. These bars then take this error into account. Looking at the graphs it can be seen that there are some anomalies this could have been due to many factors. Errors that could have taken place include the errors in the equipment and the other random systematic errors that can occur. Also there could have been parallax errors (this is an error which occurs when the eye is not placed directly opposite a scale which a reading is being taken), reading errors this is when errors come about when guess works is involved in taking a reading from a scale when the reading lies between the lines. Another error could have been creep; this is where the wire is stretching when no more weights have been added. As the wire is stretched the diameter of the wire decreases and before the wire snaps plastic deformation takes place. This reason this happens is because metals such as copper and constantan are ductile and they can have large plastic deformations without fracturing. It happens because atoms move as the plastic deformation in the crystal structure move to a place of lower stress. This causes the wire to become thinner as the atoms are moving away from the stress part. The stress then increases because the crosssectional area has decreased. This increases the ductile flow and so the metal yields and gets thinner and thinner. Once plastic deformation starts, atoms will continue to flow without any increase in stress. . Another cause for inaccuracies may be due to the fact that the 1m length of test wire may not have been accurately measured out. As the vernier scale measures in mms, but the test wire was measured out using a metre ruler and this is not accurate to 1mm. Improvements that could be made to the experiment would be use a longer test wire as it would be easier to measure the strain, for example, if we used a sample ten metres long we would have a ten times better resolution, making our results much more accurate. We would then need to ensure that the weight of the 10M wire was very much smaller that the weight we added to induce strain. Also to further improve the experiment I would test more different diameter of wire as the there is a gaps inbetween the points on the graph where we had to predict what would happen there it would be more accurate to test more wires with different diameters inbetween the points. I would also add weights at smaller intervals instead of 200g jumps, this would help in making the graphs more accurate, therefore allowing us to read of the graph more accurately getting better readings. Aspects of the experiment that were good were, the vernier scale is sensitive and the maximum extension, which could be read off it, was dependant on how much force is applied. This method is much more accurate than the clamp and pulley method which could have been used. The experiment was done in the same classroom and was done at room temperature as the temperature of the wire reduced the accuracy of the results as the wire stretches more under warm conditions because the wire is less stiff then if it was in cold temperatures. How to Cite this Page
MLA Citation:
"Calculating the Young's Modulus of Copper and Constantan Wire." 123HelpMe.com. 18 Apr 2014 <http://www.123HelpMe.com/view.asp?id=121384>. 
