This crystalline for that reason will not be able to hold the amount of tension which will be applied by the weights gradually being added on; however we can predict that the copper element will deal with much stress and therefore will experience necking as the atoms as revealed in the diagram will dislocate the atoms and for that reason they can move past each other more easily, subsequently leading to the fracture of the material. Copper is usually by itself really weak that is why it requires to be solidified and enhanced for many industrial applications.
It is therefore mixed with other metals and melted. When performing this experiment I consider that as the number of weights is increased for copper, this will gradually apply pressure and the particles will gradually pull apart as the bond will break between the molecules. The material will reach its elastic limit, where it has actually reached its point where by after if any more weights are added then it will deform and not return to its original state.
Here is a diagram listed below which highlights this: (Image drawn out from physics book).
The equations that I will obtain in this investigation to learn the objective, which is to learn young’s modulus of both materials through illustration of the charts from the outcomes I will need to utilize the following equation as this is what will help me attain this part of the objective: From my charts, I will discover the gradient and therefore be able to exercise young’s modulus by the formulae above.
I believe that young’s modulus for constantan will be high since I consider from the evidence provided that it will have the ability to take more pressure then the copper (crystalline).
I deem this simply because constantan being an alloy can take more of a load then a pure metal. Here is a typical example of a stress train graph: (obtained from my physics textbook) Fair test: Test the wire to get an average; I will do this three times. All of my figures will be to three significant figures. I will carry this out on the same day in the same conditions, using all of the same apparatus. I will keep the metre stick stuck down to the table and not move it, so that it won’t affect my results, when marking off the extension. Apparatus:
I will be using the following: Pulley Metre ruler and a marker Mass weights and actual storage unit Wooden blocks to hold the wire in place A G clamp. Safety: I will ensure that I keep this a safe experiment by: Keeping the cardboard over the wire, as when the wire snaps the wire would not suddenly lift up and cause any danger. I will also make sure there are not people crowding the experiment when it is being carried out, as the weights can cause danger if they fall. Results: I have entered the results I have been given into Microsoft excel.
From this the extension I have been given, is given in mm, but in physics we have to convert mm to metres. From the materials given I would find out the area of the wire as the area can depend on the wires, as they can have different thicknesses. Diameter: 0. 37mm The cross sectional area: pi r^2=1. 075×10-7m2 To find the out the cross sectional area I simply had worked out the radius, which was 0. 000185, I achieved this figure by dividing the diameter (0. 37) by 2000. By calculating this I was left with this figure. I will need to find out stress over strain which will give me young’s modulus.
Since the length of the wire is 2. 1metres this will be used to find out the strain. Here are my results for copper: Here is my table of results showing results from the copper wire. I have worked out the stress and strain which therefore simply allowed me to work out the young’s modulus of copper, and this I have shown on the computer. I have also shown the table showing the formulae I had input in the cells in Microsoft Excel. I have shown this below, in the last four columns where I had input the formula into the cells to aid me to work out young’s modulus of copper.
I have shown the results I had obtained for copper above, now I will produce a table showing the results I achieved for constantan the alloy which I believe would have a higher young’s modulus then copper. I had used the same length of wire which is 2. 1metres as I made sure this was a fair test when conducting the experiment. I have worked out the cross sectional area as the same in the procedure before. Here are my results for constantan: Diameter: 0. 35×10-3 Area: p r^2:9. 6210×10-8 m2 Here are my results stated above showing the results from the constantan wire.
The results show the young’s modulus for constantan at the given force. Below is the formulae table showing the formulae which were input into the cells from stress and strain. When simplifying these results it will be evident I belie that the constantan wire will have the higher young’s module, and this will be clear in the graphs I produce. I have now simplified my results so that I can easily plot my graph from these results. I have made them show the stress to the power of 10 to the 7, and strain which is ten to the power of minus three. Here are my two tables: Results for constantan (for graph)
Stress Nm times 10 Strain Young’s Modulus times by 10 (times 10 ) Stress Nm times ten Strain (e/L) Young’s Modulus times by ten times by ten Analysis: In this experiment my aim objective was to find young’s modulus from copper and constantan wire. I have shown this by taking the first step which was to produce the results table, and from this I have plotted the graphs showing the force against the average extension. Observing my graphs you can see that I have plotted two separate graphs showing force against the average extension for both materials.
Furthermore, you can also see that I have created the graphs showing stress-strain for copper and constantan. This graph typically shows young’s modulus. The wires had reacted to the weights in the way that I had expected as I predicted that constantan wire will have the higher young’s modulus and is more tough typically because it is an alloy which contains 40% nickel which makes this element extra strong, whereas the copper is a pure metal and will not be able to take the strain of the load and this is proven as the copper wire could only take 24N as it broke, whereas constantan wire could take almost double the amount 42N.
This illustrates that constantan wire needs more force to extend the wire; whereas copper is a material which is frail and would extend by a suitable weight which puts strain onto the material. We can perceive that copper is more easy to stretch by the information I have produced in the table as at 20N it had an average extension of 0. 013 metres, however constantan wire if what my theory is, then I believe that at 20N, constantan should have a smaller average extension then copper has. Looking at the table, the average extension for constantan at 20N is 0. 006 metres.
This proves my theory correct as these two results show the difference between the two materials instantly. We can now say that constantan is more tensile, as an alloy it has an enables the dislocation of the atoms which help grip the structure together and therefore give it the property of being tough, this is explained in my diagram I have drawn on page 3. I believe that the atoms in the pure metal copper, had displaced and therefore become unstable when the load was placing strain upon the wire. This would ultimately, make the atoms move out of position and break up, resulting in the wire shattering.
This is why when the copper wire had reached its maximum load which was 24N, the atoms had suffered a permanent deformation in the arrangement as they would have been changed in their formation, but unable to move back. This is the same principle with the wire, as it was being stretched and the atoms moved out of place, but the load was greater then the elastic limit could handle and this is why there is a permanent deformation where the wire does not return back to it original shape and changes length, resulting in the increase in extension.
In the constantan wire, this would be identical however the atoms would be harder to move out of place, as this material can handle far more load then the copper wire could. So at the same weight (24N) this wire would still return to its original shape because it is in its elastic state. However once it exceeds it elastic limit, then the wire loses its formation of atoms and does not return to its original shape. Here is a graph showing elastic and plastic locations in this graph, this is a way of working out young’s modulus, or by working out the gradient of a graph.
I have also found a diagram from my physics textbook, which shows the general yield stress for materials including copper and constantan. By observing the diagram this will give further evidence for my analysis upon the results I have achieved: What each of my graphs show: My first graph shows force against the average extension for the copper wire, this graph shows that the average extension had increased with the force, however only to a certain point, as this remained elastic from 0N to 24N. After this remained plastic, where the wire could not handle any more load and had shattered.
My second graph shows force against average extension for constantan wire. This wire indicated through the graph actually can handle much load, and it has a very large elastic region, as this alloy is very tough, therefore can handle large amounts of weights. This wire could handle 42N however after it then remains plastic, and broke. The third and final graph illustrates further insight into the young’s modulus of copper and constantan wire, as I have plotted the two materials on the same graph.
It is indicated that constantan has a higher young’s modulus compared to copper material. This is because copper can easily be shattered as it stretched very much compared to constantan. The gradient is smaller compared the constantans, which means copper has the smaller young’s modulus because it is a metal and nothing stronger whereas the constant material has elements such as nickel which gives it the strength it requires to dominate copper. Evaluation: I perceive that this experiment was completed under fair conditions as this was kept a fair test at all times.
I believe that repeating the experiment three times, had made this fair and given the accuracy which was needed. I had made sure that the materials were used to 2. 1 metres in length and had the same diameter. However, the errors which appeared in this experiment (uncertainties) are where when measuring the wire of the constantan or copper I had rounded up or down the value depending n whether it was greater then X. 5 or below.
In my graphs, this is shown as these have been drawn in for average extension, so there is an uncertainty error of about 0.5mm. Another uncertainty spotted I believe is where I had calculated young’s modulus on the graph, I plotted a line of best fit. The line of best fit was drawn in hand by me, however this line can cause uncertainty as this is based on human error and accuracy as everyone will have their own judgment and perception when drawing the line of best fit. Furthermore, I can see that my line of best fit is not totally wrong as looking at the young modulus of copper which is 3*10 to the power of 10, and constantan 6. 40 to the power of 10.
We can see that constantan young’s modulus was said to roughly double coppers young’s modulus value, and this is proven by these two figures given. We can see that these two figures are nearly double in difference therefore they seem to be correct. When measuring the wire with a metre stick I found there were an uncertainty of 0. 5mm, and an uncertainty of 1% with the weights. The experiment in general had gone according to plan. I’m pleased with what I had found out through the results as I believe my prediction was correct and backed up by the results from the graph I had achieved.
I believe that repeating the experiment three times meant that I had accurate results as from the average extension I plotted the graphs. Concluding this experiment I had found out that constant had the higher young’s modulus due to it being an alloy and containing the 40% of Nickel which gives it the strength property. Copper however, had been more flexible being a pure metal the atoms were easily dislocated and this resulted in copper breaking very easily as it had a small elastic limit. Improvements-IF TO DO IT AGAIN.
Bibliography:I had obtained information from the following resources: o AS physics textbook: I had found this source extremely interesting and useful as much of the diagrams I had used came from this textbook, which explained the comparison between the pure metal and alloy.
This textbook had given much information which was relevant to this coursework. 8/10 o AS physics CD-ROM: I had achieved the diagrams mostly from the CD ROM, this CD had many diagrams which were useful, however this did not contain much written information which was useful and could aid me with this coursework.6/10 o Internet:
I found that the information from these sources seemed very reliable and information I had gained, helped me understand the complex issues with the relation of physics to young’s modulus. I had obtained the various information I have included on the background information on the sensor from the following Internet sites: o http://www. emsl. com/tensile_strength. html o http://www. encyclopedia. com/html/Y/Youngsmo. asp o http://hyperphysics. phy-astr. gsu. edu/hbase/permot3. html.