Draw stress and strain graphs for the metal copper and the alloy constantan. Calculate the figures of young's modulus for copper and constantan. Discuss the physics involved.

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AS Physics Data Analysis coursework

        This coursework assignment requires me analyse and evaluate data on copper and constantan given to me. It entails investigating the young’s modulus of the metal and alloy. Thus I will use many methods during to complete my investigation.

Aims:

  1. To draw stress and strain graphs for the metal copper and the alloy constantan
  2. To calculate the figures of young’s modulus for copper and constantan
  3. To discuss the physics involved

Plan:

        

        In this investigation I have received results for extension of copper and constantan for certain forces applied to it, for which I will analyse and calculate the young’s modulus. The results I have been given are forces applied to copper and constantan, three sets of results for the metal and alloy and this can be used by averaging data to give more accurate results thus these results given to me will be used to create graphs, calculate young’s modulus and analyse data for both metals so I can complete my investigation.

        I will need to draw a force and extension graph for both copper and constantan, the extension shown will be the averaged value for each metal. I will also calculate the stress and strain values and plot this on a graph for both copper and constantan, I will plot these on the same graph and analyse the graph, hence I can find any patterns from the data and this will require me to draw my graphs accurately so I can correctly analyse the results to make judgements and conclusions.

        I will use Microsoft Excel spreadsheet program to make tables of data, with the data I have been given. I will be using formulas to calculate average extension, stress, strain and young’s modulus for copper and constantan. I will also set my tables so that all data is to two significant figures.

        I have included a diagram of the set-up (Figure 1) below which was used to obtain the results I was given.

Figure 1 (SOURCE: AS PHYSICS CDROM)

        The experiment works by a G-Clamp holding the wooden block steady, this will place pressure on the wire to keep it steady at the clamped end. The cardboard bridges keep the wire straight and in place throughout its length. The pulley allows the wire to move freely along it to keep friction minimum. As load is increased this puts pressure on wire and it may extend in length, which is the variable I will be measuring.

A micrometer has been used to measure the diameter of both copper and constantan wires, the length was measured by use of a one metre rule.

        The measurements were made three times and then averaged, thus I was supplied with the following measurements:

        The results obtained from the experiment (diameter & length of wire, force and three sets of extension readings) will be used to calculate the following:

  • Area= r² (where r= Radius of wire)
  • Strain = Extension ÷ Original length
  • Stress = Force ÷ Area
  • Young’s Modulus: Stress ÷ Strain

These calculations in turn will enable me to plot graphs. The stress over strain graphs will be analysed and linear sections used to calculate young’s modulus, as both copper and constantan data will be plotted on the same graph I can find the differences between these materials in terms of young’s modulus & elastic limits. Other factors I will be considering in the investigation will be differences in stiffness (Young’s Modulus) of both materials and if this affects the ductility, tensile strengths and other physical aspects of the materials.

Prediction using scientific knowledge:

                I would predict that the young’s modulus of constantan will be higher than copper as it is an alloy and as we know alloys are generally less ductile and harder than pure metals. So hence it would take more load to create an extension for the alloy. Hence constantan would be stiffer and so this is why its young’s modulus would be higher than that of copper.

                The young’s modulus would tell me how stiff a material is when it is stretched. When a material is stretched, an increase in it length occurs (the extension) and it is proportional to the load, this means it obeys Hooke’s law. When a load is applied to materials they would go under extension until their elastic limit is reached, this means if you remove the load/force applied to it then it would go back into its original length. However if more load/force is applied and the material exceeds its elastic limit then the material yields and it becomes permanently deformed. (Adapted from Physics CD-Rom 40s).

                The young’s modulus can be shown on a graph of stress against strain. I have included a simple stress and strain graph (Figure2) to show how a material changes with different stress and stains added to it. (picture from ).

This graph shows how the initial linear section of the graph is when strain is proportional to stress. The part marked “X” is the elastic limit or yield point, this is the point of no return from this moment on the material in question is permanently deformed and can no longer return to its original state. The linear section however can be used to calculate the Young’s modulus of the material, by stress/strain.                                 

Figure 2

        As I mentioned earlier that I believe the young’s modulus of constantan will be higher than copper, this is because it is an alloy. Constantan Copper with 45% nickel” (Quoted from ). The constantan alloy with added nickel gives copper extra strength, “The nickel content in these alloys also enables them to retain their strength at elevated temperatures compared to copper alloys without nickel” (Quoted from ). This statement shows that pure copper is less able to keep its strength compared to copper alloys with nickel e.g. constantan.

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        The structures of alloys differ to pure metals. It is this structure that causes differences in properties of alloys and pure metals. It is the presence of an other metal that makes alloys stronger than pure metals. As pure metals may have dislocations in them this makes it easy for slips to occur, as there are spaces in between atoms called dislocations, and it is easy for these atoms to slip over each other hence this is why pure metals are more ductile than alloys. As shown in figure 3, the metal alloy has its dislocation pinned, thus meaning the ...

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