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Calculating the Young Modulus of Constanton

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Introduction

Calculating the Young's Modulus of Constanton By Hannah Godfrey Introduction Constanton is a copper-nickel alloy mainly used in the for its electrical resistance properties. It has a high resistance which is constant over a wide range of temperatures. I am going to find out the Young's modulus of this wire and observe its behaviour. Apparatus * Constanton Wire * G-Clamp x2 * Pulley * Hanging weights * Ruler * Micrometer * Small marker flag * Wooden end blocks * Sponge Blocks Underlying Theory When a sample is deformed by a force, the deformation is proportional to the magnitude of the force. This is shown by Hooke's Law where: Force is equal to a stiffness constant (k) times the extension (e).The force is proportional to the extension. For a sample we can also calculate stress and strain: Where stress is equal to force (F) divided by area (A) and strain is equal to extension (e) divided by original length (l). When you plot these on a Stress-strain graph it proves Hooke's law when it is straight line but as soon as the graph curves, the sample is showing plastic deformation as it is past the elastic limit. Using this graph we can work out the Young's Modulus of a sample which is: This is also measured in Nm-2 or Pascal's (Pa). It can also be calculated by working out the gradient on the stress-strain graph. ...read more.

Middle

of its original length before the wire broke. Experiment 3 I changed the diameter again so I could record more conclusive results. I used a diameter of wire in between the diameters of the first two experiment (0.31mm) and an initial length of 500mm. I still couldn't record too accurate results as the wire didn't extend enough so I could only plot three points on a graph before it showed plastic behaviour. Further experimental changes were needed. Experiment 4 This time I changed the initial length of wire used to 800mm from 500mm. This would amplify the extension so I could measure it with the ruler because the rate of extension would increase and also the amount of extension would increase. By increasing the initial length of wire it would also decrease the percentage error in the measurement of the wire with the ruler. The percentage error goes from 0.1% to 0.063%. Experiment 5 This was a repeat to check the accuracy of experiment 4. In this experiment i encountered a few problems. The knot holding the weight hangers on kept slipping and the results found did not match the pervious pattern. Experiment 6 This was my third repeat of experiment 4. This gave me a fairly similar set of results to experiment 4. Due to time restrictions, no more experiments could be carried out to do a third repeat. ...read more.

Conclusion

- Actual mass of the weights which is an example of systematic error. Conclusion Using experiments 4 and 6 I was able to work out my young's modulus of Constanton by finding the gradient of the initial straight part of my graph. Experiment 4 = 280GPa Experiment 6 = 240GPa The real value of the young's modulus is 162GPa so I am out by approximately a factor of two. This is not too far away from the true value considering the huge uncertainties involved with my measurement technique. To improve my accuracy I would either have to improve my measurement techniques or change my method completely. In conclusion, the method was affective for demonstrating the affects of Hooke's law but not for measuring accurately the young's modulus of constanton. Modifications in the Method * Attaching the pointer to the pulley stops the pointer coming into contact with the sample of wire which could obstruct deformation but if the wire extends more than the pulley can measure then the experiment will not work. * Illuminate the pointer to produce a magnified shadow of the movement. This makes it easier to see movement and allows for more accurate measurement however you need to calculate and calibrate magnification. * Use wire that isn't wound round a real because it distorted the start point of my curve. A typical young's modulus curve starts at the origin but mine doesn't because first few hundred grams was used to apply tension to the wire to bend out the curves. ?? ?? ?? ?? ...read more.

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