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Making Sense of Data: Young’s Modulus Of a Metal and An Alloy

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Introduction

Making Sense of Data: Young's Modulus Of a Metal and An Alloy Aim: - To draw the stress- strain graphs for a metal and an alloy, calculate the Young's Modulus for both metal and alloy and to discuss the physics. A contrast will be made between both materials relating to their stiffness. More details given below: Plan: - Above is a diagram of the set-up used to obtain the results. A micrometer was used to measure the diameter of the wire. A 1m Rule was used to measure the length of the wire. To carry out the experiment, first set up the equipment as shown above. Apply a unit weight of 200g onto the hook each time and take a measurement of the distance between the staring point and the present point of the marker (overall extension). Repeat the experiment 3 times for each metal. MEASUREMENTS: Copper Constantan Length of wire: 2.10m 2.10m Area of cross section: 0.37mm 0.35mm The measurements above were each taken 3 times and averaged. PERPARATION: - The procedure shown above was used to obtain the results below. Young's Modulus = Stress/Strain Stress = Force/Area Strain = Extension / Original Length The above formulae will be used to calculate the young's Modulus and will be plotted on a graph. ...read more.

Middle

FORCE (N) EXTENSION (m) ORIGINAL LENGTH (m) STRAIN (ratio) 0 0 2.1 0 2 0 2.1 0 4 0.00133 2.1 6.35x10-4 6 0.00267 2.1 1.27x10-3 8 0.00333 2.1 1.59x10-3 10 0.00433 2.1 2.06x10-3 12 0.00533 2.1 2.54x10-3 14 0.00567 2.1 2.70x10-3 16 0.00700 2.1 3.33x10-3 18 0.00933 2.1 4.44x10-3 20 0.01267 2.1 6.03x10-3 22 0.02733 2.1 1.30x10-2 24 0.08930 2.1 4.25x10-2 The Strain is calculated by doing Extension / Original length The Young's Modulus is calculated by finding the gradient of the preceding graph. The extension given above was converted to meters by dividing the average extension for copper by 1000. CONSTANTAN: FORCE (N) STRESS (Pa ) 0 0 2 2.08x107 4 4.16x107 6 6.24x107 8 8.32x107 10 1.04x108 12 1.25x108 14 1.46x108 16 1.66x108 18 1.87x108 20 2.08x108 22 2.29x108 24 2.49x108 26 2.70x108 28 2.91x108 30 3.12x108 32 3.33x108 34 3.53x108 36 3.74x108 38 3.95x108 40 4.16x108 42 4.37x108 Diameter of wire = 0.35mm = 0.0035m Radius of wire = 0.0035/2 = 0.00175 m Area of cross section of wire = ?*r*r ?x0.00175x0.00175 = 9.62x10-6 m Stress = Force/ Area The Stress was achieved by using the formula above. I used the corresponding force and divided it by the cross sectional area (9.62x10-6 m ). ...read more.

Conclusion

There were uncertainties in the experiment, however I believe they were compensated by other measurements that had errors, which were negligible. The experiment was repeated 3 times and results and measurements were averaged. There could have been many unconsidered factors such as kinks in the wire. They are like notches in the wire, when a force is exerted and the wire is extended, the notches are like anomalies in the wire, as they do not extend. The wire should uniformly extend however the force will untangle the notches rather than extend the wire. See diagram: Another problem was the fact that the area of the cross section could vary across the length; this however could be a minor error. It could be eliminated, as when taking the average diameter reading of the wire, it should be taken three times at both ends of the wire. A 2-meter wire was used rather than 1 despite making the calculations slightly more difficult. When measuring the extension, it will now be easier to read as the extension should be larger due to the fact the wire is longer. The longer the wire, the more accurate the measurement. However this would have made the experiment impractical. Another problem would be the scale of the graphs sketched, ...read more.

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