Wednesday, April 10, 2019
Measuring Youngs Modulus of Copper Essay Example for Free
Measuring Youngs Modulus of blur EssayAimTo study the stress/ turn over behavior of atomic number 29 telegram and estimate the Youngs modulus of copperApparatusCopper disclosefit s.w.g.32 about 4 mG-clamp ?1Wooden block ?2Metre rule ?4Pulley on clamp ?1Micrometer bum suppose ?1Hanger (0.01 kg) ?1Slotted mass (0.05 kg) ?8Slotted mass (0.1 kg) ?6Slotted mass (0.2 kg) ?4Slotted mass (0.5 kg) ?1White go aft(prenominal) sticker ?1Safety goggles ?1Rubber tile ?1TheoryWhen a force F is applied to the end of a wire with cross-sectional firmament A along its length, the bendable stress =If the appendix of the wire is ?l, and its original length is lo, the tensile strain =Under elastic conditions, a modulus of elasticity of a wire, called the Young modulus E, is defined as the ratio of the tensile stress applied to a body to the tensile strain dumbfoundd. where E is expressed in N m-2 or Pascal (Pa).E is a constant when ?l is small according to the Hookes Law which verbalize that the stress applied to any solid is proportional to the strain it produces for small strain.Therefore, when a material has a larger the value of E, it resists to the elastic deformation strongly and a large stress is required to produce a small strain. E is thus a measure of the elastic stiffness of a material.However, when the backstage (deformation) of the wire is likewise large, beyond proportional limit, solid will no longer obey Hookes equity i.e. E is no longer a constant.As the stress further increases, beyond the elastic limit, the wire has a permanent lengthening that the wire is no longer elastic and it undergoes plastic deformation. The extension increases apace as the force on the wire is further increased. The wire elongates and breaks. The stress just before the wire breaks is called the breaking stress.ProceduresSet-up of the apparatus1. The apparatus was set up on the bench top as shown to a lower place The wire was firmly clamped by using a G-clamp so that it does not slip. A white label sticker was fixed on to the copper wire to act as a marker much(prenominal) that it is about 50 cm from the blocking. A metre rule was fixed alongside the wire with the manufacturing business for measuring the extension.Performance of the try1. The hanger was tied to the end of the wire so as to straighten out the kinks in the wire and the unstretched length (lo) of the wire from the edges of the wooden blocks up to the marker was measured.2. A micrometer screw gauge was used to measure the diameter of the wire at different angles for each of the 8 mess along the wire.3. The wire was loaded with slotted mass m insteps of 0.10kg and then 0.05kg and the extensions ?l after each loading were recorded until the wire broke.Data tableOriginal length of wire lo = (3.000 0.001) m component part error in lo=Diameter of the wire (mm)0.2550.2500.2250.2300.2250.2550.2250.255Average diameter of the wire = (0.240 0.005) mmPercentage error in d =Readings for the chartLoad m / kg0.100.200.300.400.500.600.65Extension ?l / mm0.51.01.52.02.53.03.5Load m / kg0.700.750.80.850.900.951.00Extension ?l / mm3.54.05.06.06.57.5BrokeData analysisYoungs modulus,where F is the tension in the wire and A is the cross-section areaSince andFrom the graph, the lurch of the best fit cast through the points of the straight line portion of the graph,Assume that the cross-sectional area did not vary as the stress increased.Errors accuracyFrom the graph,the slope of the best fit linethe maximum slopethe minimum slopeDeviations m+ m = 12.1Deviations m m- = 26.0The maximum error in slope = larger of the deviations = 26.0Slope of load-extension graph = (192.7 26.0)Percentage error in slopePercentage error in E= % error in slope + % error in lo + 2 ? % error in dYoungs modulus of copper, E = (125 22) GPa conclusion The stress applied to a copper wire (s.w.g. 32) is directly proportional to the strain it produces before the extension becomes 3.5mm. The ratio of stress to strain will get smaller and not constant when the extension beyond 3.5mm (proportional limit), i.e. after the extension reached 3.5mm, small increase in stress can produce a gigantic increase in strain. Copper obeys the Hookes law. The Youngs modulus of copper is (125 22) GPaSources of Error1. The copper wire did not break a constant cross-sectional area along its length.2. There was fractional force out-of-pocket to the pulley applying to the wire.3. Reading error in measuring the extension and the unstretched length.4. Fluctuation of room temperature might change the diameter of the wire during the experiment.5. The wire in the experimental set-up was not exactly horizontal that made our measurement of extension not accurate.6. The cross sectional area of the wire got thinner under stress so that the pass judgment stress would be less than the stress actually applied.Improvement of the Experiment1. Fixed the metre swayer by another G-clamp so that measurement of the extension can be more accurate.2. In devote to measure extremely small extension with high precision, optical lever (a mirror mounted on a small pivot) can be used instead of just using a guileless meter stick.3. Repeat the experiment several time and take come of the extension values so that more accurate result can be obtained4. The experiment can be repeated as below so that the small extension of the wire can be measured accurately by vernier scale moreover, there will be no extra fractional fore due to the presence of pulley.5. Repeat the experiment by using copper wire with different s.w.g and take an average of the Youngs modulus obtained so that we can estimate the value of Youngs modulus of copper more accurately.Precautions1. Wear safety goggle during the experiment so as to protect our eyes when the wire breaks eventually2. The load should not be too high off the floor, and there should be a suitable soft landing platform, such as runner tile right below the load.3 . The unstretched length should be at least 3m for the wire to extend.