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I feel the best way to reach accurate results is to use a vernier scale approach, a laboratory method for measuring the stress and strain in a long, thin copper wire. I have to control the temperature or make sure that the room temperature remains constant. The Young’s Modulus for a particular material is the same, so each diameter of wire should give us the same value for Young’s Modulus. Apparatus: Diagram (fig. 3) Results table: Diameter of wire, (d) 2.
32 Extension, (e) m.
The diagram fig. 3 shows the arrangement, which I would use. The advantages in using this method than another is that: 1. The scale for measuring extensions is on the reference wire. If the test wire pulls the ceiling downward, the reference wire and the scale move with it. Therefore, the scale measures only the extension, not the sag of the support. 2. If temperature changes make the test wire expand or contract, the reference wire changes in the same way.
3. A vernier is used to measure the tiny extensions accurately.
The vernier is a second scale on the test wire itself, which is accurate to 0.1mm. Dividing the extension by the original length gives the strain. 4. You use a micrometer screw gauge to measure the diameter of the thin copper wire. This is accurate to 0.001mm. This gives you the cross-sectional area, and you divide the weight of each load (in N) by the area to get the stress. I will measure the diameter of the test wire at several places and take an average because the wire may not be uniform, I will measure the extension for loads between 100g and 1100g.
I will also check that the length goes back to its original value, this is to check whether the wire has reached the elastic limit of the wire or not.
After having got this data, it could be plotted on a stress/strain graph to find the Young modulus of copper. Preliminary: I used four different diameters of wire in this preliminary; I wanted to explore how diameter affects the extension. Doing this will help me decide on which wire to use in the actual experiment. The readings I got were as below:
Diameter of wire, (d) mm Break Diameter of wire, (d) mm 0 Diameter of wire, (d) mm 0. 37 Load, Kg 0 I feel that the wire of diameter 0. 19mm is not suitable for this experiment because of the fact that it does not give me many readings to work with. There are also the matters of safety, the wire snaps suddenly with no warning so it is dangerous to use this wire.
The extension in the 0. 28mm wire is the most consistent, and I feel that it will give me the readings needed to work out the Young modulus of the copper wire. However, we would not be able to see when the elastic limit is reached because of the limit in the load applied to the wire (1. 10kg), unless we find a method of adding more weights. I need to take as many readings of extensions and forces as I possibly can to increase the accuracy of the Young modulus. The Young modulus equation is used to find the stiffness of the wire it is defined as below: Young’s modulus =.
Stress Strain We usually plot a graph with stress on the y-axis and strain on the x-axis, the Young modulus is therefore the gradient of the line, it is important to consider the gradient to be on the first straight section of the graph. The load will be varied, by adding weights and thus the extension shall increase, in the preliminary and research I have found that if we stretched a copper wire to determine its Young modulus, you’d notice that, beyond a certain point, the wire stretched more and more and will not return to its original length when the load is removed.
It has become permanently deformed. This is described as plastic deformation. I have discovered from recent class work and coursework, that the diameter of a length of wire, sometimes varies, from one end to the other. The table below shows the diameter change in a wire labelled as 0. 28mm: Diameter (mm) 0. 00m 0. 50m 1. 00m 1. 50m 2. 00m 2. 30m Average As you can see from above, the diameters of the wire, gives me an average of 0. 29mm, this in turn will affect the cross-sectional area. So the average cross-sectional area.
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