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Figure 17.12 shows an apparatus used to determine the linear expansion coefficient of a metal wire. The wire is attached to two points a distance d apart (you don’t know d). A mass hangs from the middle of the wire. The wire’s total length is 100.00 cm at 0°C. The distance y from the suspension points to the top of the mass is measured, and the results are given in the table below. (a) Find an expression for v as a function of temperature, and manipulate your expression to get a linear relation between some function of y and some function of temperature T. You’ll encounter the expression L2 where L is the length of the wire, and, because the change in length is small, you can drop terms involving α2 when you expand L2. (b) Calculate the quantities in your relation from the given data, and plot. Determine a best-fit line and use it to determine the coefficient of linear expansion a and the separation d. (c) Consult Table 17.2 to identify the metal the wire is made of. Ignore any stretching of the wire due to its “springiness”; that is, consider only thermal expansion.
Temperature. T (°C) | 0 | 20 | 40 | 60 | 80 | 100 | 120 |
y (cm) | 30.00 | 30.05 | 30.07 | 30.11 | 30.16 | 30.19 | 30.24 |
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