Chapter 17, Problem 71P

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