The following data for the density of nitrogen gas ver-

17.13 Bessel functions often arise in advanced engineering

analyses such as the study of electric fields. Here are some selected values for the zero-order Bessel function of the first kind x 1.8 2.0 2.2 2.4 2.6 J 1 x 0.5815 0.5767 0.5560 0.5202 0.4708 Estimate J 1 2.1 using third- and fourth-order interpolating polynomials. Determine the percent relative error for each case based on the true value, which can be determined with MATLAB’s built-in function besselj . 17.14 Repeat Example 17.6 but using first-, second-, third-, and fourth-order interpolating polynomials to predict the population in 2000 based on the most recent data. That is, for the linear prediction use the data from 1980 and 1990, for the quadratic prediction use the data from 1970, 1980, and 1990, and so on. Which approach yields the best result? 17.15 The specific volume of a superheated steam is listed in steam tables for various temperatures. For example, at a pressure of 3000 lbin 2 , absolute: T , °C 370 382 394 406 418 v , Lt 3 kg 5.9313 7.5838 8.8428 9.796 10.5311 Determine v at T = 750 °F. 17.16 The vertical stress σ z under the corner of a rectangu- lar area subjected to a uniform load of intensity q is given by the solution of Boussinesq’s equation: σ = q 4π 2mn √ m 2 + n 2 + 1 m 2 + n 2 + 1 + m 2 n 2 m 2 + n 2 + 2 m 2 + n 2 + 1 + sin −1 2mn √ m 2 + n 2 + 1 m 2 + n 2 + 1 + m 2 n 2 Because this equation is inconvenient to solve manually, it has been reformulated as σ z = q f z m, n where f z m, n is called the influence value, and m and n are dimensionless ratios, with m = az and n = bz and a and b are defined in Fig. P17.16. The influence value is then tabulated, a portion of which is given in Table P17.16. If a = 4.6 and b = 14, use a third-order interpolating polyno- mial to compute σ z at a depth 10 m below the corner of a rectangular footing that is subject to a total load of 100 t metric tons. Express your answer in tonnes per square meter. Note that q is equal to the load per area. TABLE P17.16 m n = 1.2 n = 1.4 n = 1.6 0.1 0.02926 0.03007 0.03058 0.2 0.05733 0.05894 0.05994 0.3 0.08323 0.08561 0.08709 0.4 0.10631 0.10941 0.11135 0.5 0.12626 0.13003 0.13241 0.6 0.14309 0.14749 0.15027 0.7 0.15703 0.16199 0.16515 0.8 0.16843 0.17389 0.17739

17.17 You measure the voltage drop V across a resistor for a

number of different values of current i. The results are i 0.25 0.75 1.25 1.5 2.0 V −0.45 −0.6 0.70 1.88 6.0 Use first- through fourth-order polynomial interpolation to estimate the voltage drop for i = 1.15. Interpret your results.

17.18 The current in a wire is measured with great precision

as a function of time: t 0.1250 0.2500 0.3750 0.5000 i 6.24 7.75 4.85 0.0000 Determine i at t = 0.23.

17.19 The acceleration due to gravity at an altitude y above

the surface of the earth is given by y , m 30,000 60,000 90,000 120,000 g , ms 2 9.8100 9.7487 9.6879 9.6278 9.5682 Compute g at y = 55,000 m. PROBLEMS 427 FIGURE P17.16 b z a ␴ z