Part 3. Background. The calculation of total force due to a distributed force is an important engineering calculation: If you have an object that is H meters tall then the total force, F, due to a distributed force (f(z) - force per unit length dz) (see Figure 2) and its line of action can be calculated as: -F H Figure 2. Distribuled force and line of action The total force due to the distributed force is F= [ f (2)dz (5) The location of the line of action, d, of F is the effective location of the force F. d= Jo z f (2) dz So f (=) dz (6) For example, if f(=) = 200= [N/m] with z ranging from 0 to 15 m. F = 200 ed= = (100=1):" = 100(15# - 0) = 2.25x10'NThe line of action would be: -15 m 1 200 d = So f (=)dz 2.25x10+ N J. 200 #-d= = = 2.25x 104 # 3 (15' - 0) = 10 m F = 2.24x10' N H = 15 m D = 10 m Z f(z) = 200z Figure 3 When f(x) is a simple function like in the example above, solving Eqs. 5 and 6 can be done analytically (by hand). However, as in Fig. 2, it is more likely that the functional relationship is complicated. For this situation, numerical methods provide the only alternative for determining the integrals. In this part of the project you need to find the total wind force exerted on the side of a skyscraper and its line of action. The force is distributed and varies with height. You only know the force per unit height, f(z) at certain discrete z values - every 30 meters starting at ground level. These values are given in Table 1 You will find the force and line of action two different ways: a. Based on the data in Table 1, determine the coefficients of a third order Newton's interpolating polynomial that represents f(z). Once you have the polynomial integrate it as in Egs. 5 and 6 to determine the total force and its line of action. F and d. b. Use your python code for Simpson's 3/8 rule to compute both F and d.C. Compare the results for F and d from each technique of calculation... when we say compare we mean numerically and to analyze how significant the differences are and why there are differences (or not). This section of your project is of equal importance to the calculation portions. This should be a complete analysis of what you did and why there are differences if any and if there are not significant differences why that is the case. Table 1. Force on side of a skyscraper. Height (z in m) Force/height (f(z) in N/m) 0 0 30 340 60 1200 90 1600 120 2700 150 3100 180 3200 210 3500