Flexure Problem Set 1. [10 pts} Calculate (by hand) the maximum flexural deflection w(x) at x=0, given the following information: Plate elastic thickness = 50 km, Young's modulus = 70 GPa, Poisson's ratio = 0.25, load height = 4 km; load width = 20 km, load density = 2700 kg/m3, mantle density = 3300 kg/m3, infill density = 1.2 kg/m3 (air). Show your work, and pay close attention to units as you calculate the load, alpha, and D. Give your answer in meters. 2. a) [10 pts} Write a Matlab script to calculate the flexural deflection w(x) for x=0:700 km given the above information. Include your script and a plot of the deflection (w) vs. x. b) [2 pts} Based on your plot, give the x position and height of the peak of the flexural bulge. c) [3 pts} Using your Matlab script, change the infill density to that of water (1030 kg/m3) and give the x position and height of the peak of the flexural bulge. d) [3 pts} Modify your Matlab script from (c), changing the elastic thickness to 30 km and give the x position and height of the peak of the flexural bulge. e) [5 pts] Make a general statement summarizing how the density of the infilling material and the plate elastic thickness affect the maximum deflection and flexural bulge