You need to measure the material constants of the cell by atomic force microscopy. Your atomic force microscope has a cylindrical cantilever of radius R = 0.45 µm, length L = 200 µm, and the Young’s modulus Ecl = 90 GPa. The cantilever tip is conical with half-angle \alphaαα = 30°. Your measurements show that the vertical displacement of the cantilever \DeltaΔΔz is proportional to the square of the penetration depth (sample height) \deltaδδ, with a coefficient of proportionality equal to 9,000 µm-1. Determine the Young’s modulus of the cell provided the Poisson’s ratio of the cell is 0.5.

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?