1. You are working on a revolutionary new tricycle and need to machine a 1.90" diameter, 8" long axle shaft. It is very early in the morning and you have not had coffee yet so you have placed a long section of 2" cold-rolled round bar stock in the lathe with 8" sticking out of the chuck and started machining. A load cell just so happens to be hooked up to the tool holder and measures a force of 4.2 kN in the 'X' direction when the tool is facing the end. Assume that the material is isotropic, no plastic deformation takes place and the lathe components are perfectly rigid. a) What is the maximum deflection of your work piece? b) If you set a cutting width of 0.010" for each pass, describe qualitatively whether and how the diameter would vary along the length of the shaft after you have taken several passes. c) What are two methods that can allow you to machine your axle properly?