Using the governing equation for the axial deformation of a bar, argue why the displacement field must be quadratic (independent of the boundary conditions for the bar) in the presence of a constant distributed body force; i. e. for the case where b(x) = bo a constant. Assume AE is constant.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.