For each of the plane stress states listed below, draw a mohrs circle diagram properly labeled, find the principal normal and shear stresses, and determine the angle from the x axis to s1. draw stress elements as in fig. 311c and d and label all details.
a) sx 5 10 kpsi, sy 5 24 kpsi (b) sx 5 10 kpsi, txy 5 4 kpsi ccw (c) sx 5 22 kpsi, sy 5 28 kpsi, txy 5 4 kpsi cw

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.