The fracture strength of glass may be increased by etching away a thin surface layer. It is believed that the etching may alter the surface crack geometry (i. e. reduce crack length and increase tip radius). Calculate the ratio of the etched and original crack tip radii if the fracture strength is increased by a factor of 5 when 62.0% of the crack length is removed.

Which of the following components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated? a)- proportional b)- derivative c)- integral d)- on/off.

A-mn has a cubic structure with a0 0.8931 nm and a density of 7.47 g/cm3. b-mn has a different cubic structure, with a0 0.6326 nm and a density of 7.26 g/cm3. the atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. determine the percent volume change that would occur if a-mn transforms to b-mn.

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.