Avariable-speed belt drive consists of the two pulleys, each of which is constructed of two cones which turn as a unit but are capable of being drawn together or separated so as to change the effective radius of the pulley. if the angular velocity of pulley 1 is 3.5 rad/s (constant), determine the angular acceleration α2 = ω˙2 of pulley 2 in terms of the rates of change r˙1 = 6 mm/s and r˙2 = 8 mm/s. the instantaneous effective radii are r1 = 85 mm and r2 = 60 mm.

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?