An axis has a horizontal leadscrew that moves a 150 lb load. the screw has 5 threads per inch (p = 5 rev/in), ⇢ = 4.48 oz/in3 density, 42 in length, ⌘ = 0.75 eciency and 1.5 in diameter. the linear bearing friction coecient is µ = 0.15. the motion profile is trapezoidal with ta = td = 150 ms, tm = 1s, tdw = 0 s and vm = 2 in/s. all coupler inertias and carriage inertia are negligible. the servomotor has jm = 6.56 oz in2 inertia. calculate the peak and rms torques (in units of oz in) required for this application

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.