Using a forked rod, a smooth 3-lb particle is forced to move along around the horizontal path in the shape of a limaçon, r = (5+sin θ) ft. If θ =LaTeX: \frac{1}{8}t^21 8 t 2 rad, where t is in seconds, determine the force of the rod and the normal force of the slot on the particle at the instant t= 3sec. The fork and path contact the particle on only one side.

At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2