In this problem, we will design a plate cam with a flat-face follower. the displacement is given as ݕሺߠሻ ൌ ൝ 0 if 0 ൑ ߠ ൏ ߨ/2 1 ൅ cosሺ2ߠሻ if ߨ/2 ൑ ߠ ൏ 3ߨ/2 0 if 3ߨ/2 ൑ ߠ ൏ 2ߨ the displacement is measured in cm. (1) obtain the derivatives ௗ௬ ௗఏ and ௗమ௬ ௗఏమ. (2) determine the optimal radius r0 of the prime circle to avoid the undercut. use the minimum radius of curvature for the cam profile rhomin = 2 cm. (3) determine the minimum face width for the follower.

A2-m rigid tank initially contains saturated water vapor at 100 kpa. the tank is connected to a supply line through a valve. steam is flowing in the supply line at 600 kpa and 300 c. the valve is opened, and steam is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. a thermometer placed in the tank indicates that the temperature at the final state is 200°c. determine (a) the mass of steam that has entered the tank (b) the amount of heat transfer.