An open top railroad car (initially empty and of mass Mo) rolls with negligible friction along a straight horizontal track and passes under the spout of a sand conveyor. When the car is under the conveyor, sand is dispensed from the conveyor in a narrow stream at a steady rate AM/At = C and falls vertically from an average height h above the floor of the railroad car. The car has initial speed vo and sand is filling it from time t = 0 to t = T. Express your answers to the following in terms of the given quantities and g.Use "v_0" when you want to enter "vo" and "M_0" when you want to enter "Mo". a. Determine the mass M of the car plus the sand that it catches as a function of time t for 0 < t < T. symbolic formatting help b. Determine the speed v of the car as a function of time t for 0 < t < T. symbolic formatting help c. i. Determine the initial kinetic energy K, of the empty car. symbolic formatting help ii. Determine the final kinetic energy Kf of the car and its load. symbolic formatting help iii. Is kinetic energy conserved? Explain why or why not. d. Determine expressions for the normal force exerted on the car by the tracks at the following times. i. Before t = 0 ii. For 0 < t <T iii. After t = T 0 symbolic formatting help *symbolic formatting help **symbolic formatting help