So, the initial setup an assembly of two small dense spheres, each of mass, m, whose centers are connected by a rigid rod of length , l and negligible mass. An astronaut has a device that will shoot a lump of clay mass, m, speed, [tex]v_o[/tex] express your answers in terms of m, [tex]v_o[/tex], l, and fundamental constants. for the first problem, the clay ball is shot directly perpindicular to the assembly and sticks to the midpoint of the rod. 1) Determine Total Kinetic Energy of the system (assembly adn clay lump) after the collision. So this would be Translational Kinetic energy plus rotational kinetic energy right? [tex] K_t + K_r = (1/2)mv_o^2 + (1/2)Iw^2 [/tex] w = omega and the initial and final rotational kinetic energy values are zero right, b ecause the clay ball strikes directly perpendicular at the midpoint The answer I got was [tex] K = mv_o^2 [/tex] 2)Determine the change in kinetic energy as a result of the collision so since there is no rotational kinetic energy [tex] (1/2)3mv_o^2 - (1/2)mv_o^2 [/tex] I don't know if its all right or not.... and then the next problem the assembly is reset, and this time, the clay ball is lanched perpendicularly at one of the clay balls in the assembly. The launched ball sticks to the one already on the assembly (right side) 1) Determine the distance from the left end of teh rod to the center of mass os the system (assembly and clay lump) immeadiately after the collision. (assume that the radii of the spheres and clay lump are much smaller than the seperation of the spheres. i got [tex] (L/2) [/tex] as the center of mass, but I know thats not right, but don't know how to fix it... 2) Indicate the direction and motion of the center of mass immeadiately after the collision I have no idea how to do this, mainly becasue I don't have the center of mass right. 3) determine the speed of the center of mass immeadiately after the collision again, no idea... 4) determine the angular speed of the system (assembly adn clay lump) immeadiately after the collision .... 5) Determine the change in kinetic energy as a result of the collision no idea... please help..