In a nuclear reaction carbon nucleus, 12c collides elastically in a head-on collision with an unknown nucleus. the initial speed of the carbon nucleus is 110 km/h and the speed of the unknown nucleus is 400km/h. after the collision the carbon nucleus moves in opposite direction to its original direction with a speed of 145km/h. i) determine the ratio of the mass of carbon nucleus and the unknown nucleus. ii) what is the velocity of the unknown nucleus after the collision?

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.