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3.1 (5 points) A railroad flat car ow weight W can roll without friction along a straight horizontal track as shown. Initially a man of weight w is standing on the car which is moving to the right with speed vo. Man then runs to the left and jumps off the car at the left end with velocity Vrel relative to the car. Show that the change in the velocity of the car is mar W 3.2 (10 points) Consider a perfectly elastic head-on collision between two bodies A and B. If the two masses are equal and one of them (say B) was at rest while the other was moving before impact, we have seen that A will come to rest and B will move with the velocity that A was originally moving at. In this case the initial kinetic energy is completely transferred to the second body in addition to the complete transfer of momentum. 3.2.1 (6 points) Now, let the masses be unequal. Still assume that B is at rest before collision and A was moving. Show that the fractional decrease in the kinetic energy of A post collision is given by - 8 = 4 MA MB MA MB 3.2.2 (1 point) What is the advantage of expressing o in terms of the ratio x = mA/MB ? 3.2.3 (1 point) Plot S vs x = - choosing appropriate scales. Provide physical interpretation of the plot. 3.2.4 (1 point) A (non-relativistic) neutron in a reactor makes an elastic head-on collision with the nucleus of a carbon atom initially at rest. If the initial kinetic energy of the neutron is 1.6 x 10-13J, find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision. 3.2.5 (1 point) In Nuclear Engineering, a neutron moderator is a medium that reduces the speed of fast neutrons. Calculate the fractional loss of kinetic energy of neutron when neutron collides with lead nucleus, carbon nucleus (done above) and hydrogen nucleus. Based on these calculations is hydrogen rich material a better moderator or lead rich material is a better moderator