Application A 30,000-kg freight car is coasting at 0.850 m/s with negligible friction under a hopper that dumps 110,000 kg of scrap metal into it. (a) What is the final velocity of the loaded freight car? (b) How much kinetic energy is lost?
Step-by-step solution In this problem a freight car is coasting with negligible friction under a hopper that dumps scrap metal ,so calculate the final velocity of the loaded freight car and the loss in kinetic energy as per the given data respectively. Step 1 of 7 (a) For a collision, the momentum is conserved. Therefore the expression of conservation of momentum is, Here is the mass of freight car, is the mass of scrap metal, is the velocity of freight car, is the velocity of scrap metal and is the velocity after collision. Step 2 of 7 Substitute, , for , and in the above expression of the conservation of momentum, Hence, the recoil velocity is . Step 3 of 7 (b) The expression of initial kinetic energy is: Here is the mass of freight car, is the mass of scrap metal, is the velocity of freight car and is the velocity of scrap metal. Step 4 of 7 Substitute in the above equation, Hence, the initial kinetic energy is 10837.5 J