Question
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?
Final Answer
- of kinetic energy was lost.
Solution video
OpenStax College Physics, Chapter 8, Problem 36 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. A railway car that has a mass of 30,000 kilograms is coasting along at a speed of 0.850 meters per second and then sometime later, this hopper will dump some scrap metal into it and it will have a new speed which we will call just letter v with no subscript and it's gonna be dumping 110000 kilograms of scrap metal into it. So the momentum initially is going to equal the total final momentum and the final momentum is going to be this total of the mass 1 plus mass 2— the rail car plus scrap metal mass added together— multiplied by whatever speed they are going together with, v, that momentum equals the initial momentum of the rail car when it was coasting by itself which is m 1v 1. So we are gonna solve for v by dividing both sides by m 1 plus m 2 and then switching the sides around. So we have v is m 1v 1 over m 1 plus m 2. So that's 30000 kilograms times 0.850 meters per second divided by 30000 plus 110000 giving us a speed of 0.18 meters per second. It's kind of hard to know how many significant figures to put in this number so I chose 2 and we'll assume that this has two significant figures. Okay! So the loss in kinetic energy is gonna be the difference in kinetic energy after the scrap metal is dumped in minus the kinetic energy when the rail car was coasting by itself. So that's gonna be one-half times the total mass of rail car plus scrap metal times its speed squared minus one-half times mass of the rail car multiplied by its speed when it was coasting squared. So that's one-half times the total mass times this speed that we calculated in part (a) squared minus one-half times 30000 times 0.850 meters per second squared and that is negative 8515 joules. So we'll round that to two significant figures and say that 8500 joules of kinetic energy was lost. And of course the energy still exists as energy cannot be destroyed, it can only be changed into one form or another; it's gonna be changed probably into thermal energy mostly, little bit into sound energy... okay! There we go!