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I was reading about elastic collisions and energy changes, and I found in a book that suppose, when 2 balls collide and bounce off of each other, the total kinetic energy of the system is same before and after the collision. However, when these 2 balls will collide, they will create a sound, which is again a form of energy. So, how come total kinetic energy is conserved?

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  • $\begingroup$ If you hear a sound, then the collision is not elastic, and kinetic energy is not conserved. $\endgroup$
    – garyp
    Jan 18 '16 at 1:31
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When studying physics, it is often necessary to make simplifying assumptions in order to keep the math manageable. In the case of an elastic collision between two balls, the textbook example ends with the kinetic energy of the two balls being conserved through the collision. As you've noted, this ignores the energy lost to sound - it also ignores the increased thermal energy of the molecules of the two balls and of the air they travel through, energy lost to gravitational waves, energy lost as radiation when the charged particles are accelerated while being thrown and during collision, etc.

If you experiment by throwing two golf balls or steel bearings against each other, and measure very precisely the initial and final kinetic energy, you'll find that the energy is lower after the fact. You could stop there and argue that conservation of energy is violated based on your data. Even just shooting two electrons at each other would come to that conclusion in an atmosphere, and that's about as fundamental as interactions get. But then someone would come along and ask "what about the sound wave?" and somebody else would ask "what about the temperature difference?" and so on: and eventually, with enough people working on enough little calculations, you can find where all that energy went.

And when I say "enough people," keep in mind that an experimental setup with two 100g ball bearings and 1kg of air has something like 7.4x10e26 particles involved, and even that is making the simplifying assumption that the system is isolated. To really account for it all, you have to consider energy transfer between the experiment and the lab, and between the lab and the environment, and keeping in mind that "the environment" is the entire visible universe... You'd never have enough people. So we simplify by assumption, and through small assumptions we acquire small inaccuracies in our final numbers, but it's a necessary practice given our computational resources.

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No collision is perfectly elastic. Everything loses energy in the form of heat. Some processes (like aspects of photosynthesis and LEDs producing light) are nearly 100% but never exactly 100%. In quantum mechanics, there are reversible events (which may be the same as being in superposition) that are 100% efficient. As soon as the probability of reversal becomes low enough, you're going to lose photons, the process becomes irreversible, and energy is lost to the environment. (I.e. entropy happens.)

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