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so if a very un-bouncy object hits the floor and crashes into it rather than bouncing, where does most of the energy go? Does it simply turn into heat from friction? Or does it go into the Earth's movement by an imperceptible amount?

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The energy has several options to get dissipated into:

  1. Major part of it is turned into heat as a result of friction.
  2. Some part gets transmitted into sound energy, causing the sound we hear when the object falls.
  3. A very feeble amount gets transformed into light energy.
  4. Another miniscule portion is utilised in deforming the object and thereby increasing the internal energy of the body.
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  • $\begingroup$ I'm not sure I agree with the static friction part - the majority is dissipated as mechanical deformation (including internal friction), some of which you get out as sound. I'm mainly questioning the 'static' part of your answer. $\endgroup$
    – Jon Custer
    Jan 21, 2016 at 17:54
  • $\begingroup$ @JonCuster But if you look at it, it goes like this.... the ball falls, does not rebound, there is friction force between the ground-surface and the ball-surface and this friction cannot be overcome, so there is no movement of the ball. This friction is static friction, obviously. :-) $\endgroup$ Jan 21, 2016 at 17:58
  • $\begingroup$ Well, but all the energy is lost to heat and deformation, not to static (non-moving) friction. $\endgroup$
    – Jon Custer
    Jan 21, 2016 at 18:21
  • $\begingroup$ @JonCuster Okay, I have edited it. is it fine ? $\endgroup$ Jan 21, 2016 at 18:25
  • $\begingroup$ I would say is not friction if there is no component tangential to the surfaces. If the ball does not bounce back it means it deformed beyond repair, like a clay ball would. $\endgroup$
    – rmhleo
    Jan 21, 2016 at 18:28
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The majority of the energy is dissipated as mechanical deformation (as Jon Custer has stated).

Visualizing the situation can help a lot. All matter is somewhat elastic - there's no such thing as infinite elasticity. When an object collides with something, the force of the collision takes time to spread out across the object. Imagine a slow-motion view of crash-testing a car. It crumbles as it decelerates, and is unlikely to "bounce back," although this does happen with enough energy. A bean bag is also unlikely to bounce, as it is designed to deform and absorb the collision.

Hard objects are very likely to bounce because they don't deform as much (or as permanently). So instead, the waves that propagate through the object will be "corrected" and the matter will fall back into place. This causes the object to bounce, and produce an audible sound. The lack of deformation is what causes the bounce. This is why billiard balls bounce so well - if ceramic deforms, it breaks.

Heat is the final source of dissipation. Back to the car wreck in slow motion, the bending metal will create measurable heat. Also the bean bag will produce heat with friction between the internal components. Do this sometime: get a piece of metal and bend it back and forth over and over. It will get hot. Same thing with a piece of plastic. The deformation directly causes heat to be produced.

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