Conservation of momentum between two bodies of mass:
38.67e6 kg drops 3.6576m impacting a floor of mass 2.47e6 kg at 8.47m/s
KE 'usage' due to conservation of momentum = 83.33e6 J
Resultant velocity of whole mass = 7.96m/s
What we have is 2 bodies of mass changing velocity, both actions require energy. (It still requires energy to decelerate a moving object)
1) 38.67e6 kg decelerating from 8.47m/s to 7.96m/s (requires 5.01e6 J)
2) 2.47e6kg accelerating from rest to 7.96m/s (requires 78.32e6 J)
Add them up, we get 5.01e6 + 78.32e6 = 83.33e6 J
No deformation of materials. 100% of the energy exchange accounted for by velocity change of the 2 bodies of mass.
Ryan is wrong.
End of story.
iAi caramba!
My response to you in post #888 is correct. So are the various objections raised by others in this thread. I'll show you, using your numbers.
So we've got two objects, call them M1 and M2, with masses 38.67 Gg and 2.47 Gg respectively. Before impact, M1 is moving at velocity V1 = 8.47 m/s, and M2 is stationary, V2 = 0.
We specify the collision is fully inelastic, so after collision, the masses have the same velocity, which we'll call V3. To find this velocity, we apply conservation of momentum -- momentum is conserved in any type of collision, whether elastic, partially inelastic, or fully inelastic.
Conservation of momentum simply states that the momentum before and after impact is the same. Momentum before is equal to M1 V1 + M2 V2. Since V2 = 0, the momentum before is just M1 V1 = 38.67 Gg x 8.47 m/s = 327.53 Gg m/s.
This is the same as the momentum afterward. Mass is also conserved, so the mass after collision is just M1 + M2, and we already said the new velocity was V3, so we have (M1 + M2) V3 = 327.53 Gg m/s. Since M1 + M2 = 41.14 Gg, this means V3 = 327.53 Gg m/s / (41.14 Gg) = 7.96 m/s.
So now let's talk about energy.
Before the collision, mass M1 had a kinetic energy equal to M1 V1
2 / 2 = 38.68 Gg x (8.47 m/s)
2 / 2 = 1387 Gg m
2/s
2 = 1387 MJ.
After the collision, the combined mass (M1 + M2) has kinetic energy equal to (M1 + M2) V3
2 / 2, or we can rewrite this as M1 V3
2 / 2 + M2 V3
2 / 2. In other words, we can either look at the kinetic energy of the whole blob, or we can look at the energy of each now mashed-together piece. Either way, we get the same answer.
Let's do it the latter way. The new kinetic energy of mass from M1 is 38.68 Gg x (7.96 m/s)
2 / 2 = 1225 MJ. Likewise, the new kinetic energy of mass M2 is 2.47 Gg x (7.96 m/s)
2 / 2 = 78 MJ.
So let's now follow the path of the energy. Before collision, mass M1 had 1387 MJ, and mass M2 had none.
After collision, mass M1 has 1225 MJ left. It has lost a total of 162 MJ of energy.
Mass M2 has acquired 78 MJ. Some of that came from M1. The remainder that M1 lost, or 84 MJ,
is unaccounted for.
What this means is we require an additional 84 MJ energy sink, and if we don't, then the two pieces have no reason to stay together. If M1 keeps that energy, it will move at a different velocity, and we won't have a fully inelastic collision anymore. If we had instead specified an elastic collision, then kinetic energy as well as momentum would be conserved, and it would mean M1 and M2 would exit the collision at different speeds, i.e. not stuck together at all. There is no other solution to the problem.
The most common energy sink is physical deformation. The reason for this is quite simple: In this problem, we've exchanged momentum between two objects. The flow of momentum between objects is a force, and the flow of momentum
within objects is
stress.
Now, whether we have an elastic or inelastic collision depends on how this stress affects the objects. If we have very strong objects, such that the strain is small, then the stress is elastic and very little energy can be dissipated -- the objects will bounce apart again after collision. This is because below the plastic limit, most solids behave much like springs.
Above the plastic limit, the object absorbs energy through deformation. That's the expected result. You can hit two objects harder and harder and harder, and they'll keep bouncing back, until you hit them so hard that the stress they feel at impact is no longer "small" and they start to deform as a result. At that point, you can start absorbing large amounts of energy. That is the transition from elastic collisions to inelastic collisions. It is no coincidence that the word "elastic" appears both in collisions and in material behavior.
If you smash them together harder still, not only will you deform the objects, but you will eventually cause them to yield, either causing rupture or fracture. At this point you are not only deforming the objects, but actually destroying them -- this is the mechanism responsible for most of the concrete crumbling during collapse, for instance. As you crumble or fracture the objects, they absorb more and more energy, as more and more of the initial mass is stressed to its yield point.
If you smash together even harder, you start to see new mechanisms arise. After things crumble, they start to fuse, friction between particles raising the temperature. You can also have fluid dissipation mechanisms come into play here. Keep going and eventually you can start causing static electrical effects or more radical molecular change. Keep cranking it up and you will start to see vaporization. Even more and you start making plasma. With still more you can start shedding UV or X-rays, then gamma rays, and finally you start in with relativistic effects like spontaneous pair creation. There really is no limit.
Fortunately for us, our problem is much slower and simpler. For us, mere deformation and fracture will dominate. There will be some attendant heating, but not much, mostly through compression of materials and hysteresis of solids. Friction is there too, but really only affects the contact surface, not the whole body until we've already caused widespread failure. But to say that there is no deformation in an inelastic collision is absolutely ludicrous. This is practically a contradiction in terms.
----
Now,
femr2, the next thing I want from you, here or anywhere, is an acknowledgment that you understand the above. I'm not interested in anything else. I won't sugar-coat this -- if you cannot understand the above, and you continue to fail at basic conservation of momentum and energy, then you have no hope whatsoever to correctly apply and interpret your own model. Your options at that point will be limited to two: Either acquire the expertise, which you should do on your own time; or stand aside and let those who understand the physics have the floor.
Sorry it turned out this way, but you really should have listened to me and kept this private.
ETA: Typo -- I had kJ instead of MJ throughout. The long-hand units were correct. Sorry for the confusion.