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The difference is only in the properties of the material of a body. You can see in this video If it is elastic (happy ball) it can deform itself (thus absorbing KE) and then recover the original shape, giving back roughly the same amount of KE, which is considered as temporarily stored in the lattices If it is not elastic the body will stay ...


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No, the elasticity of the collision depends on a couple of factors. 1) the properties of the materials. The carpet is easily deformable, and the fibers are not elastic, if one removes the ball that fell they return to their original form after some time, or, even don't return. So, the kinetic energy of the falling ball does the work of deforming the fibers. ...


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When one says that "kinetic energy is conserved in an elastic collision" that means that the total kinetic energy of the system of particles involved in the collision doesn't change. It does not mean that the kinetic energy of each particle is unchanged. For a two particle system, the kinetic energy of each will change, but the sum won't. Also, your ...


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yes, the equations of motion with collisions behave chaotically and from an observers point of view behave randomly. What can be shown is that there is some structure in that chaos, for instance, the distribution of energies among the molecules follow the Maxwell-Boltzmann distribution. This probability distribution indicates which speeds are more likely: a ...


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This may be obvious to Fermi, but not to the rest of us. One has to keep in mind the context of the derivation, Fermi is talking here about ideal gases. In other words, gases which are very dilute, such that the interparticle distance is much much larger than the range of the interparticle interaction. This means that particles don't see each other ...


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I am a bit lost in your problems with $mc^2$, but in the special relativity for a massless particle your identity can be proved as follows. First observation is $$ v_x = |v| \frac{p_x}{|p|} = c \frac{p_x}{|p|}, $$ as far as for a photon the speed is always speed of light, $|v|=c$. Then $$ \sum p_xv_x = \frac{c}{|p|} \sum p_x^2. $$ Then one can observe that ...



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