Originally Posted by
StainlessSlide
Ok, we are moving to a different level of approximation.
In completely inelastic collision, there will definitely be some energy loss, that's what inelastic means. This assumption fixes an energy loss for a given collision. I concur that this is a good assumption.
You mean E2 = (1/2 x (M3 + M2)) x (v2)^2 , since you don't want M1 in your equation, and you need the parentheses.
E2 is not the energy available to operate the system, though, since the buffer energy is going into the spring also (we are using "energy" as a shorthand for "kinetic energy"). You need to add on 1/2 x M1 x v1^2 to get the total energy, which of course does depend on the buffer mass.
Since v2 = v1 * M2 / ( M2 + M3 ), the energy loss is E2/E1 = M2/(M2 + M3) (The derivation is a bit lengthy for this venue). E2/E1 should be very roughly .75. This factor is independent of buffer mass, and the buffer does not lose energy in this collision. If the buffer mass is, say, 70% of the carrier mass, it will carry about 40% of the initial energy. The energy loss to the total system buffer/carrier/bolt will then be a factor of about .85.
Where did it go? The buffer is moving backwards and compressing the spring, if it's in contact with the carrier or not. Its energy is still going into the spring. The buffer will eventually stop, and it is stopped by the spring (ignoring a possible low velocity collision with the extension). Since the out-of-contact buffer will decelerate rapidly, it will recontact the carrier, and there will be more slightly inelastic collisions that will be difficult to model. If this happens over a significant period of time, we cannot assume that total carrier/bolt/buffer momentum is conserved, because the spring is exerting a force. But we could assume that there is one recontact collision and that it is completely inelastic. The relative velocity will be small though, so I don't think the energy loss will be significant.
No, as we have said, the energy of the buffer/carrier/bolt is what operates the system (to our current level of approximation). And no, energy is proportional to momentum squared at fixed mass, E = p^2/(2m). This came up in an earlier post. And we are changing the mass by changing the buffer.
A good time series of carrier position with different buffers from a high speed camera would be much more conclusive than this freshman-level analysis. This should be the next step, especially since we can't seem to agree on our application of elementary classsical mechanics.
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