In alt.usage.english, in article
<
6929747c-7b39-4aba...@googlegroups.com>,
Arindam Banerjee <
banerjee...@gmail.com> posted:
Forwarded post from five years ago:
[ Subject: The derivation of e=0.5mVVN(N-k)
[ From: Arindam Banerjee <
adda...@bigpond.com>
[ Date: Wed, 12 Oct 2011 15:24:01 -0700 (PDT)
[
[
[ With the update of Newton's first law, that a body can
[ move from inertia with internal force, as evidenced from
[ winds, currents, explosions, etc. all caused by the three
[ fundamental forces - gravity, em, and strong nuclear - it
[ is very easy to derive e=0.5mVVN(N-k).
[
[ Assume a body attached to an internal force engine,
[ totally of mass M. It rests in reference R. A burst of
[ internal force, acting over a time t, raises the velocity
[ to V - with no help from any outside agency by
[ definition. That burst of force required loss of the
[ body's internal energy, by a factor E. Constant such
[ bursts, will raise the speed to NV, if such bursts are
[ directed linearly. With respect to R, the kinetic energy
[ is now 0.5MVVNN.
[
[ The internal energy used up is NE.
[
[ E is always 0.5MVV times some efficiency factor k which
[ is greater than unity.
[
[ The important conceptual leap here is to internalise that
[ it is most significant that the body never knows whether
[ it is a V, 2V, or any multiple of V. It is totally
[ oblivious to the external environment. Its motion is not
[ dependent upon pushing back something, or throwing out
[ something. So if we allow that it can at all move from
[ whatever V it was to the next interval, the amount of
[ internal energy required will have to be the same.
[
[ So the net energy gained from such kinetic interactions,
[ in this case N successive hits directed linearly is
[
[ 0.5MVVNN - 0.5MVVNk, or
[
[ e = 0.5MVVN(N-k)
[
[ is the free or surplus or created energy that is always
[ getting formed from kinetic interactions, and which can
[ cause light, motion, etc, pass through different forms,
[ before finally getting destroyed. The destruction of
[ such energy, is referred to as the rise in entropy today.
[
[ We note that the formula works the other way too. Like,
[ internal force such as used in all braking (using brake
[ pads) can bring a body to rest very tidily indeed from
[ very high speeds.
[
[ Cheers,
[ Arindam Banerjee
End of forwarded post.
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Om Shanti
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