Pasted below is a message I have pestered others with
recently. If it has already been posted here, I
apologize for the redundancy.
"How come energy can be dissipated (and usually is)
during a collision but not momentum?" OR, "Why can
energy either be dissipated within a system or to its
surroundings, but momentum can ONLY be dissipated by
leaking OUT of a system?" Consider a system consisting
of 2 Pasco carts on a low-friction track, one parked
and the other moving arranged to have an elastic
(bouncing) collision. The before and after speeds are
measured so as to minimize the effects of rolling
friction. So the system energy is initially stored
solely in the moving cart (as Ek). I believe there is
only one mechanism for the transfer of both energy and
momentum within the system (ie, from cart 1 to cart
2). That mechanism is the force of the moving cart
acting on the parked cart during the collision. The
integral of this force with respect to time yields the
momentum gain of the parked cart which is exactly
equal to the momentum loss of the moving cart; ie,
perfect conservation of momentum. The integral of this
SAME FORCE with respect to distance yields the energy
gain of the parked cart which is equal to the energy
loss of the moving cart EXCEPT that a large portion of
the energy is "spilled" in the process showing up as
Ediss at the expense of Ek. That is, the energy pie
that was 100% Ek immediately prior to the collision is
now less than 40% Ek immediately after the inelastic
collision. At least at the macroscopic level, it seems
to me that the process is fundamentally the same for
both energy transfer and momentum transfer - the
application of a force by one object on another for a
specific time and distance interval. "How come" the
transfer process for Ek is highly dissipative while
the process for momentum (fundamentally the SAME
process) is perfectly conservative? If some of the
force vs. distance integral (energy) is "used up" in
producing vibrations and distortions within the
system, "how come" none of the force vs. time integral
(momentum) meets the same fate? It's the same force.
(Isn't it?)
A related question came up in class today. We were
modeling energy transfer by a pulse traveling through
a medium consisting of point masses connected by
springs.
The energy (amplitude) dissipates due to internal
friction in the stretching and recovery of the springs
(as a mental model). BUT what happens to momentum?
Isn't this a series of elastic collisions between
point particles? That would suggest conservation of
momentum but the PARTICLE velocity slows as the
amplitude decreases even though the PULSE speed stays
the same. So how is particle momentum conserved if the
particle velocities are decreasing? John Barrere
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