Re: Momentum conservation

On Aug 18, 11:02 am, Peter <Poakfi...@xxxxxxx> wrote:
On Aug 18, 11:04 am, PD <TheDraperFam...@xxxxxxxxx> wrote:



On Aug 18, 8:46 am, Peter <Poakfi...@xxxxxxx> wrote:

Hi! When a point object, like a steel ball, collides (without rolling)
in one dimension with another identical object at rest, and stops on
impact, the target object is supposed to acquire the momentum of the
incident object. However, in all real collisions some heat and noise
is always generated, which, of course, is energy that is dissipated.
Where does this energy come from if momentum is conserved? How could
momentum be conserved, if this energy comes at the expense of the
kinetic energy of the object?

Hello Peter, I see you are back to worrying about basics.
Momentum does not come from energy, and energy does not come from
momentum. They are conserved wholly separately.

In any collision, linear momentum of a closed system is conserved. As
long as the heat and noise in the collision is distributed
isotropically in the case above, the momentum (a vector) carried by
that heat and noise will be zero and so will not affect that result
for the colliding particles.

In any collision, total energy is also conserved. However, unlike
momentum, energy can be redistributed into several different forms, so
that some of the initial kinetic energy before the collision can be
turned into heat and sound energy, leaving less kinetic energy after
the collision.

Most simple textbooks illustrate how in an elastic collision momentum
is conserved AND kinetic energy is conserved (no losses to other
energy dissipation in the collision), and how in an INELASTIC
collision momentum is STILL conserved even though some kinetic energy
is diverted to dissipative losses. The numerical examples worked in
those books show you explicitly that the momentum beforehand is equal
to the momentum afterwards, even though the kinetic energy afterwards
is much, much less than the kinetic energy beforehand.

PD

Hello, PD. Thanks for replying. To be specific, if the momentum of the
incident ball before the collision is mv, its kinetic energy must be
(1/2)mv^2. For momentum to be conserved, the momentum of the target
ball (which is identical) must be mv. How can the target ball have
less kinetic energy than (1/2)mv^2?

Trying to divine where you're going with this...
If you have two identical balls, and there is noise and heat released
in the collision, then not all of the first ball's momentum will be
transferred to the second ball. You will find that if there is noise
and heat released, and if you measure the velocity of the two balls
sufficiently precisely so that the amount of energy released in sound
and heat is not below the precision of your measurements, then it
simply will not happen that the first ball will transfer all of its
momentum to the second ball.

A collision where noise and heat is released is a dissipative
collision, not an elastic collision. Only in a *completely* elastic
collision will the momentum of the first ball be completely
transferred to the second ball.

PD

.

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