Re: Momentum conservation

On Aug 18, 5:18 pm, Peter <Poakfi...@xxxxxxx> wrote:
On Aug 18, 4:36 pm, Ray Vickson <C6...@xxxxxxx> wrote:

On Aug 18, 9:06 am, Peter <Poakfi...@xxxxxxx> wrote:

On Aug 18, 11:18 am, Ben Rudiak-Gould <br276delet...@xxxxxxxxx> wrote:

Peter 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?

In practice I think the striking object would not come to a complete stop.
This leads to a lower total kinetic energy after the collision, because
(x-k)^2 + k^2 < x^2 for 0 < k < x.

-- Ben

In practice, the incident ball does stop dead on impact.

Peter

Let A be your initially moving ball and B be the initially stationary
one. Analyze the collision in the CM (center of mass) frame, which
moves to the right with velocity v/2. In this frame, before the
collision ball A moves to the right with velocity v/2 and B to the
left with velocity -v/2. If the masses are the same, the total
momentum = 0 in the CM frame. If kinetic energy is not preserved, A
will move to the left with velocity -v/2' and B to the right with
velocity v'/2, where v' < v. The loss of kinetic enerty is (1/2)m v^2
- (1/2)m v'^2 > 0. In the original (lab) frame, after the collision, A
moves with velocity -v'/2 + v/2 > 0 and B moves with velocity v'/2 + v/
2 ( < v). Thus, if energy is lost, ball A does not come to a complete
stop. In practice, the effects will be so small that doing them on an
ordinary lab bench will be misleading (due to friction, etc.) You
should do them on an "air hockey" table, which reduces friction to
almost neglibible levels.

Of course, similar effects occur in the collision of elementary
particles, but the transformations need to be done relativistically.

R.G. Vickson- Hide quoted text -

Thanks. I think that in collisions of subatomic particles, it is
impossible for one of the particles to be at rest;

Why not? Look at Rutherford's experiments for instance.

thus, it cannot be
known what happens. In a lab, using Newton's cradle, a steel ball can
be made to collide with another steel ball at rest, and see that the
incident ball indeed stops dead on impact.

Only under certain conditions. Newton's cradle works because
the masses are equal.

- Randy

.

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