On 11-06-11 01:58 PM, David Jonsson wrote:
Hi
This obvious fact from hot air balloons and rising smoke is also the
case in constant volume. Just do the math if you can't see what I mean.
Imagine a ball on lying at rest in a box. This is equivalent of a cold
gas. All pressure from the ball is on the bottom of the box. The
weight of the ball is just added to the box. Now let the ball do very
fast bounces up and down. The box will not weigh as much as before
because the ball is also bouncing on the ceiling of the box with
almost as strong impulse as it is bouncing on the bottom. The box +
ball weighs less.
Wrong.
You are claiming that a bouncing ball violates conservation of momentum,
which is certainly false. What's more, you're attempting to show it
with a gedanken experiment, based on the Newtonian mechanics model of
the world, which includes conservation of momentum in its postulates!
You can know with certainty before you start that the effect you're
claiming isn't going to show up in your gedanken, unless arithmetic
itself is logically inconsistent!
If momentum is conserved, then total impulse on the ball due to impacts
with the sides of the box, over a period of time, must exactly negate
the total impulse delivered by gravity. Otherwise the ball's net
momentum will change, and it obviously doesn't (at the end of the
experiment, in the middle of a cycle, the ball's moving at the same
speed it was, in the middle of a cycle, at the beginning of the experiment).
Net weight of the ball is the average force needed to hold it up, which
is the total impulse delivered to it divided by the total time. That
*can't* change, by conservation of momentum, no matter how you assume
the ball moves within the box.
Do a real experiment, and demonstrate this, and you will have proved
Newtonian mechanics is busted. That's very unlikely, but not absolutely
ruled out on logical grounds.
But using the Newtonian mechanics model itself, if you arrive at the
conclusion that the box is lighter when the ball is bouncing, you can
safely conclude that you did something wrong. That's not a conclusion
you can ever get to from the Newtonian model.
