On Sun, Jun 12, 2011 at 10:50 PM, Stephen A. Lawrence <sa...@pobox.com>wrote:
> > > 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. > > OK, sorry, but I also later came with a correction. Lets change the setup so that the ball bounces sideways. Do you agree that it now becomes lighter? This is because the centrifugal forces. The increase and decrease does not balance to zero. Do you also agree that with the sideways bouncing ball there is also a small torque on the box, due to the same differences in centrifugal acceleration? David
