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If a can of compressed air is pierced on the right, air pushes out, and the can moves to the left.

If a vacuum container is pierced on the right, which way does it move? Right? Left? Not at all? Oscillate about its original position?

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The last one oscillate about it's original position is a silly option. :D. But it must be doesn't move at all. –  ABC Apr 28 '13 at 17:02

2 Answers 2

Why does a pierced compressed air can move? One answer is: when it is not pierced at 'the target point', there is a pressure acting on the target point (I should say area, but nevermind) on the right from the inside, as well as on its mirror point on the left, and so for every pair of points, so that the total force is zero. When you pierce the can, there still is some pressure acting on the mirror point, but there is no pressure acting on the target point, so that the total force acting on the can is not zero, and is directed to the left. (One can check that the force is the same as if you use conservation of momentum for the whole can+air system). What is pressure? Pressure is transition of momentum from air to the walls. When you pierce the target point, the momentum goes not to the can, but to the environment, and gets absorbed somewhere there.

What changes when you pierce a vacuum can? Now the pressure acts from the outside, and now, when you pierce the can, the force on the mirror point is again not compensated and is directed to the right. So one may conclude that the can should move. But one thing is different: the momentum that was to be transfered to the target point from the outside (but was not, because there is now no surface at the target point) is not absorbed "somewhere", it goes inside the can, and is finally absorbed by it exactly canceling the momentum received by the mirror point.

So, in this case there is a rather subtle cancelation. However, I believe that there are some further subtleties, which may cause a small difference in these momenta, and if you try to measure the force really hard, then you will see it.

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-1 Momentum must be conserved. The can will still move in a vacuum. This is how a thruster works (en.wikipedia.org/wiki/Thruster) –  Brandon Enright Apr 30 '13 at 4:22
    
@BrandonEnright, Please, read the question carefully. –  Peter Kravchuk Apr 30 '13 at 4:39
    
Yep, my mistake. I read it as a can pierced in a vacuum container. I will take back the -1 if SE lets me. –  Brandon Enright Apr 30 '13 at 4:44
    
@BrandonEnright I'll give a +1 explicitly to undo that -1 :) –  Volker Siegel Jun 18 at 11:36

If we consider the air (outside the vacuum can) and the can as an isolated system, then in the absence of external forces, the position of the center of mass should stay the same. As the air enters the can through the hole on the right of the can, the position of the air's center of mass will move to the left. To compensate, the can will move slightly to the right. Once the can fills with air, the air's center of mass will stop moving, and so will the can. So the can moves to the right, for a brief period, and stops, with the distance moved determined by the mass and volume of the can and the density of the air.

Of course, there are probably various fluid dynamics considerations that I do not know and have completely neglected...

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