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Q & A: The Vacuum Can...Where will it Move?

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Most recent answer: 10/22/2007
Q:
If a can of compressed air is puntured and the escaping air blows to the right, the can will move to the left in a rocket-like fashion. Now consider a vaccum can that is punctured. The air blows in the left as it enters the can. After the vaccum is filled the can will: a)be moving to the left b)be moving to the right c)not be moving
- Kcal (age 15)
Madison, WI, USA
A:
Kcal-

The can will......not be moving, or at least not very much..

With compressed air, the can feels more pressure from inside than from outside of the can. So, when the can gets a hole in it, the air pushing on the can from the inside can escape out the hole, propelling the can in the opposite direction. With a vacuum can, the pressure is greater on the outside of the can than on the inside, so when a hole is punctured, air rushes in, filling the can. The can briefly moves the opposite way from the air, toward the hole.

What happens when the can fills up? It's hard to keep track of all the changing forces, but we can use a basic physical idea. According to Newton's third law, something called momentum is conserved. If nothing was moving to begin with, and then something is moving to the right, there must be something moving to the left to make the total momentum still add up to zero. With the compressed air can, the escaped air keeps moving (say to the left) so the can must be moving off to the right. With the vacuum can, the air that rushed in is then trapped in the can, moving along with it. To keep the total momentum at the starting value (zero) the can and its trapped air must not be moving.

Actually, in problems like this there are often slight complications. The air rushing in to the can will stir up some air currents outside the can. Generally, these will have a little momentum, so the can will be moving very slightly. I believe that which way this small motion goes depends on the shape of the can and the hole, which determine which way those outside winds blow.

-Kim- and Mike W. and Mike S.

(published on 10/22/2007)

Follow-Up #1: Leaky Can Momentum

Q:
Your conservation of momentum explanation would apply equally to a pressurised can that develops a leak. If the system is at rest initially, then the system should be at rest after the air has jetted from the can.

We know that this isnít true of the pressurised can (or a pressurised balloon). I contend that itís not true of the vacuum can either. I suggest you reconsider your answer.

Hint: there is work being done in both cases...
- tim
Ballarat, Australia
A:
I disagree. The air that escapes from the pressurized can does not then return its momentum to the can. That momentum spreads out to neigboring air an then gets taken up by the surroundings. So conservation of momentum tells us that the can must go the other way, at least until it dumps its momentum into its surroundings via friction.

In contrast, the air that rushes into the vacuum can very quickly reaches the same average velocity as the can itself. If we can ignore minor changes left in the surroundings, that average velocity must then be zero.

I have tried to consider your thought about work being done, but since in a problem like this in which things are very far from equilibrium (i.e. not quasi-static) energy is quickly converted to thermal forms, I don't see how you draw a conclusion from that line of reasoning.

Mike W.

(published on 10/22/2007)

Follow-up on this answer.