simple really .... if the airs getting pulled out then the can will want to pull in that air so
        __
air <-()__) the can will need the air back in it so it will suck the same way as soon as the - preshure is released (sorry cant spell im spanish)
anyways cann would be moving left (sorry if this is wrong i got linked from a difrent site)

the can will not move because of the probability of the cans weight divided by the pressure of the air comming in the can.

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i think its got to do wth the pressure acting on the can. when its not punctured, that time pressure is the same all thruout its soides. when punctured and as long as the air is getting in the can will move to rite with a acceleration, n there after wneh the air is completely in it will move with a constant velocity. thats coz 1ce the air is in pressure will be again same throughtout, as earlier n no unbalanced force acting. i will describe the motion to rite side as the pressure on left side is more than on right side coz of the tiny hole on the rite side ( pressure meaning air pressure)
 if found ne thing wrong wth my reasoning plz inform me. i wd learn from it.. sagar_gambhir@rediffmail.com

I assume that there is friction--a lot of friction! Therefore, by the time the can fills with air, it is no longer moving.

Consider the can and the air around it as the system.

The crux is that since their is no ground friction , there is no HORIZONTAL external force on this system.Hence the position of the COM of the system remains on the same vertical line at all time.

Now, as the air starts to enter the hole the COM OF THE AIR shifts to the left and hence the can (being a rigid body) should shift to the right. BUT, when the can is completely filled, the COM of the air molecules would have returned to thir starting position, and hence the COM of the can must also have returned to its initial position.

All said, i believe the can would move to the right initially but at some point turn back and return to its original position AND stay there.

The physics of this solution seems fine to me , but there could exist a flaw. Would someone please do this experiment and write what actually happens?

Edited by author 01-20-2007 05:10 AM
The amount of motion depends on the mass of the can, air pressure, and size of the hole. (assuming no friction)

How far would the can move?

I think the air's momentum equals the can's momentum. I think the can moves right while filling and then stops from the air colliding with the left wall.

Don't forget that the can does not suck in air. The external air pressure forces air into the can.

The air is accelerated by constant pressure from the right. Think of a plunger with some mass (a frictionless disk that starts in contact with the right side of the can) getting pushed in by the incoming air. It mass gets accellerated by the incoming air (air pressure means force on the disk -- Force= PressurexArea) until it hits the left wall. The same thing happens to the air when the disk is not present.

Meanwhile the imbalance of left and right forces on the can (due to the area of the hole) causes the can to accellerate right. Note that the air forced into the can is through a hole whose size determines how fast the can moves right. It's not hard to imagine that the energy imparted to the air is the same as the energy imparted to the can since both are caused by the same hole. Then they meet and stop.

BTW Bob, my sentence about heat amd momentum was totally off.

Bob,

There is no problem with the air continuing to move leftwards - and there is no need for some kind of 'pulse' to do so either, as diffusion will result in some kind of a bulk motion of the air as a whole. Imagine throwing a pebble into the sea - eventually the pebble will transfer all of its momentum to the water, get tired, and flop to the bottom - and the momentum which it once had will be shared amongst many water molecules in some complex fashion. Same thing here, so I don't think there is anything to worry about here. Also, there is nothing wrong with air molecules going off to infinity - that's exactly what it would do if there were nothing else in the way. If you are an astronaut doing a space walk in the middle of nowhere, and happen to be holding a cricket ball which you throw in some direction, it will just keep going off to infinity, while you will go spinning off in the opposite direction (rather more slowly, I should imagine, unless you have been on a diet) to 'negative' infinity. There is nothing mysterious about that.

And of course the air outside must move - at the very least it must replace the air that gets sucked into the can. I think the motion would be very complex - and I agree that there may not be much net momentum of the air whichever way the can ends up going, but there most certainly will be motion, and lots of it. There is plenty of potential energy to distribute after all, in various forms, including kinetic. Note that even heat will eventually be converted into kinetic energy through dissipation.

Your momentum argument seems incorrect - when the air enters the can, it will do so with much greater velocity than the the can's rightward motion, so I don't think you can naively reach the conclusion that the air's momentum is less than the can's (though admittedly I do think that it probably is).

meBigGuy - you argue that the air molecules entering the can first will be 'pushed' to greater velocities by air molecules entering after them - this is true, but this increase in momentum will be exactly balanced by the loss in momentum of the molecule that hit it, so the total momentum imparted remains the same.

Bob - I doubt the can would reach as far as Fiji. The polar bears and penguins can be well separated if you like, but would you prefer that they starved to death rather than let nature take its course. Even cute and furry animals get eaten by predators - it is a fact of life. Of course we can make a conscious choice way one way or the other if we so wish as there are alternatives, but you wouldn't deny me the pleasure of eating the odd penguin now and then, would you? I am sure penguin korma would taste quite nice. And what about starfish - do they not have rights too? Or are they not cute enough?

Tyler - The can will certainly move - don't know for sure which way (probably rightwards, based upon earlier arguments), and be reassured that there is no problem with the air moving leftwards.

I was wrong, it will not move, please disregard all previous posts, its been fun.

Edited by author 01-18-2007 04:24 AM
Hello?

Energy can convert to whatever form it likes, but momentum is momentum. If net rightward motion develops in any system, net leftward motion must develop outside of that system. This can only be caused by some force of interaction (both ways), or by some net flow of matter, across the system boundary. Apologies if I'm misinterpreting you, but if you can't understand and agree with that then we're a bit stuck, no?

Edited by author 01-18-2007 01:11 AM
Tyler

I am not sure how you can assume the air molecules rebound elastically off the left side of the can. I don't know exactly what they do, just don't understand the basis for your assumption.

So, you are saying that the plunger analogy is not valid because the nature of the entering air column can't be compared to a plunger.

Think about shooting a pressure stream of air at a can. It shoots left. That is what is happening here.
 
Your basic assumption is that the nature of entering air causes energy loss due to turbulence and reflections. Therefore the air's energy gained by the leftward pressure is not applied to the left side of the can. And, the difference in area between the left and right means the external rightward pressure is no longer balanced, so the can moves right after filling.

Bob's assumption that something moving right means something else must be moving left need not hold if energy is converted to heat.

But, I think the collision is much less elastic than you think. One data point is the post that described flouresent tubes shooting left after their right ends were broken off.

So, how can you prove your assumption of an elastic collision imparting little or no leftward momentum?

Edited by author 01-17-2007 04:52 PM
tyler -

Near-elastic collisions mean minimum kinetic energy loss, but maximum momentum transfer. Which means the faster-than-average, denser-than-average stream going into the can packs more punch than anything else going on. I see no reason why they shouldn't balance - I think you're underestimating it.

all -

I think I've got an argument for it not being in motion at all. See what you think.

I've been thinking about a system consisting of the can, its contents, and all the air to the right of it (think of the space that would be mapped out by an infinite translation of the can to the right). If the can is going to keep move right, something outside of this system has got to keep moving with equal momentum to the left. (Air to the right of the can can't keep moving left without leaving this system, unless a strange leftward pulse shuffles rightward to infinity!) Bear in mind that any air moving left that enters or hits the can will give up its leftward momentum to the can, not carry it away as is required. The air is (or at least may well be) a lot lighter than the can, so the movement of air to the left must be either much faster or much greater in volume than the movement of the can.

I can't see why any air outside of this system should move a great deal at all, especially not to the left. The volume of air required to fill the space where the can was when it moves is tiny in comparison to the volume of the can, unless the can is very light indeed - so that doesn't do the job.*

Is anyone following me here?

If you can agree that for the can to end up with motion to the right, there must be a leftward flow of air around the can (not to the right of it) that is much greater than the space left by the can as it moves, then would you agree that, unless there's some identifiable physical cause for such a movement, we can infer that the can does NOT continue in motion once full?

I'm thinking so. I'm thinking that there is no physical reason, i.e. no force or pressure gradient, that would cause air to start flowing left, and to continue to flow left without entering this system, as a result of the puncture appearing. The boundaries of this system are potenitally at a considerable distance from the hole.

So I don't think it can sustain any motion at all. If it does, it'll be on much, much tinier scale to the 'poof' case. It may end up drifting very slowly left after all (post 394).

Away from Greenwich.
Towards Fiji.


*Consider the ratio of the mass of the can to the mass of the air in it when full. The momentum of air moving back to fill the space as the can moves forward is less than the momentum of the can moving forward by the same ratio. So if the can moves right, this effect alone cannot make up the missing leftward momentum - we need some other reason for the flow of air.

Yes, Bob that force to the left you are talking about is the slowly increasing force of pressure (P=F/A). It is less than the force of pressure outside. When the initial jet of air bounces of the back wall this is the beginning of the pressure rise and it is very small. This initial jet does not stop and bounce the back wall off of it, giving it all of its energy, it rebounds elastically, with very little momentum loss. This tiny momentum loss the can feels as the tiny initial rise in internal pressure. This rebounding air is now colliding with all the incoming air, the situation becomes very chaotic very quickly. Because of all the random collisions the incoming jet sees, its force is essentially acting simultaneously at all times on all of the inside surface areas of the can. This is the internal pressure of the can. It is always less than the force felt on the outside until the pressures are the same. During this time, that inbalance of forces is what accelerates the can, it will also accelerate slightly the random air molecules that are hitting the back of the can during that time. This is how the can and the air inside will both be travelling together, the air is chaotic in all directions but the bulk motion is with the can. Now when the pressures equalize, I cannot see any unbalanced forces that are stopping motion other than air friction on the outside of the can.

Sab, I think it is incorrect to say that the forces acting on the inside left side of that can are the same is the same as the force that was operating on the right side of the can before the puncture. The air entering the can increases in velocity as it enters and travels (it has a pressure pushing it to the left) and then it actually builds momentary pressure against the left side of the can when it hits (due to inertia gained). I think this force will cause the rightward motion of the can to stop, much as in my space analogy. Also, consider my earlier plunger analogy.

If, for some reason that I don't understand yet, the momentum increase in the entering air column and the momentum increase of the can are not equal (excluding friction and turbulance), then there will be a resultant motion after filling. I think the increases are the same because the pressure and area in both cases are equal. But, there could be a subtlety of air entering a vacumme through an orfice that I don't understand.

Unfortunately, the polar bear dies due to Artic temperature increases.