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Topic: Balloon in car (Read 7234 times) |
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snags697
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Balloon in car
« on: Aug 8th, 2002, 11:44am » |
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The question, paraphrased from the easy riddles:
A helium balloon is in the middle of the ceiling of a car. The car
accelerates from a stop. How does the balloon react?
So here's a hint, somebody else can post the solution.
When the car accelerates, *everything* in the car gets pressed toward the back, exactly like when the car is standing still, *everything* is pulled toward the ground. So which way will the balloon go? How about when the car goes around a corner? And the big question, why?
(Side note: the two situations above are almost identical according to general relativity.)
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Kozo Morimoto
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When car accelerates from a standstill the air inside the car "seems" to go towards the rear and tends to "increase" the air density towards the rear, thus the balloon will float to the front of the car and it will float to the rear if the car came to a sudden halt.
When turning, the balloon will float toward the centre of the turn (ie it will float towards the curve and NOT away).
I suppose this is related, but why when riding a motorcycle or a boat (on water), you lean into a corner but when you are driving in a car you lean out? Like, if you go too fast around a bend, your car can flip over AWAY from the curve, where as if you spin around too fast in a boat, you flip INTO the corner.
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Archon
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Re: Balloon in car
« Reply #2 on: Aug 9th, 2002, 6:57am » |
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Oh Kozo, where do you come up with it?? 
The balloon is a mass at rest. It has inertial mass. For it to move, a force must be applied to it. The only force to be considered here is friction between the roof of the car and the balloon, but clearly this wont come into play until the two surfaces are moving with respect to each other (or want to).
As to your question about motorcycles etc....
When riding a motorcycle, you lean the bike into a curve because gyroscopic precession will then make the spinning wheels want to turn in the direction of the lean. IE, leaning makes the bike turn, turning the bike does not make it lean inwards. In fact, it wants to lean outwards.
If you're in a car and you turn to the right, the friction between the road and the tyres are what turn the car, but you keep wanting to go forwards (again, inertia). Hence it feels to you like you are sliding to the "left" (it's actually the car trying to move your body to the right).
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| « Last Edit: Aug 9th, 2002, 7:01am by Archon » |
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snags697
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Re: Balloon in car
« Reply #3 on: Aug 9th, 2002, 7:20am » |
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Archon, the friction force between the balloon and the roof isn't the only force on the balloon. The air itself exerts a force.
Kozo has it right. When the car accelerates, the air does in fact (not just seems to) go toward the rear. This change in density (more dense toward the back) pushes the balloon toward the front of the car with enough force to make the balloon actually move forward relative to the car. Note: I have since realized that the change in density is insignificant. See my later posts and the drawing by Aaron.
As far as the motorcycle/bicycle, you lean into the turn so that you don't fall over when you turn the handlebars. Gyroscopic forces on the wheels are actually fairly small (you can operate at low speed, right?). If you didn't lean into a turn, you'd fall right over toward the outside of the turn.
When you skid out, there is a sudden decrease in the road force, which is the only thing keeping you from leaning all the way over and falling. This makes you fall toward the inside of the turn as you slide toward the outside of the turn.
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| « Last Edit: Aug 12th, 2002, 5:50am by snags697 » |
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Archon
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Re: Balloon in car
« Reply #4 on: Aug 9th, 2002, 8:55am » |
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Hehe, I guess we'll have to agree to disagree on the balloon one, because I've seen it first hand
And as for the motorcycle, gyroscopic forces are indeed small at low speeds, which is why you dont actually have to lean at all at low speeds, you can just turn the handlebars. But gyroscopic precession is the determining factor at higher speeds. In fact, you actually turn the front wheel <i>away</i> from the turn at high speed in order to lean the bike in. I should know, I've been riding for a while 
The road force isn't keeping you from falling, either. I could, in principle, lean the bike "all the way over" and maintain a turn. The force trying to keep you upright is indeed gyroscopic. As you say, a skid occurs when you lose traction, but the unbalancing is what causes people to fall. If I were riding on wet ice, I could lean the bike in at some angle and slide along the ice sidways without falling. Indeed, you can see motorcross riders doing this all the time.
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snags697
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Re: Balloon in car
« Reply #5 on: Aug 9th, 2002, 9:56am » |
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We may be talking about the same force. A true gyroscopic force is a strange torque on a spinning object that causes it to turn in a different direction than the way you push it. You can test this by grabbing a bicycle wheel by the axle, holding it out in front of you, and spinning it. If you try to change the direction of the axle to the left, the axle will actually turn toward or away from you, depending on which direction you spun the wheel.
I think what you're calling a gyroscopic force is really the centrifugal force. A centrifugal force is what you feel toward the outside of a turn as you go around it. Your description is pretty good if you replace the word gyroscopic by the word centrifugal.
But admit, when the road force gives out, you fall toward the inside of the turn. That is, the leg that is closer to the road ends up down. By this argument, the road helps hold you up.
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S. Owen
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Re: Balloon in car
« Reply #6 on: Aug 9th, 2002, 11:36am » |
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on Aug 9th, 2002, 7:20am, snags697 wrote:| Kozo has it right. When the car accelerates, the air does in fact (not just seems to) go toward the rear. This change in density (more dense toward the back) pushes the balloon toward the front of the car with enough force to make the balloon actually move forward relative to the car. |
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If we're considering air, wouldn't the air moving towards the back have a larger and more immediate effect on the balloon, moving it backwards? It seems that this reasoning would lead us to conclude that blowing on a balloon moves it in the opposite direction of air flow.
My guess is that the air has some effect, that accelerating the car will cause the air to flow a little inside the car. However I think this movement is almost negligible, and the precise nature of the air currents moving backwards and fowards would be hard to guess.
I think that the real issue is the force of friction between the balloon and roof, and whether it will be sufficient to accelerate the balloon with the car. My guess is that it would not, in general, and the balloon would move backwards a bit.
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snags697
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Re: Balloon in car
« Reply #7 on: Aug 9th, 2002, 12:20pm » |
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Whoops, I just realized that my previous answer is misleading (or wrong). The balloon moves forward when the car accelerates because the air has more inertia than the balloon. So the air gets pushed toward the back of the car (just like you are in your seat) and the balloon has to move forward to replace the air that moved (just like the air that moves around to the front of your head when you get pressed back in your seat).
If you immersed yourself in mercury (not recommended) and accelerated the tank, you would also get pushed toward the acceleration, just like the balloon in the car.
As far as the ceiling friction, a balloon tied to a string also moves forward, and you can't say the string is pushing it forward.
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Archon
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Re: Balloon in car
« Reply #8 on: Aug 9th, 2002, 2:06pm » |
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When I say I've seen it first hand, I really mean it. I've been in a car with helium balloons in it and watched them fill the back windscreen when we started moving off. We had to tie them in place to prevent obstruction of view. I agree that in an ideal situation (sealed car etc) this may not happen, as the helium balloon is clearly lighter than the air around it, but in a real car, it certainly does
As for centrifugal force, theres no such thing. Centripetal force, yes, being the force exerted on an object in orbit (whether gravity, or twirling a weight around on a piece of string, etc).
Yes, people generally "low side" when coming off a motorcycle, meaning they fall into the turn, but it's not strictly speaking the road holding you upright. You could skid sideways while leaned over and executing a turn. In fact, the road wants to flip you the other way (the road exerts a centripetal force on the tyres of the bike, the inertia of the upper parts want to keep going straight, resulting in the bike "wanting" to lean to the outside of the turn).
(edit)
Actually, I see that what I've written here is somewhat contradictory. I have said that the road doesn't keep you upright, but that it does want to lean you out of the turn, opposing the inwards lean, so you're right, It does oppose your lean. I guess I took issue with the statement that it wants to keep you "upright", because it actually wants to unbalance you in the opposite direction. For completeness, the things that "want to make the bike upright" are the gyroscopics of the wheels and to a minor extent (or major, depending on the engine design) the flywheel, but the list of things that keep you stable in a lean does certainly also include the road... but more correctly, it is the inertia of the bike trying to go straight, not the road itself.
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| « Last Edit: Aug 9th, 2002, 2:26pm by Archon » |
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Pj
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Dam ! I remember this question from my 3rd year mechanical engineering degree. Its all to to do with 3rd 4th 5th moments of inertia or something like that, gyroscopes too. Didnt understand all that nonsense. When the car slows the balloon moves backwards and when it speed ups moves forward. Oh yes youll all be pleased to know I design commercial aircraft. Its not what you know, its what people think you know ;¬)
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Kozo Morimoto
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I've seen on a science show on TV that the balloon does indeed float to the front of the car. I believe what you really saw must have been caused by something else and external to the 'riddle' at hand. The show on TV was a controlled experiment.
Everyone has pointed out the motorcyle lean in/out thing, but no one has touched the boat on the water leaning in effect...
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Aaron
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Re: Balloon in car
« Reply #11 on: Aug 11th, 2002, 1:05pm » |
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In a controlled experiment, it should float to the front.
Acceleration is the same as gravity. A forward accelaration is has the same effect of a horizontal component of gravity fro mthe back of the car. In essence, this is the same thing as tilting the car head up, and the ballon will be pushed to the "higher" position now by the havier air dropping down. (see the ilustration below)
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AlexH
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Re: Balloon in car
« Reply #12 on: Aug 12th, 2002, 12:56am » |
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I too have seen it in practice in a car with the windows closed and the balloon moved forward when we accelerated and backward when we decelerated. Archon did you have the windows open or AC/fans blowing?
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Archon
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Re: Balloon in car
« Reply #13 on: Aug 13th, 2002, 5:44am » |
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Nah no a/c or windows. But the car wasn't sealed of course. Not even "nearly" sealed I guess. Clearly there was some kind of airflow towards the rear of the car which helped the balloons to move backwards. Or perhaps the balloons had reached perfect buoyancy and were the same weight as the air by the time we got them into the car. In any case, as I said this was a particular "real life" situation and I would expect a different result under controlled conditions.
Kozo, I can't explain the boat thing... perhaps I don't understand what you mean when you say the boat flips "into" the curve.... you mean it rotates around it's axis, or that it actually translates towards the centre? If its rotation, it could simply be similar to the motorcycle case, but I don't believe it would translate towards the centre, that makes no sense to me.
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snags697
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Re: Balloon in car
« Reply #14 on: Aug 13th, 2002, 6:53am » |
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I think the boat tips toward the inside of the curve because of the force that is turning the boat. Say you're turning right. Then there's a leftward force at the rear of the boat caused by either a rudder or an engine. If you turn too hard, this force can be large, pushing the bottom of the boat to the left, making the top fall toward the right.
This is just my guess.
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radster
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Maybe you should look at it a different way:
The air in the car is in fact _not_ being "pushed back". It is merely standing still. However the car starts
to move. And since the back of the car will not allow
the air to pass it, will "collect" air as it moves along. Thus the pressure rises at the back of the car.
Consider it a wave of air building up that will eventually reach the balloon and push it away (from the back).
So the balloon is really surfing towards the front
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S. Owen
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Re: Balloon in car
« Reply #16 on: Aug 14th, 2002, 9:12am » |
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I believe all of those that say they've seen the balloon move forward in this situation. However I'm still having a hard time believing it is really due to movement of the air.
When you accelerate, even hard, it's not as if the air in the car moves significantly to the back, leaving a vacuum in the front. It's not even close to that. I'd accept this argument if the car were full of water or something.
If we consider this effect, then the fact that air is moving backwards and pushing the balloon backwards seems an equally important force to consider.
Am I nuts or does this explanation seem insufficient? I don't have the background to tell either way, really.
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Archon
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Re: Balloon in car
« Reply #17 on: Aug 14th, 2002, 8:48pm » |
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You can test it yourself...
Fill a clear glass half way with water. Drop a toothpick in. Now swing the glass around in a circle (hold on tight!). The toothpick won't sink. As snags said, gravity is equivalent to acceleration, shown by relativity.
I still find it hard to believe that this would be seen in a car, because I find it hard to believe that you wouldn't get a "wind" of some kind blowing through the car. Clearly the car can't really be sealed or people would suffocate on long trips! In that sense, I think buoyancy would be less significant than the inertia of the air / balloon system and the friction between the balloon and the ceiling, but I agree that the theory is correct.
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schiefaw
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Re: Balloon in car
« Reply #18 on: Aug 15th, 2002, 12:06pm » |
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I can see where the balloon would move to fill the relative vacuum caused by air rushing (relatively) to be back of the automobile, but that does not take into effect the inertia of the baloon itself and the fact that the air is not going to compress that much. I could see if you were to sustain the acceleration for a while, or if you we accelerating at an obscene rate, but in a relatively sealed system for a short period of acceleration, I would think that inertia would win.
At least, I would think the ballon would go back first and then forward as the pressure differential built up.
Tony
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radster
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There is really no airflow towards the back of the car that would pass the balloon by. It's the back of the car
that pushes itself into the air in the back and thereby increasing it's pressure. And the front of the car is moving away from the air in the front, reducing the pressure there.
So the air moves WITH the balloon towards the front!
If you have a little pond and throw rocks into it on one
side and dig a hole on the other the water will move towards the hole. And any ship on it will follow.
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Archon
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Re: Balloon in car
« Reply #20 on: Aug 16th, 2002, 5:31am » |
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Radster, by that argument the atmosphere of the earth should dissipate into space, because the higher pressure near the surface will push air towards the lower pressure higher up
I have just remembered something I read in the paper yesterday. A bridge on Sydney Harbour is no longer of adequate height, and much expense is required to build a new bridge. Some bright spark wrote in to the paper, complaining about the expense and saying that much money could be saved by simply dredging a trench in the bottom of the harbour where the bridge is, thus lowering the water there
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S. Owen
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Re: Balloon in car
« Reply #21 on: Aug 16th, 2002, 6:42am » |
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on Aug 16th, 2002, 4:45am, radster wrote:There is really no airflow towards the back of the car that would pass the balloon by. It's the back of the car
that pushes itself into the air in the back and thereby increasing it's pressure. And the front of the car is moving away from the air in the front, reducing the pressure there.
So the air moves WITH the balloon towards the front! |
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That's a truer statement of what's going on, but I still have the same problem with this explanation.
OK, right - as the car starts to move, the air inside does not. The car scoops the air forward and begins to move it as it accelerates, and the balloon goes with it.
But - the same argument applies to the balloon, no? It stays still as the car moves forward (thereby moving to the back), and eventually floats back towards the front as it and the air in the car is scooped forward.
In the "real world" there is a bit of friction with the roof (and attraction from the static charge?), and this provides a forward push to the balloon. In fact, I'd guess this is a bigger factor than airflow.
To those that say the balloon really does move forward - are these forces perhaps the extra kick that allows it to do so?
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Archon
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Re: Balloon in car
« Reply #22 on: Aug 16th, 2002, 9:28am » |
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The "push" by friction between the balloon and the car cannot exceed the push on the car itself. In other words, friction can't push the balloon forwards relative to the car. Besides which, friction will always work against motion.
To get the "go forwards" reasons, just go back to what Snags said in the first post.
Gravity == acceleration. Think of it this way. Assume you were in a giant, sealed, air filled box, out in space, that was accelerating (in some uniform direction) at 9.8 m/s/s, exactly the same acceleration as that due to gravity on earth. How could you tell the difference? IE, how would you know the box wasn't just sitting on the earth somewhere?
Now put a balloon in the box. How can it tell the difference? So which way will it go?
I think I shouldn't have mentioned the real life scenario that I witnessed, it seems to have complicated things
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S. Owen
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Re: Balloon in car
« Reply #23 on: Aug 16th, 2002, 9:54am » |
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Yeah sorry, I am getting disconnected here... agreed that friction alone can't move it forward. I thought maybe friction sort of holding it in place plus the air movement might be an explanation, since people report that it really does go forward in the real world.
But yeah, overall, this still goes against my intuition - I'm still not really comfortable with that explanation.
I do agree that the air moves to an extent... and agree with your argument that it might move forward eventually, "rising" above denser air at the back. But I still would think the immediate motion is with the rest of the air, towards the back.
Well anyway, I accept that it does go forward... some variation on the explanations offered here must be right.
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Chronos
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Re: Balloon in car
« Reply #24 on: Aug 17th, 2002, 12:38pm » |
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Is this a sudden acceleration, or a steady one? It does make a difference. If we start off at rest and then suddenly floor the gas, then yes, for a brief period of time, the balloon will move backwards. But for a car, this period of time will be very brief indeed. Once the car has been accelerating for a while, we've got a steady-state situation where nothing is moving relative to the car, the air pressure is slightly higher in the back, and the balloon is stuck up against the front windshield.
And Archon, I see that you're talking trash about my buddy centrifugal force . I feel obligated to come to his defense, since nobody else has yet.
It depends on which frame of reference you're in. If you're in an inertial (i.e., non-accelerating, which means non-rotating) reference frame, then there is no centrifugal force, and you can do everything in terms of the centripetal force, the force which is causing the thing to move in a circle. But what if you're in the (non-inertial) co-rotating frame? Now, you can't say that there's a centripetal force causing the object to move in a circle, because in that frame, the object isn't moving at all. We can still use Newton's laws in a non-inertial frame, though, if we introduce "fictitious" forces. These are gravity-like forces which aren't actually exerted by anything (which is why they're not "real" forces), but are felt (in the comoving frame) by things with mass. Centrifugal force is an example of such a force. In some situations, using these forces will make a problem much simpler.
If you really don't like fictitious forces anyway, then I should point out that gravity is another example of a fictitious force. According to Einstein, the reason we're all stuck here on the surface of the Earth is that the surface is continually accelerating upwards at 9.8 m/s2
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