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I noticed that when I had a helium filled, latex balloon inside of my car, it moved forward in the cabin as I accelerated forward. The faster I accelerated forward, the faster the balloon went from the back of the car to the front of the car. The balloon didn't have a string. This became a game with my 4 year old as we drove home. We figured out where the balloon would go based on how fast I accelerated, turned corners etc. I expected that it would act a lot like the water in a cup does, but it was the total opposite it seemed. What forces caused this behavior? I assumed it has something to do with the fluid dynamics in the closed cabin, but I can't figure it out.

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user33986
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9 Answers9

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It travels forwards instead of backwards in an accelerating car for the same reason that a helium balloon travels upwards instead of downwards under the influence of gravity. Why is that?

In an accelerating car, for all intents and purposes the acceleration can be considered a change in the amount and direction of gravity, from pointing straight down to pointing downwards and backwards. The balloon doesn't know and doesn't care if the acceleration is from gravity or from the acceleration of the car; it just tries to move in the direction it naturally moves, namely, against the direction of the acceleration. Thus, it moves forwards when you accelerate. Hopefully you find this explanation intuitively satisfying.

Another more rigorous way to view the problem is through Lagrangian minimization. The balloon can be considered a low-density object embedded in a higher-density fluid constrained within the confines of the car. Under the influence of gravity pointing sideways, the total system potential energy decreases the farther forward the balloon is situated. Since the force is the gradient of the potential, the balloon will try to move forward.

DumpsterDoofus
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    The explanation is pretty good, but I would add the following: If your car accelerates forward the pressures change in such a way that at the end of the car the pressure is higher than at the beginning. And like DumpsterDoofus explained this is similar how gravity influences the pressure (higher as you go closer to the center). But the ballon doesn't want to "against" the acceleration but simply to the lower pressure area which in the front of the car. – xZise Nov 16 '13 at 16:51
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    Yeah, I didn't even think of the pressure picture when I saw the question, although it's undoubtedly equivalent and probably more intuitive than my explanation for a lot of people; the first thing that visually popped to mind was Lagrangian minimization. – DumpsterDoofus Nov 16 '13 at 18:41
  • I do not think that they are equivalent. We do not have any pressure difference in the Earth atmosfere. I think that DumpsterDoofus explanation is more general. You do not need the gradient for the baloon to antigravitate. It "antigravitates" for the same reason as we have in the atmosphere: the ordinary air is heavier than helium and, thus, attracted stronger. You do not need the pressure gradient. I can say that the forse of attraction compensates the pressure gradient, whichever it exists. So, pressure gradient does not play any role. – Val Nov 17 '13 at 14:37
  • You do not say anything about pressure difference when explain the fenomena of oil on the surface of the water or helium balloon lifting. – Val Nov 17 '13 at 14:41
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    @Val, of course we do have a pressure difference. The atmosphere up high is at a lower pressure than the atmosphere at sea level. This happens BECAUSE of gravity - no gravity, no pressure difference (or atmosphere for that matter). DumpsterDoofus's explanation is spot on if you look at it from a slightly physics-educated person's point of view. The acceleration induces a faux-gravity effect, which creates the pressure difference, which causes buoyant forces on the balloon. – pho Nov 17 '13 at 17:05
  • Do you say to your children that butter floats on the surface of water because there is "a pressure difference" or use the "physics educated point of view" saying just that butter is lighter? Why do you answer me without reading my comment? Why do you want to make the stupid laymen from the kids who are initially educated physicists? The heavy body falls through the atmosphere despite of your "pressure difference", BTW. – Val Nov 17 '13 at 17:18
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    @Val: I'm sorry, but Pranav is almost certainly correct on this. I am also a bit baffled by why you think there is no pressure difference in the atmosphere; I thought that was middle school science knowledge. – DumpsterDoofus Nov 17 '13 at 17:22
  • Why do you need the school if you reason by logic which says that stones must fly? – Val Nov 17 '13 at 17:25
  • @Val: You seem to have some very strange misconceptions about how pressure and buoyancy work, as evidenced by the fact you think that the existence of a pressure gradient in the atmosphere would mean that rocks should spontaneously levitate. You can learn more about pressure effects in a class in fluid/solid mechanics, or in general science books. – DumpsterDoofus Nov 17 '13 at 17:42
  • @Val, yes, stones could levitate, provided the buoyant force acting on them turned out to be more than the weight pulling them down. What I meant to say was: to a layman, the explanation of pressure differences makes sense immediately, while the "apparent gravity due to acceleration" concept requires some explanation. Forgive me if I offended you, I did not mean to question your expertise at all. – pho Nov 17 '13 at 17:47
  • @DumpsterDoofus I do not have misconceptions. I say that saying that "pressure explains levitation" is wrong. The baloon raises up because it is lighter rather than there is a pressure gradient. I do not understand why the only true explanation "lighter" works alone, without pressure, when you are standing still and you need to entail "pressure" aspect when you are accelerating in car. I do not think that fluid/solid mechanics book will explain this to me, especially you have answer saying that the effect in car is absolutely the same. – Val Nov 17 '13 at 17:48
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    @Val, the balloon rises because the pressure higher is less than the pressure at a lower height (and, of course, the resulting buoyant forces are less than its weight). Consider you're in a weightless environment (which eliminates the atmospheric pressure gradient). The balloon wouldn't rise in this case at all. – pho Nov 17 '13 at 17:52
  • @Val: If you are saying that "pressure explains levitation" is wrong, then you indeed have a misconception. The steady-state solution to a uniform compressible fluid in a closed domain experiencing a constant acceleration is a gas configuration with a constant pressure gradient in the opposite direction of the acceleration. Thus the integral $\int_{\partial\Omega}p\mathbf{I}\cdot\mathbf{n}dS$ over the balloon surface yields a force in the opposite direction of the pressure gradient, and is the origin of the buoyant force. Therefore, my answer and Pranav's answer are equivalent. – DumpsterDoofus Nov 17 '13 at 17:57
  • There is no need to entail the pressure. It won't raise just because it is not lighter in that direction. That is, pressure does not explain anything. Weight explains everything. If you want to explain why lighter files up, you better argument in terms of displacement, http://physics.stackexchange.com/a/86795/16114. Otherwise, the stones should fly. – Val Nov 17 '13 at 17:57
  • @Val, here's another attempt at an explanation: How do you define "up"? I could say "up" is the direction in which I would have to go to encounter a decrease in pressure of a stationary fluid. – pho Nov 18 '13 at 00:46
  • @PranavHosangadi Children and uneducated physicists feel gravity rather than the pressure (gradient). It is obvious that heavier bodies go down quickly, lighter slowly and very light, lighter than air, go up. Ligher that air things antigravitate. This is utterly obvious even for the children and is exactly what dumpster had in the answer. Your pressure it is not visible and it implies that stones can fly. Just say that heavier gravitate stronger and evict the lighter to the heights. – Val Nov 18 '13 at 08:43
  • I also looked at gravity separation and it says only about the wight: heavier/lighter. Gravity separation is never explained in terms of pressure. I suppose it is because explaining in terms of pressure is difficult, bad and incomplete. – Val Nov 18 '13 at 08:43
  • @Val: I don't have the space to go through a full fluid-static derivation of buoyancy in a comments section. Pressure and uniform acceleration are intimately-related in closed domains. Pressure is the reason you become near-weightless in a swimming pool. Pressure is a fully-equivalent way of seeing why the balloon moves forward. You keep attacking Pranav by idiotically repeating that pressure gradients imply stones can fly, and my only response is that you are not making a detailed analysis when you come to that conclusion. – DumpsterDoofus Nov 18 '13 at 14:58
  • @Val The pressure gradient applies an upward force on everything. The helium just takes less force from gravity so that the upward force is stronger. This is because of how light helium is COMBINED with the pressure gradient resulting in a NET upward force. The key is that UPWARD FORCE DOES NOT IMPLY LEVITATION – Cruncher Nov 18 '13 at 15:09
  • Water pushes oil to the upper layers because oil is lighter, not because there is a pressure. The notion of wieght already includes all the pressure data. Pressure does not include the weight aspect. You do not need pressure to explain why light objects levitate. Gravitational separation is never explained in terms of pressure. – Val Nov 18 '13 at 16:11
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    @Val: Water pushes an oil droplet upwards because of pressure. This fact is intimately related to their densities. Gravitational separation can be explained in terms of pressure. – DumpsterDoofus Nov 18 '13 at 22:27
  • @Val, in the presence of a gravitational field, there WILL be a pressure gradient in a body of fluid. Any object contained inside said body of fluid will hence experience a buoyancy force. Whether it floats or not depends on whether the buoyancy can overcome the weight. – pho Nov 19 '13 at 00:44
  • Please do not have long comment discussions on the main site. Feel free to continue this by creating a room in [chat]. – Manishearth Nov 19 '13 at 07:09
  • @DumpsterDoofus Air and water push the stones upwards because of pressure. Yet, this cannot explain why they fall and sink. Therefore, gravitational separation is explained in terms of weights instead of pressure. – Val Nov 19 '13 at 08:09
  • @Val: As Manishearth said, this discussion needs to stop. If you would like to chat further about this, I will be available in PSE Chat starting at 7PM US Eastern time. – DumpsterDoofus Nov 19 '13 at 13:36
  • '-1' suppose the observer is standing at the foot-path watching the balloon inside the car accelarating in the direction as that of the car's acc. . For this observer gravity hasn't changed. so balloon shouldn't accelerate forward. But it does. – user31782 Dec 25 '13 at 13:05
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    This is a rather fascinating discussion and has made me realise I don't actually understand how the floating force caused by displacement works. I'm completely unconvinced that it is due to a pressure gradient in the supporting medium. At ground level the pressure gradient must be tiny. – Benjohn Jul 01 '14 at 06:52
  • @benjohn (I know this is years later, but could be useful to people reading) Water is fairly heavy and has a noticable pressure gradient. Air not so much, but that's only part of the picture. The reason buoyancy force depends on volume is because the wider the object the greater the net force due to pressure gradient (force = pressure ×area), so the volume of the displaced fluid determines the net force for a closed object. And the heavier the fluid, the higher the pressure gradient, thus more force. It works out to the same as Archimedes Principle (force=$ \rho g V$) – JMac Oct 23 '21 at 15:26
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When your car accelerates forward, the air inside moves back relative to the car. This creates a slightly high pressure in the rear of the vehicle and a low pressure up front.

Since helium is lighter than air, it moves away from the region of high pressure. A similar balloon filled with $CO_2$ would move back, since it is heavier than the surrounding air

pho
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    Looks like I need to have a couple different balloons filled with varying density gases to fully explain that to the budding scientist in the back seat. – user33986 Nov 16 '13 at 15:06
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    Of course, if the balloon is filled with a gas heavier than air, it won't be floating so it wouldn't have room to roam like the helium balloon. But you could suspend it from the roof. – WinnieNicklaus Nov 16 '13 at 15:54
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    I prefer your answer - like you would explain it to your grandmother, as old Einstein said :-) – Riegardt Steyn Nov 17 '13 at 13:52
  • @Heliac This answer says that stones should fly because there is a lower pressure at the heights. So, pressure aspect is incomplete answer. Other answers are better because they just say that heavier things gravitate stronger and evict the lighter ones to antigravitate. Einstein was an Occamist and could never say that we should entail pressure since it is uncomprehensible for laymen and does not explain anything. Your kids will understand that lighter things fall slower and very light fly up. But, they won't understand the pressure and it is never used in gravitational separation explanation. – Val Nov 18 '13 at 09:17
  • @Val, lighter things fall slower? That is not true. – pho Nov 19 '13 at 00:42
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    My kids don't think that lighter things fall slower. Just for the record. – user33986 Nov 19 '13 at 03:10
  • Pranav, please be nice. – Manishearth Nov 19 '13 at 07:08
  • lol, @Manishearth, I see you have ensured that. I will in the future :P – pho Nov 19 '13 at 07:54
  • @user33986 Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. Do you think that he was an idiot? No, these are your children who do not see the obvious things. It is meaningless to discuss the behaviour of the baloon in the car with them. I guess that you just overloaded their intuition with Galileos's law so that they stopped to see the apparent things and correct the falling speed as if there is no atmosphere. Others simply have eyes to see that feather drops slower than hammer. – Val Nov 19 '13 at 08:49
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    @Val If I dropped a million feathers, it would be heavier than the hammer, but fall much slower. Therefore heavier things fall slower than light things! – Cruncher Nov 19 '13 at 18:02
  • @Val, With regards to Aristotle's "teachings", what if I dropped a ball of ice and a ball of lead, both identical in shape? Which one would hit the ground first? – pho Nov 19 '13 at 21:03
  • @PranavHosangadi of course the heavier ball will touch the ground first. The identical ball, filled with vacuum or Heilum will not touch the ground at all. – Val Nov 20 '13 at 11:53
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    @Val: Aristotle's statement about falling speeds has been known to be completely wrong since the 1600's. I find it impossible to believe that you actually have an account at this site and hold on to such bizarre, ancient medieval notions. Again, I suggest you take introductory science courses, they can be a very valuable resource for learning. – DumpsterDoofus Nov 21 '13 at 23:33
  • It is impossible to believe that you do not understand that helium lifts up just because of the atomsphere -- where Aristotle's logic is in action. All children on the Earth observe the Aristotles laws of nature. You must know that Galileo is appropriate only in vacuum, i.e. on your Moon, where no helium flies. I wonder how "true laws of nature" make people blind to deny the obvious laws of the Nature and insising on laws in vacuum when discussing the lifting force of the air. – Val Nov 22 '13 at 09:58
  • @Val, do you think a helium balloon rises up in the ISS? No it doesn't, because buoyancy effects are non-existent in microgravity. Check out this presentation by NASA, read pages 5 onwards. The reason why the balloon rises on Earth is because of the gravity-induced pressure gradient in the atmosphere. contd... – pho Nov 22 '13 at 16:24
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    @Val Now you can continue hurling insults and screaming that Aristotle's laws are what children observe, but there's a reason that Aristotle's laws aren't accepted any more - they were proven to be erroneous, and however counter-intuitive the currently accepted model is, it matches our observations so you can accept it, or scientifically prove why our current notions are wrong and collect your Nobel prize – pho Nov 22 '13 at 16:25
  • @Val, and everyone else: Please be nice. Personal attacks will not be tolerated and will get you suspended. I have edited the message out for now. – Manishearth Nov 23 '13 at 12:16
  • As far as the discussion here goes, it would be better if it as held in [chat]. Also, it seems to me that this stems from a disagreement as to what "heavier" means. Some are taking buoyant force and drag into account while measuring the heavyness. – Manishearth Nov 23 '13 at 12:18
  • @Manishearth Exactly. They try to build the system out of the first principles: in "true" physics you have neither atmosphere nor friction and you add the gases onto your planet. In Aristotle's dynamics you however already have the planet configured with air. That is, despite more "true", the Galileo's laws are more outlandish. It makes no sense to ground the asked explanation on them. I wonder how drilling the "true" laws of Nature washes away the ability to observe the "unture" rules around us. You cannot deny the Aristotle's friction saying that "true laws of nature are reverisble". – Val Nov 25 '13 at 13:05
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Fun question. Here's my "me-too" answer.

Suppose the car has just emerged from a river, so there's a lot of water in it, and the balloon is tied to the floor.

Then you drive away.

enter image description here

The air in the car is just like a bunch of water :)

Mike Dunlavey
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    This is very intuitive – Cruncher Nov 18 '13 at 15:40
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    I just find the diagram confusing. Which direction is the car travelling, where's the front of the car? Is that a balloon submerged under water? Why? – wim Nov 18 '13 at 17:09
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    @wim: It's accelerating to the left. Yes, the balloon is tied to the floor. The balloon seeks the surface so as to have the least water "above" it. – Mike Dunlavey Nov 18 '13 at 19:15
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    @wim baloon was submerged under the water in order to increase the weight contrast. Heilum raises up because it is lighter that air. It is even lighter than water. The lifting force in the water is much stronger therefore. Secondly, the blue water edge also shows you the direction of acceleration. The diagram is intuitive to the extreem, therefore. – Val Nov 19 '13 at 13:17
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    @MikeDunlavey It was not at all clear that the car was accelerating to the left ;) – Alfred Dec 26 '21 at 16:28
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It acts precisely like water in a cup. Or, more specifically, like the air in the cup. Since the helium is a much lower density than the nitrogen and other gasses in your car, it can be visualized like an air bubble in a bottle. The container for the helium(the balloon) has negligible mass.

When you accelerate forward, the water in a bottle will move backwards, just like you'd expect. The air bubble will appear to move forward to fill that void left by the water, just like the helium balloon.

Additional forces may come into play as well. There is friction from the rubber on the ceiling. Also, when you accelerate, the center of gravity of your car moves backwards on the wheelbase. The nose of your car lifts, and the tail of your car sinks. When you stop, the opposite happens, and when you turn left, your car leans right, as you can feel. This may tilt the ceiling allowing the balloon to move in response to the tilted ceiling. This could have an effect as well.

jfa
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    I like your answer the best of all of these. Seems like some people are guessing at the answer saying that the movement of the car is like a "gravity". This is like saying an airplane flies because the propeller cuts through the air in front of it. I don't see any formulas in any of these answers. But I bet you could write one regarding the conservation of energy, with mass and acceleration. Or newton's laws of body in motion tends to stay in motion, body at rest tends to stay at rest. – badweasel Nov 17 '13 at 05:24
  • Think of having a lever in the car where the sides move forward or backward instead of up and down. Like a sideways teeter-totter. Imagine a heavy weight on one side and a lighter weight on the other side. When accelerating forward the heavier side would try to stay at rest and therefore would move backwards relative to the car. Just like your water in the cup analogy. The lighter side of the lever would then have to move forward relative to the car.

    The ballon is the same. The air in the car moves back because of inertia which because of air displacement forces the ballon to move forward.

     – badweasel Nov 17 '13 at 05:25
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    The answers with a lot of upvotes are technically right. However, this answer makes it much easier to understand. – Loren Pechtel Nov 18 '13 at 21:36
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I am not good at explaining things but here it goes

try to understand it this way enter image description here

assume the rectangle to be you car, now the dotted area is filled with normal air and their is a helium balloon in between

So when you accelerate everything in the car tries move backward with respect to the car even the helium balloon, so then why the balloon goes forward,

As you may know helium is less denser than the air and so it is lighter then the air, so when you accelerate the air starts moving backwards but as the helium is lighter it is pushed forward by the air collecting at its back the same phenomenon when you fill a bucket and a ball kept at its bottom starts rising up because it is less denser than water.

Deiknymi
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When you're in an accelerating frame of reference, the acceleration is perceived as gravity. For instance in an accelerating train, you stand on an angle, in the direction of motion. It feels like you're on a slope, and de facto, you are.

The helium-filled ball is simply moving against the direction of what looks like gravity: the same thing that it does when you're not in an accelerating frame. It does that for the same reason: buoyancy due to being lighter than air.

When you let go of the balloon in an accelerating train, it will not move directly forward, but on an angle: forward and up. That is the same angle at which you stand, if you balance without support. If while standing in this position you hold a balloon on a string, the string will point in the same direction, parallel to your body, and if you let go of the balloon, it will move in that direction. That is the direction which corresponds to "up", slanted due to the vector combination of the force of gravity (which acts on you downward perpendicularly to the floor) and the fictitious force which appears to be pulling you backwards due to acceleration.

So, in summary:

  1. A balloon rises "up" due to buoyancy.
  2. What determines which way is up "up" is a vector combination of gravitational pull, and the fictitious force caused by acceleration, which mimics gravity.
Kaz
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The simplest way to think about the helium balloon in the accelerating car is to invoke Einstein's Principle of Equivalence: a constant acceleration is the same, in all respects, as a gravitational force. To make matters as simple as possible, we'll ignore the real force of gravity (i.e. what's pulling the car toward the Earth) and just think about the forward acceleration of the car. According to the Principle of Equivalence, the effect of this acceleration is exactly the same as a gravitational force pointing to the rear of the car. But everyone knows what a helium balloon, immersed in air, does in the presence of gravity: it rises, i.e. it moves in the direction opposite to the gravitational force.

So when the car accelerates, the balloon moves forward. Incidentally, the Principle also explains why, when the car accelerates, a passenger is jerked backwards: because, unlike the balloon, the passenger falls downward, in the same direction as the gravitational force.

In answering this question, I'm assuming you accept that a helium balloon rises in the presence of Earth's gravity. Because helium has a smaller density than air, the buoyant force of air will push it toward the sky against gravity

gksingh
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  • '-1' suppose the observer is standing at the foot-path watching the balloon inside the car accelarating in the direction as that of the car's acc. . For this observer gravity hasn't changed. It is only the pressure difference which caused the balloon to acc forward. The pressure diff is introduced due to the movement of car . – user31782 Dec 25 '13 at 12:35
  • My exact first thought. – vs_292 Jun 21 '17 at 17:42
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I wondered this myself...

Then it hit me, the analogy in my head of a ball rolling on a surface was wrong... the balloon isn't something floating in nothing, it is a body that is less massive than the air it is displacing.

So when you break, everything tries to move forward, but the air wins because it has more inertia, and the balloon is forced backwards.

it is essentially the same thing as what normally happens with a ballon, only with the vectors turned on their side... normally all air and balloons and helium are pulled to the earth, but since the air is more dense it is pulled more... and displaces the balloon with the helium.

Grady Player
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  • would you elaborate on the point"_So when you break, everything tries to move forward, but the air wins because it has more inertia, and the balloon is forced backwards. _" – user31782 Dec 25 '13 at 13:12
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    He means... apply the breaks, to slow down the car. – Guill Jun 25 '14 at 18:28
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The answer that makes the most sense to me is based on exercise 88 in chapter 12 of University Physics by Young and Freedman (13th Ed.):

Consider a tube of air with cross-sectional area $A$ extending from the windshield to the back. Suppose the pressure at the front of the tube is $p_0$. Consider some section of this tube a distance $x$ from the windshield with width $\Delta x$. Let the pressure on the front be $p$ and the pressure at the back $p+\Delta p$. So there's a force on the front of this volume of air of magnitude $pA$ (pressure is force per unit area) and there's a force on the back of magnitude $pA+\Delta p A$. So, the net horizontal force on it is $\Delta p A$ towards the windshield. The mass of this volume is just $A\Delta x \rho$, where $\rho$ is the density of the air. So, by Newton's second law, you get $$\Delta p A = A \rho \Delta x a$$ which we can rearrange to get $$\frac{\Delta p}{\Delta x} = \rho a$$ We're assuming here that the density of the air is constant, which isn't strictly true but it doesn't change all that much for like, a normal acceleration a car might have so it's a decent approximation. You can take the limit of the above expression as $\Delta x \to 0$ to get $$\frac{dp}{dx}=\rho a$$ So the pressure increases linearly with distance as you go back in the car, so we get $p(x)= p_0 + \rho a x$. Notice that this is very similar to how pressure behaves as you go deeper underwater.

Using the same reasoning as in the archimedes principle, imagine some volume $V$ in the car. The net horizontal force on it depends on the pressure gradient of the car and its surface, so it'll be the same if the volume contains air or if it contains a balloon. Suppose this force has magnitude $F$. If it's air, this net force keeps it accelerating with car, so by Newton's second law, we have $$F=\rho V a$$ because its mass is $\rho V$. If this same force acts on a balloon with average density $\rho_{b}$, then by Newton's second law again, we have $$\rho V a = \rho_b V a_b$$ where $a_b$ is the acceleration of the balloon (wrt to the ground). We can rearrange this to get $$a_b = \frac{\rho}{\rho_b} a$$ Since the car has acceleration $a$, the relative acceleration of the balloon wrt to the car is $$a_b-a=\left( \frac{\rho}{\rho_b}-1 \right)a$$ So, if the balloon is lighter than air, like a helium balloon is, then it will have an acceleration forward relative to the car, and if it's heavier, it'll have an acceleration backward relative to the car.

PS: I know this is a very late response but I was looking around on the internet to check my answer to this question and couldn't find anything outside of chegg/numerade/etc. so I thought I'd post it here for anyone else in the future looking for the same, hope necroposting isn't against the rules.

NJjmOWVo48y5Tw
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