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Balloon Business

You’re sitting in a stationary car. There’s a helium balloon tied to its floor. You accelerate and, obviously feel like you’re being pushed backwards (against the direction of your acceleration). Which way will the balloon move?

Note: I found this puzzle and its explanation at physicallyincorrect.com

The helium balloon will actually do the opposite and get thrown forwards as you press on the gas. At first, this is quite counter intuitive, since we’re all accustomed to being thrown backwards. There are several ways to reason about this, but let me give you an elegant solution: a Helium balloon tends to “want” to move opposite of gravity. After all, if you let go of such a balloon outside, it will float up – opposite of ‘down’, which is where gravity points – to the sky. This has to do with the fact that Helium is less dense than air, so it floats because of buoyancy. But the reason isn’t as important to the solution as the observation itself.Now, when you accelerate, you’re creating “fake gravity”. If you accelerate forwards, you’re actually creating a fictitious force pointing in the other direction in the accelerating car’s frame. Given that, where will the Helium balloon naturally tend? That’s right, just opposite of the fictitious gravitational force, which is forwards. Put slightly different, it will ‘float forward’, just as it floats upwards in the Earth’s gravitational field.

Incidentally, The notion that acceleration and gravity are interchangeable is at the very heart of Einstein’s general theory of relativity. It’s called the (strong) equivalence principle, and states that inertial and gravitational mass are interchangeable. Einstein has called this observation the “Happiest Thought” of his life – but that’s a different story, and a different puzzle.

Comments


Aakash

These balloon questions always get me.


Genious22

Pretty interesting. but who will consider friction? the balloon will not go against atmospheric pressure which ahould have been mentioned in the Q.


Kranthi Krishna

The balloon needs some kind of force to move forward (Newtown's first law). The only force that's available is car's acceleration. But that is not acting on the balloon's COM (centre of mass). So it's highly unlikely that the balloon moves forward


Tarun245

Forward? cause it is helium


Ajay Pratap

this is not the proper explaination. helium doest acts opposite to gravity. it float over the air because it has light weight then composition of air. gravity acts on each and every element that exits. and when car accelerates the air pushes it backward therefore it will do backward bold not forward

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about 5 years ago
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Difficulty 4.0 ?

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