eli5: Motion of a helium balloon in a car

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I heard that if a car accelerates from rest, a balloon would move forwards instead of backward. Why is this? Science says it’s because of density, but I don’t get their explanation. It also seems like it’s violating newton’s first law.

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The helium balloon moves forward for the same reason that it floats! Acceleration and gravity act very similarly (we can fake gravity with acceleration and acceleration can feel like gravity).

Helium balloons float because as much as they want to be lower (because of gravity pulling them down), the air around them wants to be lower more.

For a helium balloon to fall down a bunch of air has to move *up* out of the way (effectively swapping place with the balloon). But the air that would have to move weighs more than the balloon does, so the force due to gravity pulling the air down is more than the force pulling the helium balloon down [this is where density comes in; same volume of stuff, but the air is more dense so has a higher mass]. So the air wins; the air goes down, the balloon goes up!

Same thing happens in the car. Everything in the car wants to move to the back. But the air (with more mass per volume, so more inertia) wants to move to the back more than the balloon does. So the balloon ends up “floating” towards the front. *Something* has to fill up that space at the front of the car, and the balloon is the lightest thing.

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On Newton 1, there are a few ways of stating it, but a convenient way of stating it here is:

> An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line **unless acted on by an unbalanced force**.

This gets applied slightly differently depending on our perspective.

If we look at things from inside the car (taking the car as our “reference frame”), we’re in an accelerating reference frame (accelerating forwards), so everything in the car experiences a pseudo-force pulling it backwards (this is what you feel; being pushed back into your seat). Newton 1 doesn’t really apply then as the balloon is being acted on by an unbalanced force (pseudo-force of the acceleration pulling it backwards, reaction force of the air pushing it forwards, air force > acceleration force, so balloon accelerates forwards).

If we look at things from outside the car, as the car accelerates it pushes the air inside the car forwards, and that air pushes on the balloon (pushing the balloon forwards); so again, unbalanced forces, the balloon can accelerate without Newton 1 causing us problems.

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