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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Imagine your balloon is in a car parked on a steep hill (facing upwards). From the point of view of the car, the force of gravity is pointing diagonally downwards towards the rear wheels of the car, and the balloon’s buoyant force is pointing diagonally upwards towards the top of the windshield, so the balloon will float diagonally upwards.
When you accelerate your car, let’s say at 1g, from the point of view of everything inside, it’s almost the same situation as being parked on a hill.
In the accelerating frame of reference of the car, all objects inside the car experience (a) the force of gravity accelerating them straight down at 1g, and (b) a fictitious force (due to the car accelerating) that accelerates the objects straight backwards at 1g (this is what pushes you back into your seat). These forces add together to make a ~1.41g force accelerating everything diagonally down-and-back.
So, it’s mathematically the same as if you had your car parked on a hill on a planet with slightly stronger gravity. “Gravity” is pointing diagonally downwards, so the balloon’s buoyant force is pointing diagonally upward, so that’s where it goes.
Talking about fictitious forces in accelerating reference frames might have made this even more confusing, but the key is to realize that gravity and acceleration act the same way on everything inside the car, so it’s just like tipping the front end of the car up. In fact, in general relativity, acceleration and gravity are *literally* the same thing, and this is the principle that flight simulators are based on: tipping the flight simulator upwards or downwards makes the occupants feel like they are accelerating or decelerating, because from the inside, they feel exactly the same.
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