You are a hobo and you have a helium filled balloon...?

General relativity basically states there is no difference between a gravitational field and an accelerating reference frame. So, just think how things would behave if you just jacked up the front end of a stationary box car a little, thereby having gravity supply the rearward 0.1 g. From your perspective, the balloon, still pointing straight up, would appear to lean forward in the car.

From another viewpoint, heavier air pushes the balloon out of the way, forcing it forward.

Believe it or not, it will float forward, in the direction of travel. The reason is I used to be a hobo and I was curious about exactly this same question so I got a balloon and .... hehe!

No,seriously, it's simple. The acceleration of the sealed boxcar also inparts an acceleration to the air inside of it. This results in the same result, only sideways, that gravity has on it - the air density will be slightly greater at the end of the boxcar opposite the acceleration, i.e, the trailing side. And of course, slightly less density at the leading side. The balloon will initially be moved toward the rear during the transition from zero acceleration to 0.1g due to the mass of air moving toward the rear. Once acceleration is constant, it should move back to it's original center position, which I would expect to be the plane of density that is equal to the non-accelerating density. I would also guess that if the balloon was tied down initially forward of center, it would try to drift backward toward that same plane, and if tied aft of center, it would try to drift forward toward the same plane.

You are under constant accleration, the baloon will want to float to the rear.

The only 2 figures you need are the accleration due to gravity

and the accleration due to the forward motion. Find the

normal when you combine the two.

At rest under 1G the ballon will rise straight up, if you move

forward at 1G the baloon will be at normal at a 45degree angle to the rear... you can solve this with simple trig. to find

the direction the string needs to apply the normal force. Use

opposite sides to be 1 and .1, the hypotenuse is perpendicular to the direction of force.....

It will lean forward. The angle from vertical would be arctan .1.

The train is accelerating. Everything including the air is also accelerating. Acceleration produces a reverse force opposite to the forward force. Everything in the train will therefore TEND to move backwards at the same acceleration as the forward acceleration.

(Why do you think that, as you accelerate in your car, you're pushed against the back of your seat ?)

I think the baloon travels in the opposite direction of your acceleration based on newtons third law...(equal and opposite reaction). Hope this helps.

I don't know the answer, but I dub this the most intriguing subject line of the day.

As long as there is no air moving around inside of the car, the balloon will float straight up because of the relative air, balloon, and car movement is equal. It is all relative, you see. Good day.

it wont move, since the balloons in a moving boxcar, the balloon itself is moving at the same speed. Objects in motion tend to stay in motion...

Just point straight up, depending on no wind blowing it around (ie: the doors are closed).