Will a helicoper which is hovering inside a closed box move with the box when we move it?

Question

I got this micro helicopter to play with, you know that cheap double bladed ones you can find for $25 or so. Anyway last night I was on bed trying to sleep and I got this idea, what if we put the helicopter inside a box and then seal the box, then we hover the helicopter inside the box. While the helicopter is hovering what will happen if we move the box left and right or up and down? will the helicopter move with the box without me controlling it so it's position will be relative to the box? or will it keep the position relative to the room and the box will move until it hits the blades? and why?

Sorry if this question is not about physics, physics was never my favorite and please if this is answerable here try to provide a "for dummies" answer :)

UPDATE: I just remembered something, when we are in a plane, we move with the plane! so logic says the helicopter will move with the box, correct?

Please excuse my MS Paint skills.

Answer 1

Objects don't accelerate because they're inside other objects. Objects accelerate because other objects make forces on them. The chain of cause and effect here is that the box can affect the air, then the air can affect the helicopter.

The answer to the question depends on how rapidly the box is accelerated.

To pick an extreme case, suppose that the box is accelerated so rapidly that the wall hits the helicopter at greater than the speed of sound. Until the wall hits it, the helicopter will not have felt any "disturbance in the force" from the air, because any disturbance in the air can only travel at the speed of sound.

At the opposite extreme, let the box be anchored to the earth's surface. The earth's surface is accelerating due to the earth's rotation. Clearly the helicopter won't collide with the walls when the acceleration is this small.

Answer 2

You move with the plane because kinetically you are part of the plane's body. When you sit or walk in the plane gravity attaches you to the floor/body. you are going with the same velocity as the plane as everything in it. If you throw a ball in the air it will have the velocity of the plane already so no effect will be seen. We see effects in the plane when there are accelerations and decellerations:things in the air then will not be acquiring the extra velocity of the acceleration and will accordingly demonstrate the difference . This is because to first order air at atmospheric pressure tranmits very little energy, that is why we walk through air.

Now to the original question, a hovering helicopter in a box can only be influenced by forces at the limits, as @BenCrowell explains, so it will hit the wall when the box is moved.