You ride in a train, you have this helicopter toy. The train is not yet running when you flew your helicopter on a constant altitude (say 1 meter above the train's floor).

Question: What will happen on the flying helicopter toy when the train accelerates?

  1. Will it stay relative to you and the train?

  2. Will it move backward relative to you and the train and bump to the rear part of the train?

  3. Will it move backward relative to you and the train for few seconds and then stay?

  4. Any other thoughts?


The question Manishearth mentions is certainly closely related.

If the helicopter is flying then it is affected only by the air around it. Experience of riding in trains suggests that when the train starts the air moves with the train - at least I don't recall feeling any air movement when the train starts.

So the answer is either 2 or 3 depending on how fast the helicopter is affected by the air around it. When the train starts the helicopter is initially unaffected so the train passengers see it start to move towards the rear of the train. As the train accelerates the helicopter will feel an increasingly strong wind blowing from the rear to the front of the train, and this wind will start to accelerate the helicopter towards the front of the train. Whether the helicopter accelerates fast enough to avoid being hit by the rear of the compartment depends on how fast the wind accelerates it.

  • $\begingroup$ If the air in the train is moving together with the train, then the air will move forward with respect to the helicopter, right? So will it push the helicopter forward too? $\endgroup$ – Angelo Mar 29 '12 at 8:10
  • $\begingroup$ Yes, that's correct. But the air won't immediately accelerate the helicopter to the same speed as the train. How fast the helicopter catches up with the train depends on how heavy it is. The usual toy helicopters are very light and will very quickly be moving at the same speed as the train. A real helicopter weighing several thousand kg wouldn't be accelerated fast enough to avoid hitting the rear of the compartment. $\endgroup$ – John Rennie Mar 29 '12 at 8:17
  • $\begingroup$ How about the speed of the train, will it affect the scene? I mean what about in bullet train? Will a very light helicopter toy stay at its place (relative to me) in high speed train? I really wanted to test this but we don't have the capability to do it. I hope someone can do it (or at least some kind of this scenario) and post it somewhere. :) $\endgroup$ – Angelo Mar 29 '12 at 9:04
  • $\begingroup$ The important thing is the acceleration of the train rather than it's speed, because it's when the train is accelerating that the helicopter feels the wind. Once the train has reached a steady speed the helicopter should settle down, and it doesn't matter how fast that speed is. I would guess that most trains accelerate at about the same rate regardless of their top speed, because excessive acceleration would risk spilling passengers drinks and/or knocking them off their feet. $\endgroup$ – John Rennie Mar 29 '12 at 10:55

In modern trains, with closed windows and doors, between carriages, the air in the carriage moves en block, much as it would in a plane, before or after pressurization, or a car, with windows closed, and no blowers on, or vents open. The air does not rush to one end of the carriage, leaving a partial vacuum at the other end. Since the helicopter is very light, and set to hover, at a fixed point in the air, its momentum change will be very small. I suspect there will be very little movement. You could try this using a Helium balloon. This could even be in a car, if the car has no air leaks. I am not sure if they would let you on a plane, with a Helium balloon, so will not suggest that!!!!!

There might be a small difference, since the helicopter is using energy to hold it in the air, at a set position, relative to the air.

Just my conclusion on a logical basis, have made no tests.

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    $\begingroup$ This is wrong, the accelerated train is not an inertial frame. So psuedoforces crop up. See JohnRennie's answer above. $\endgroup$ – Manishearth Mar 29 '12 at 16:25
  • $\begingroup$ I agree entirely with what JohnRennie's says, but to a lesser extent with regards to forces involved. Can you elaberate on "Psuedoforces crop up" please. Since the mass of the air and helicopter are so small relative to the trains mass, they can all be in there own inertial frames, but since they are moving at constant velocity with respect to each other, they can make up a set in one frame. The front of the carriage is accelerating at the same rate as the back of the carriage, so the air is moving at the same velocity, as the carriage. Frictional forces will hold the HC&air together nospace $\endgroup$ – Clive Ballard Mar 29 '12 at 19:31
  • $\begingroup$ Since the mass of the air and helicopter are so small relative to the trains mass, they can all be in there own inertial frames--> I don't see how this is true. so the air is moving at the same velocity --> Not when the train accelerates. The air will move slightly slower. In the carriage frame, we will feel a psuedoforce since it is noninertial, and the air will move along with the helicopter due to this psuedoforce. The air won't move much, due to frictional forces, but the copter will be pushed back. Ever been pressed against your chair when a train starts? $\endgroup$ – Manishearth Mar 30 '12 at 3:00
  • $\begingroup$ Thank you for your reply. I ran out of space with my previous comment,otherwise I would have added that the passengers could have their own inertial frames, but these cannot be added to the set, because in general there mass, will be significantly greater than that of the air or HC.Mass as related to inertia of a body can be defined by the formula F=ma Here F is force, m is mass, and a is acceleration. By this formula, the greater its mass, the less a body accelerates under given force. The body mass slows its acc'n with respect to the train. Friction overcomes any small lost acc'n in the HC $\endgroup$ – Clive Ballard Mar 30 '12 at 4:35
  • $\begingroup$ Newtons laws are only applicable in an inertial (non accelerating) frame. To apply Newton's laws to an accelerating frame, you must apply a "psuedoforce" $m_ia_{frame}$ to each body $i$ of mass $m_i$. Note that in this case, acceleration due to psuedoforce will be constant for every body and will be $a_{frame}$. This comes directly from inertia, in the accelerating frame, the body will try to remain at rest wrt the ground and will thus accelerate wrt the frame. Independant of its mass. $\endgroup$ – Manishearth Mar 30 '12 at 5:11

2:it will move backward relative to you and the train and bump to the rear part of the train

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    $\begingroup$ Hi & welcome to Physics.SE. This is not some kind of quiz. If you think you can clarify it in a better way, please try to add why do you think it's doing that ;-) $\endgroup$ – Waffle's Crazy Peanut Aug 18 '13 at 18:39

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