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Motion question

  1. Aug 18, 2004 #1
    Well guess what, I'm confused again....

    OK. Subject A is in a train which is moving eastbound along a track. If A throws a ball straight up into the air, it comes straight down as expected into his/her hands rather than landing behind (westbound of A), because the train and the air in it are all moving along at the same pace.

    Now, if A starts running backwards (westbound) towards the back end of the train at the exact speed of the train moving eastbound, then to an observer on the platform outside the train, A would be staying in the same place, and would be able to wave, and even have a conversation through the window if desired with the outside observer. Right?

    Now, lets say the train were much larger, and moving much faster, say at 200 km/ph eastbound, and it happened to be a very long train. Imagine a helicopter (A) sitting inside of the train. This helicopter (A) could take off straight up (still inside the train moving eastbound) and hover, without any forward or reverse motion relative to observers on the train.

    Now, to go back to the first analogy, if A gradually started to fly back towards the end of the train (westbound), gradually accelerating until it was finally also travelling @ 200 km / h, only in the opposite direction, then an outside observer on a platform could hypothetically be watching the helicopter "hover - stay in one place" inside the train moving eastbound directly in front of them, even though in relation to the inside environment of the train, the helicopter would be moving at 200 km/ph westbound. Same as someone running, only faster. - Makes sense, right?

    OK - Question time - Lets say that the train was not a regular train (we know this already due to it's enormous size of course), but that it had a completely open back.

    So what happens when the A runs out of train, that is arrives at the end of it's environment? Once the train were gone would it stay there hovering in line with the observer, drop suddenly to the ground, or take off directly westbound at 200km/h, or perhaps at another speed?

    A had a lot of (westbound) motion relative to it's environment while it was in the train, so if that environment suddenly dissapears what happens?

    Thanks for your feedback as always -

  2. jcsd
  3. Aug 19, 2004 #2


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    Fine. When A releases the ball (straight up as far as he is concerned), it has the same horizontal velocity w.r.t. the ground as A does. If nothing accelerates it in the horizontal direction (like in your proposed problem here) it will continue to have the same horizontal velocity w.r.t. the ground, meaning it has zero relative velocity to the thrower (A).

    Right, except for the window part; all of the windows are flying by between the two of them. I think you get that part: A is stationary w.r.t. the ground but is moving w.r.t. the train (with relative speed= twice the speed of the train).

    Well, once the helicopter takes off, it's no longer connected to the train. If it's just hovering, it will remain stationary w.r.t. the ground, not the train.

    Ok I guess, except for my last objection about the helicopter. So at this point, you've defined:

    vT/G = +200
    vA/G = 0
    vA/T = -200

    where + is eastbound, - is westbound, A is the helicopter, G is the ground, T is the train, and the subscript order x/y means of x with respect to y.

    What's changed in the situation? Not much as far as the helicopter is concerned. vA/G = 0 is still true. The train velocities are either undefined (if the train vanished or blew up or somehow ceased to exist) or 0 if the train has stopped somewhere. I hope that helps.
  4. Aug 19, 2004 #3
    "Well, once the helicopter takes off, it's no longer connected to the train. If it's just hovering, it will remain stationary w.r.t. the ground, not the train."

    Thanks for your response James, everything makes sense to me except this line. In my mind I picture the hovering helicopter remaining stationary wrt the train. Picture me sitting on a train with a remote control helicopter. If I fly the helicopter into the air, it floats around the train comfortably with respect to it's environment even though it is not "touching" anything, because it is touching the air which is moving at 200 km / h. I would not need to fly the toy helicopter forwards @ 200 km /h to avoid it smashing into the back end of the train, so wouldn't that be the same story for a larger helicopter in a larger train?
  5. Aug 19, 2004 #4
    If the helicopter is hovering inside the train, then its has the same velocity as the train does when viewed from the outside person, however, if the helicopter is hovering OUTSIDE the train relative to the earth, than if you were to look down from that helicopter, you would see this train whiz past you at 200km/hr. So a person on the ground would just see this helicopter hovering, meanwhile some accela train flys underneath it at 200km/hr. Now i think from what your saying is what if the helicopter were flying inside the train, but looked statioinary to an outside person. Since the air inside the train is not flying out the back, as you observed, you with your remote control, would have to make that helicopter fly 200 mph away from you in the opposite direction of the train. In other words, you would open all the doors to the cars behind you, and fly your helictoper through them at the exact same speed, but opposite direction the train is traveling in. Once it reaches the end of the train, you can make stop it from having any velcoity. You would cut the throttle immediatly, and let it just hover there the instant it left the train. The reason is that as long as its inside the train, it will move with the same speed as the train relative to the ground. The moment it runs out of train, its just going to go 200km/hr backwards, since it does not have that 200km/hr forward speed of the train to cancel it out. Hope that helps.
  6. Aug 19, 2004 #5
    Take the observer on the gorund as the reference frame first.
    While the helicopter is "hovering" inside the train, the train is moving forward at 200 km/h, and the air is also moving 200 km/h forward. If you draw the free-body force diagram, you will realize that the helicopter depends on pushing the air to move forward. So, once the helicopter gets out of the train, it will meet with air that no longer moving at 200 km/h forward. So, pushing on this air, the helicopter will move backward and reach a terminal velocity of 200 km/h some time. If you want the helicopter to stop, you must have it stop the exact moment it leaves the train, and then let it drop onto the ground vertically.
  7. Aug 19, 2004 #6
    I don't want the helicpoter to do anything in particular. My question is just this - If it was flying along at it's speed opposite to the motion of the train, and the environment of the train suddenly disappeared, what would the helicopter do?
  8. Aug 20, 2004 #7


    Edited: :eek: I read the word pace as path before and wrote something.
    I appologise and have edited it.

    Unless and other wise A is given some force he\she can’t move forwards because of inertia.
    So it will stay at that point in relative to the train and in relative to the observer standing on a plat form. So, you are right.

    Once the helicopter took off and started to accelerate the observer on a plat form will see that the helicopter is moving not hovering in the specific point. Let us say when the helicopter reaches at the back end of the train it’s speed becomes 200. Then, if the back end is completely opened the helicopter will move in that direction with constant speed.
    If the back end is closed once the helicopter reaches the end with a speed of 200. It will explode inside!!!!!

    That’s all
    If you have a question, you are welcome.
    Last edited: Aug 20, 2004
  9. Aug 20, 2004 #8


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    The key to your question is in the phrase "the environment of the train". If the air inside the train was moving at 200 khp, and the chopper went 200 kph (indicated airspeed) the other way to keep stationary to an outside observer, then when it reaches the end of the train, and finds itself suddenly "outdoors", the air against which it had been pushing would now be gone somewhat abrubtly. I say "somewhat" because the chaneg in wind would not be instantaneous, as the air behind the train is being sucked along by the train's passing but, once the train has passed and there are no longer walss and floor and ceiling to keep the air moving, it will come to rest (relative to the observer on the platform) fairly quickly.

    For the chopper pilot, this will be like getting a sudden gust of 200 kph tailwind, and he will experience rather drastic acceleration. To the observer on the platform, the helicopter will appear to LURCH suddenly and take off to the west (if the controll settings were left as-is).
  10. Aug 20, 2004 #9


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    LOL "LURCH"...good explanation. This makes perfect sense to me. Just to clarify though...does that mean that based on all of the preceding discussion, this statement...

    ...is incorrect?

    I think it is incorrect, because if I let go of a book while in the railway car, it doesn't fly backwards...it retains the same forward velocity that I (and everything else in the cabin) had, and is therefore stationary w.r.t the train, not the ground. Same with a small helicopter that you launch and have hover...its forward velocity w.r.t outside observer is that of the train's. Inside the cabin, it appears stationary w.r.t. the cabin (and therefore the air in it).
    Last edited: Aug 20, 2004
  11. Aug 20, 2004 #10


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    I'll admit I'm probably wrong. My thinking was that the helicopter has its own independent control system and flies how it wants to fly regardless of how some train moving under it, but not connected to it, moves. That's why I did not consider it analagous to a projectile, like the thrown ball or the dropped book. Just ignore my statements; sorry for adding to any confusion.
  12. Aug 21, 2004 #11


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    Oh hey...no worries. I'm sorry I put you on the spot. I only intended to make sure I was understanding things properly. I guess that's what the discussion's all about.
  13. Aug 21, 2004 #12
    I don't want the helicpoter to do anything in particular. My question is just this - If it was flying along at it's speed opposite to the motion of the train, and the environment of the train suddenly disappeared, what would the helicopter do?

    Like said before, if the train suddenly dissapears, there is no forward velocity of 200km/hr to cancel out the rearwards velocity of the helictoper, so if it suddenly dissapears it will just shoot off at 200km/hr to the left when viewed by an observer on the ground. This is because it had to move 200km/hr to the left, to cancel out the train moving 200km/hr to the right, but now that you have eliminated the train, the system is no longer balanced at zero.
  14. Aug 21, 2004 #13

    Doc Al

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    The only thing affecting the helicopter's motion is the air that supports it. Nothing happens to the air when the flatcar train passes by. For the helicopter to hover it moves with a speed of zero with respect to the air (and ground).

    And if a second train were moving alongside at twice the speed, the helicopter would have twice as much relative motion with respect to it. So what? All that matters to the helicopter is what happens to the air that supports it.
  15. Aug 21, 2004 #14
    For the helicopter to remain over a fixed point on earth realtive to the moving train as you suggest it has to have its rotor angled foward (or to the rear of the train). Now when it flys out of the rear of the train it is hovering in relation to the earth but it still has its rotor angled to the west. The helicopter now accelerates in a westerly direction until its wind speed is equal to what it was in relation to the train.
  16. Aug 21, 2004 #15

    Doc Al

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    "open back" causing confusion?

    In Sidewalk's original post he specifically mentions an "open back" train. If I interpret this to mean a flat car, then the helicopter's speed has no causal relation to the speed of the train, since the train does not carry the air along with it.

    But if he meant that the car is closed (thus bringing along its own air) except for an open door at the rear, then things are different. As several have explained, the helicopter must push against the moving car air (to counter drag) to maintain an apparent speed of zero with respect to the ground. As Lurch (and others) explains, when the helicopter "runs out of train" it will lurch forward (to the west) with respect to the earth.

    I'm guessing that the variety of answers hinge on the ambiguity of "open back". :smile:
  17. Aug 23, 2004 #16
    Thanks Doc

    Yup, you're right. I meant a closed car train just like a regular train car, only with no back, so the helicopter wouldn't explode and smash into it once it arrived.

    So it sounds to me like we've established that the helicopter, upon exiting the train environment would suddenly move from 0 km/h (with respect to the outside environment like the platform and the observer), to 200 km/h.

    Wouldn't this be exceedingly and unusually bizarre to watch standing on the platform? Not to mention from the perspective of the helicopter pilot - For him it would appear (if he were looking outside the train) that he had in a split second jumped from 0 to 200 km/h.

    I assume there would be no G forces etc on the pilot, and that as he was going 200 kmh wrt the train, and then 200 kmh wrt the ground the effect would just be a visual illusion?

    Still, this is pretty weird to me. Would the acceleration appear gradual, or instantaneous ?

    Thanks to all who've responded, apologies if I was a little unclear...

  18. Aug 23, 2004 #17


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    I haven't been following this thread but a helicopter would NOT suddenly go from 0 to 200 mph relative to ONE frame of reference. The helicopter will have one speed relative to the ground, irrespective of whether it is "inside" the train or not.

    If I understand what you have been saying, the train is moving at 200 mph relative to the ground. The helicopter takes off, straight up, inside the train (which boggles my mind, incidently!) and hovers, relative to the train. Okay, the helicopter is now going at 0 mph relative to the train and, therefore, 200 mph relative to the ground. Now, the helicopter accelerates toward the back of the train, eventually going at 200 mph RELATIVE TO THE TRAIN towards the back of the train. The helicopter is now going at 0 mph relative to the ground. Keeping all other things the same, when the helicopter exits the train, it will still be going at 0 mph relative to the ground.
    Now, there are complications, due to that ridiculous image of a helicopter hovering or flying at 200 mph INSIDE a train! The helicopter is moving on the air. Is the air inside the train moving relative to the train or the ground? What happens to the AIR after it exits the back of the train. If you ignore the problem of what happens to the air that is supporting the helicopter THEN you get the situation in the previous paragraph. If not, then you have to specify exactly how the AIR is moving through the train in order for your question to make sense.
  19. Aug 23, 2004 #18
    The air

    Halls of Ivy: First of all, I do think I'm wrong, cause it doesn't make sense to me either, but I'm not sure why, and this is how I picture it.

    First of all, in order to lose the ridiculous image of this helicopter in a train, either picture the train as being MUCH larger, like a moving warehouse on a track, or picture the helicopter being much smaller, like a powerful radio controlled sized helicopter.

    Anyhow....I would say that the air inside the train is moving along with the train @ 200 km/h, and the air outside the train is not moving with the train. Correct?

    So, the helicopter is moving the other way @ 200 km /h with respect to the train and the people on it, and the air it is slicing through, and therefore "hovering" at O km/h with respect to the ground, and the air outside the train and the people on the platform.

    Moments before it gets to the end of the train, it's still flying through air moving towards it @ 200 km/h, and then upon exiting the open back it immediately encounters air which is no longer doing so.

    I think (although it does sound wrong from a logic perspecitve) that the helicopter would immediately go from 0 to 200 from the frame of reference of the observer on the platform.

    I know you disagree, but the helicopter's speedometer was at 200 km/h a split second before it left the train, so it can't suddenly be hovering there the moment it exits?

    I'm sure you're right, but I still don't know why. Please feel free to explain further if you're not already completely sick of this bizarre hypothetical scenario...

  20. Aug 23, 2004 #19
    Actually as stated a few times, the helicopter upon leaving the confinements of the train would appear to hover for an instant (or maybe even be pushed back somewhat by the drafting wind). It would then begin to accelerate in the direction going away from the train (because its rotors are still pitched in a direction that gives it foward momentum) not instantly from 0 to 200 but much as it would accelerate from a hovering position any other time.
  21. Aug 23, 2004 #20

    Doc Al

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    Whoa.... I never said that! What will happen is that the helicopter will lurch forward. Why? Because it's entering still air with its rotors at full tilt. So the helicopter will accelerate forward.

    The helicopter will not go from 0 to 200 in a split second. For the pilot it would feel like he just slammed on the gas.

    The pilot and helicopter will be accelerated until equilibrium is reached. What visual illusion? From the viewpoint of someone on the ground the helicopter starts from rest and accelerates (at some rate).

    Assuming a simple-minded model of flight, I would say that the helicopter would start off with maximum acceleration; that acceleration will then decrease to zero as the helicopter speed approached 200 km/h and drag increased.
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