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Acceleration in a closed box.

  1. Mar 9, 2013 #1
    It's said that it is not possible to tell the difference between acceleration of objects within a closed box and acceleration due to gravity.
    Is this allways the case.Does the acceleration of objects within a closed box act uniformly or does this depend on the gradual acceleration of the objects.
    In other words if objects of different mass within the box are subjected to a violent or sudden acceleration will they still react as if they were in a gravitational field.
  2. jcsd
  3. Mar 9, 2013 #2
    Yes, this is always the case.

    Yes, it will feel like you fell on the ground, or jumped off a building, etc.
  4. Mar 9, 2013 #3


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    Yes, locally, it is impossible to distinguish between motion of an object because the closed box is accelerating, constantly around an object or the object is acted on by a "gravitational" force. Since the acceleration is constant, I do not know what you mean by "gradual" or "sudden".
  5. Mar 9, 2013 #4
    What do you mean by "locally"?
  6. Mar 9, 2013 #5
    In Gravity, if you build a tower and climb up, you will find up there that the force of gravity is less as you get further from the surface of the Earth. In a closed space, this doesn't happen, and you would know you are not in gravity (or that you just haven't climbed far enough up to detect the difference). In Gravity, if you drop a plumb line, and then if you move off along the floor some distance and do it again, you will find that that these two plumb lines are not pointing in the same precise direction, since both are pointing toward the center of the earth. In your accelerating room, this doesn't happen. The plumb lines should be completely parallel.
  7. Mar 9, 2013 #6
    Essentially, in the box.
  8. Mar 9, 2013 #7
    By gradual I mean a slow or steady constant acceleration.
    Sudden acceleration would be caused by a violent or explosive acceleration.
    Say you had a bowling ball and a pool ball side by side within the box and there was an explosive force underneath the box which propelled it upwards.
    Presumeing the floor of the box was able to withstand the propellant force, would the bowling ball being more massive than the pool ball make more of an indenture in the floor and therefore take off from the floor at a slower speed than the pool ball.
    If the pool ball and the bowling ball were just released at the same time in a gravity field they would fall at the same rate.
  9. Mar 9, 2013 #8


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    Depends on details of the floor.
    You are considering the situation after they bounced on the floor? Probably, but that is exactly the same in a gravitational field then.
    That is true in the accelerated box, too. It is even more obvious there, as the balls stay at rest (and at the same relative position), while the box accelerates.
  10. Mar 9, 2013 #9

    It seems to me you have a fairly common misconception regarding gravity and acceleration.

    The problem is that the proposed experiment is from the start not valid if it sets out to compare gravity from a source point acting radially (in all directions) and a force of acceleration which is acting in parallel.

    The reason gravity (usually) falls off with distance is due to the fact that it is originated from a spherical body, not because of the inherent nature of gravity. It has to do with the nature of 3-dimensionality, not the nature of gravity. You can calculate the gravitational flux within a closed surface, but at a greater distance from the source the area is greater and with the same amount of flux there is less flux per area.

    A couple of ways you could make the experiment valid would be…

    You can make the gravitational lines be parallel so that they match the parallel acceleration of the “elevator”. You could do that by using a rectangular plate for your gravitational source instead of a sphere.

    If you wish to keep that spherical gravitational source, you could also make the adjustment on the acceleration side of the experiment if you could construct it so that the “lines of acceleration” extend radially such that they match the spherical gravitation.
  11. Mar 9, 2013 #10
    Not sure if it does, unless it's made of unobtanium.Perfect rigid bodies not allowed.
    Trying not too. I am considering the situation as the box starts to accelerate and causes a bounce.
    That's not the case I am describeing It might be if it's a slow acceleration but maybe it's not true when objects are accelerated quickly.
    It might also be not be true when objects are accelerated slowly but not obviouse.
  12. Mar 9, 2013 #11
    The plumb lines not pointing in parallel might be a tidal effect. Which in this situation is usualy acceptable.
  13. Mar 9, 2013 #12
    MFB addressed this, but please allow me to reiterate.

    If there is an indentation on the floor due to the bowling ball, it is due only to the nature of the floor and the bowling ball. There will be no difference between the cases of gravity or acceleration. The dent in the floor will be the same in both cases.

    The speed of acceleration will also be the same in both cases, assuming you have set up your experiment to withstand the forces you are putting on it without breaking your experiment.

    Yes, and in an acceleration field they would hang motionless for the same amount of time as that of the freefall time in the gravitational field (until the accelerated floor catches up with them). Again the situation is exactly the same in both cases.
  14. Mar 9, 2013 #13
    That's right.
  15. Mar 9, 2013 #14
    It is an example where not keeping your tests sufficiently local reveals which situation you are in.
  16. Mar 9, 2013 #15
    Well yes I was assuming that generally when comparing gravity with accelerated box, the comparison is done between the accelerating box vs earth's (or some other planet's) surface. The nature of gravity (nearly always encountered and thought-experimented on) is in the context of a sphere. It won't remain constant.
  17. Mar 10, 2013 #16
    No it can't be the dent on the floor will be variable because you won't be able to maintain both the speed of acceleration in the experiment (which will vary stop start etc,) to that caused by gravity.
  18. Mar 10, 2013 #17


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  19. Mar 10, 2013 #18


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    Yes, this always the case, as long as:
    1) the acceleration of the closed box is constant
    2) the closed box is small enough that tidal forces and other large-scale gravitational effects cannot be observed.
  20. Mar 10, 2013 #19


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    Here's a bit more...



    Well, this is a 108 page pdf... I guess that's a bit more, than a bit more... :wink:


  21. Mar 10, 2013 #20
    Understood. The gravitational effect is the weakest force and is normally only a concern regarding celestial bodies.

    The problem is that confusion often arises with regards to the equivalence principle. Based on your original post, that seems to be at the heart of the disscussion here. That’s where care must be taken to insure that a proper comparison is made. The deeper meaning behind the equivalence principle is completely lost if confusion arises due to misunderstandings of tidal forces or the inverse square law.

    Didn’t mean any disrespect. Cheers.
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