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Terminal Velocity in a bottomless vacuum

  1. Nov 19, 2003 #1
    How would you calculate the terminal velocity of a massive object falling through a bottomless vacuum?

    As nothing can go faster than the speed of light the object must have a terminal velocity also due to E=mc^2, and A=F/M....

    I am just wondering if you can calculate the terminal velocity from the objects static mass.
     
  2. jcsd
  3. Nov 19, 2003 #2
    sorry I should have added, with a constant force acting on the object, like g on earth...

    :smile:
     
  4. Nov 19, 2003 #3

    NateTG

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    Well, gravity isn't constant on the surface of earth, just close to constant.

    In Newtonian mechanics, the object goes faster and faster forever.

    In Special Relativity, if the force is constant, the mass that the object gains through kinetic energy will decrease the acceleration preventing it from ever getting to c.

    In General Relativity (which I'm not familiar with) it might be possible to demonstrate that a constant acceleration (not constant force) path like that leads into a black hole.

    For more information, you should look into information on particle accelerators.
     
  5. Nov 19, 2003 #4
    Thanks, Yep I understand special relativty, however I was wondering if there was a formula for calculting what the terminal velocity would be, If you know the constant force accelarating the object and the static mass of the object...

    Here is the senario I have conjered up:

    An object of know mass, has a solar powered engine of knowen mass attached to it and has a thrust of know quanity applied to the system when knowing the total mass of the system could you cacluate the terminal velocity in a vacuum....

    :)
     
  6. Nov 19, 2003 #5

    HallsofIvy

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    There is no terminal velocity in the sense of a velocity which the object reaches after a finite time.

    The objects velocity approaches c as a limit.

    If you wanted to calculate the velocity as a function of time, you would have to specify the force as a function of time.
     
  7. Nov 19, 2003 #6
    Force as a function of time, is this not power.... or am I missing the point...
     
  8. Nov 19, 2003 #7
    Sorry I am not with you 100%... How can the velocity approach C if the mass increase as the KE increases, surely there must be a point where the mass approaches inifite and therefore the accel. becomes 0 if you are applying a constant force (a=f/m)....

    can you explain what you said with a little more depth?

    thx
     
  9. Nov 19, 2003 #8

    russ_watters

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    Yes, I think you missed the point - Hurkyl gave you the answer: C.

    And power is force times distance times time.
     
  10. Nov 19, 2003 #9

    jcsd

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    What Hall of Ivy means is that you have to specify f(t) = F, though looking at your first post you have specified F = k, where k is a constant.

    From your point of view you would just keep on accelrating under this force, as after all it is a constant force, but if we take an observer who was in your rest frame when the force was applied he would view your velocity appraoching c as time approaches infinity.
     
  11. Nov 19, 2003 #10
    by K you mean Kinetic energy, well if my velocity increase how can K be constant...

    Forgive me if I am coming over as stupid :)
     
  12. Nov 19, 2003 #11

    krab

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    Russ: Power is force times distance over time, or Force times velocity.
     
  13. Nov 19, 2003 #12

    jcsd

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    I just used k as a generic constant, i.e. the force is always constant and always equal to some fixed value k
     
  14. Nov 19, 2003 #13
    ok let me rephraze my initial post, I was looking for a solution to a riddle which I thought you could do this way but obviously not exactly (I am sure by approximizing you could) The initial Riddle I was asked was,

    "How would you "weight" a plane without scales?" If you can think of any other way you could do this I would be much obliged...

    thx
     
  15. Nov 19, 2003 #14
    I do know that the terminal velocity would not be c. The object would continue to accelerate until the downward acceleration force balanced out with the increase in mass due to special relativity (I might not have phrased that clearly, but hopefully someone will understand). I don't have the skills to do the math, but I'm sure someone on this site does.
     
  16. Nov 19, 2003 #15

    NateTG

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    How about mass spectrometry?
     
  17. Nov 20, 2003 #16

    russ_watters

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    Oops. I do that sometimes.
     
  18. Nov 21, 2003 #17
    Good idea!! :)
     
  19. Nov 22, 2003 #18

    Haelfix

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    Without probing the plane with gravity (eg a scale or some sort) you would have to use EM forces to probe the exact mass.

    Eg count all the constituent particles, go ot the rest frame, add up the energies presto mass.

    You can do it with gravity too, for instance, measure the curvature of space that the plane induces on the metric. Eg, measure light deviation the plane causes.
     
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