1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Terminal velocity in a vacuum?

  1. Sep 23, 2014 #1
    If an object is dropped in a hypothetical infinitely long vacuum tube, will it reach a terminal velocity? I assume that it must because according to Einstein, no object that has mass can travel at the speed of light. My guess would be that the terminal velocity of an object in a vacuum would depend on its mass. I suggest this because I imagine some parabolic graph to denote the effect of mass on terminal velocity within a vacuum; not just a simple "does it have mass or not". I am just a junior in high school and have no great knowledge of relativity, but I post this to simply gain knowledge that I was unable to acquire from my school as my physics teacher disregarded my question as "too advanced for the class to comprehend".
     
  2. jcsd
  3. Sep 23, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    That's actually true. Some people would say its because the object's mass increases as its speed increases and so it becomes harder and harder to accelerate it until a point that for any force, the acceleration is zero and there it stops increasing speed and so doesn't reach the speed of light.
    But I don't like relativistic mass(and I'm not alone in that), so I prefer to say that in special relativity, Newton's second law of motion is changed somehow that as the speed approaches the speed of light, the acceleration, for any force, approaches zero.
    These explanations are equivalent and it depends on you which one to accept.
     
  4. Sep 23, 2014 #3

    phinds

    User Avatar
    Gold Member
    2016 Award

    What makes an object travel faster and faster is a force applied to it. In the concept of "terminal velocity" we are talking about the force of gravity. It doesn't matter. Force is force. (Let's ignore for the moment the GR description of gravity as spacetime curvature since in this case, it has the same effect).

    Forces applied to one object to make it move faster relative to another object (and all motion is relative) are subject to, and you can Google this, "relativistic velocity addition", which is what keeps things with mass from going as fast as c.
     
  5. Sep 23, 2014 #4

    phinds

    User Avatar
    Gold Member
    2016 Award

    Uh ... no, it's not due to the object's mass, as the OP stated and you seem to be agreeing with. See my post above.
     
  6. Sep 23, 2014 #5
    Relativity does not really factor into the value of terminal velocity, unless you want to consider a very massive object onto which the object is dropped, and where the velocity of the object could become relativistic.

    An object "dropped" onto the earth would be able to achieve a calculable terminal velocity ( at impact with the earth the velocity would be maximum through a tube of vacuum ) no matter how far the object is placed from the earth. Drop the object onto the sun, or other larger masses, and the terminal velocity would be greater. Consider that space is mostly vacuum anyways, we really do not need a tube of vacuum, even if the sun or earth has an atmosphere surrounding it, as most of the increase in velocity will be accomplished in space if the object is sufficiently far away.
     
  7. Sep 23, 2014 #6

    ShayanJ

    User Avatar
    Gold Member

    I don't get it. Could you explain more clearly?

    Why not? How is it different from any other situations where we try to explain why things can't go at c or faster?
    And notice I said I don't accept relativistic mass and so don't use it for explaining what OP asked. I just mentioned it so that the OP knows about different views.
     
    Last edited: Sep 23, 2014
  8. Sep 23, 2014 #7

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    That doesn't make any sense. If the OP asks about relativistic limits of free fall under gravity, you have to use GR. SR is not compatible with Newtonian gravity.
     
  9. Sep 23, 2014 #8

    phinds

    User Avatar
    Gold Member
    2016 Award

    OK, I agree, but are you going to contend that an object travels faster that c? The point I was making was that Einstein Velocity Addition applies. I didn't want to get into a discussion of whether or not gravity is a force or a curvature of spacetime since the end result is the same.
     
  10. Sep 23, 2014 #9

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Not in a local inertial frame.

    How exactly?
     
  11. Sep 23, 2014 #10

    phinds

    User Avatar
    Gold Member
    2016 Award

    I guess I don't know, I'm just confident that you can't exceed c.

    I do know that the acceleration due to gravity at the EH of a BH is c, which is why even light can't escape, so it would seem that the acceleration inside the EH would be even more, but what I have read is that inside the EH, things become time-like instead of space-like so that seems to be the difference. Still, I don't think that applies here.

    What's your explanation?
     
  12. Sep 23, 2014 #11

    phinds

    User Avatar
    Gold Member
    2016 Award

    I thought about this after logging off last night and realized that the whole discussion is moot anyway. "Terminal velocity" in the sense being discussed here is a ballistic velocity. Take an airless huge planet, oven a solar mass planet (but not a black hole) and shoot a gun directly away from the center of mass of the object. The terminal velocity of any object falling back is the same as the escape velocity of the bullet, even if that velocity is an appreciable fraction of c (that is, a "relativistic velocity") but it is not possible for a bullet to reach c, so it is not possible for a free falling object to reach c (again, ignoring black holes)

    EDIT: OOPS .. I didn't see 256bits post. He beat me to it.
     
  13. Sep 23, 2014 #12
    Infinitely long means anything that could affect the object is infinitely far away from it, thus exerting no influence on the object, hence the object's velocity won't change at all.

    If you still want the object to be subject to something affecting its velocity in the infinitely long tube, you will need to specify exactly what influence it is.
     
  14. Sep 23, 2014 #13

    russ_watters

    User Avatar

    Staff: Mentor

    It is a bit disappointing that no one gave the correct answer, but instead people got distracted by the possibility of Relativity playing a role. Relativity doesn't apply here except if the object falling toward is really massive and dense (like a black hole).

    The object falling accelerates until impact, reaching a specific speed: escape speed (velocity).
     
  15. Sep 23, 2014 #14

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    The OP explicitly asks about the limits due to Relativity

    And what is the maximally possible escape speed, according to Newton?
     
  16. Sep 23, 2014 #15

    russ_watters

    User Avatar

    Staff: Mentor

    Yes; that was his guess at an answer. It wasn't going down the right path.
    Depends: are we talking about real objects(among other framing issues)? I think we should be. But either way, "escape speed" is the core issue here, not relativity's limit on escape speed.
     
  17. Sep 23, 2014 #16

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    All objects consistent with Newtonian mechanics. Also note that nothing in the OP states that the fall ends at the surface of a spherical mass.
     
  18. Sep 23, 2014 #17

    russ_watters

    User Avatar

    Staff: Mentor

    Then there is an additional potentional framing issue with the op in that s/he may be trying to say the object falls for an infinite distance. But eventually you have to hit what you are falling toward.

    Fixing the framing (implied or not) of the question is an important part of answering it.
     
  19. Sep 23, 2014 #18

    Doug Huffman

    User Avatar
    Gold Member

    An infinitely long tube has as much mass in front as behind and no net gravitational attraction. OP mistakes the size of infinite.
     
  20. Sep 23, 2014 #19

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Not if it has a hole. So is there anything in Newtonian mechanics, that restricts escape speeds to a finite value?
     
  21. Sep 23, 2014 #20

    russ_watters

    User Avatar

    Staff: Mentor

    That's enough with the games, A.T.

    This is the OP's thread and regardless of where he wants to go with it AFTER learning how escape speed works, the point is that none of those other potential alternate scenarios can be discussed until AFTER escape velocity is introduced.

    At this point it would be best if we allow the OP to catch up and see where he wants to go.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Terminal velocity in a vacuum?
  1. Terminal velocity (Replies: 9)

Loading...