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Physical Effects of ball moving at 0.9c

  1. Jul 21, 2012 #1

    cepheid

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    I only just discovered this today:

    http://what-if.xkcd.com/1/

    I didn't know about it before. My question is simple: what do you think of Randall's analysis of the physics here? Is he "on the ball?"
     
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  3. Jul 21, 2012 #2

    ghwellsjr

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    It starts off with magic to accelerate the baseball to 0.9c. Take away the magic and you realize you need a tremendous source of energy to get the ball up to that speed. Just think of the effort it takes to get individual particles up to that speed and you'll see that the explosion happens long before the ball even gets started.

    But it's a fun read.
     
  4. Jul 21, 2012 #3

    cepheid

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    Yeah I understand that it takes a tremendous amount of kinetic energy to get a particle to 0.9c, let alone a macroscopic object.

    My question is if the *consequences* described are accurate. Nuclear fusion etc
     
  5. Jul 21, 2012 #4

    ghwellsjr

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    I would think so, since that is one of the things they do with particle accelerators, which is the reason they do it in vacuum. It would be a little fairer if they placed the experiment on the Moon and had astronauts in space suits so that the ball could actually travel some distance undisturbed. The article points out that the hitter would have very little time to react to the sight of the approaching ball. Of course, normal reaction times would make it impossible for him to swing the bat in time but if he anticipated the "pitch" and got the bat in place for the collision, then it would be a similar explosion.
     
    Last edited: Jul 21, 2012
  6. Jul 21, 2012 #5

    HallsofIvy

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    I believe the whole thing was meant humorously.
     
  7. Jul 21, 2012 #6

    cepheid

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    The questions being asked may not be very serious, but the point of the site certainly seems to be to use real physics to treat these frivolous topics, as accurately as possible:

    TpLLX.png
     
  8. Jul 21, 2012 #7

    pervect

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    I wasn't particularly convinced by the claims of "fusion". What's supposed to be fusing with what to yield what product, exactly? And why fusion, rather than fission?

    I really don't have much intuition as to what happens if you bombard a baseball with .9c oxygen and nitrogen ions - and I don't think the author of the cartoons really knows either :-(. If he does, he didn't document it convincingly.

    In some sense, these are minor quibbles. The major energy input into the system is going to be the magic that accelerates the ball to .9c. And you can pretty much guess that the result is going to be a big nuclear-style fireball when that energy is released. Showers of various particles, ionizing radiation, and fireballs of the sort typically associated with nuclear weapons all seem to me to be reasonable predictions.
     
    Last edited: Jul 21, 2012
  9. Jul 21, 2012 #8

    PeterDonis

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    Given the types of atoms in the air and the ball (mostly hydrogen, carbon, nitrogen, and oxygen), it would seem that fusion reactions are overwhelmingly more likely than fission reactions, if nuclear reactions are taking place at all.

    As far as whether nuclear reactions would actually take place, the kinetic energy of the baseball at speed 0.9c corresponds to a temperature of about a trillion degrees, far higher than what is required to overcome Coulomb repulsion and allow nuclei to get close enough to each other to fuse. However, xkcd's analysis did leave out one key point: a trillion degrees may actually be too *high* a temperature for many fusion reactions to occur at significant rates (basically, the nuclei fly past each other too fast to stick together).
     
  10. Jul 21, 2012 #9
    Well the real question is which of the consequences are dominant, for example if i threw a ball at some mundane speed, 4m/s, the electrons inside are moving with respect to the batter, hence he should in principal feel a magnetic force.
    But as we know, such forces are tiny and unmeasurable, same concepts are present in this scenario. Now a few things come to mind.

    First is that the the space-time around the ball would be severely curved due to the energy-momentum of the ball, thus making everything after that uncertain as we do not understand physics in this scenario. Some very strange things happen when you have energy densities like that, some very very strange things.
     
  11. Jul 22, 2012 #10

    DaveC426913

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    ... and the protons ...
    ...no net force.

    :smile:
     
  12. Jul 22, 2012 #11
    i doubt you could find a baseball, or anything macroscopic that is perfectly neutral
     
  13. Jul 22, 2012 #12

    OmCheeto

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    I saw this on the 10th and posted in Random Thoughts.
    (I don't have time to start a thread and discuss or analyze such things)

    Then I noticed someone had already started another thread earlier in the day.

    Interesting problem.

    Perhaps we should call up CERN and get them to accelerate a single nitrogen nucleus to .9c and smash it into a baseball and see what happens.

    We can interpolate from there.

    This isn't just an interesting problem, this is a fun problem. :smile:
     
  14. Jul 22, 2012 #13

    PeterDonis

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    No, it wouldn't. Even if we leave out various subtleties in attributing "extra" spacetime curvature due to the ball's motion (briefly, curvature is not frame-dependent, but the ball's kinetic energy is), the relativistic gamma factor at 0.9c is a little more than 2, so the ball's total energy is a little more than twice the energy equivalent of its rest mass. The curvature due to the ball's rest mass (given the ball's volume) is negligible; a little more than twice negligible is still negligible.
     
  15. Jul 22, 2012 #14

    pervect

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    I'm sure collisions at much higher speeds have been done, for instance in the relativistic heavy ion collider (RHIC). No idea of what the results are though.
     
  16. Jul 22, 2012 #15

    OmCheeto

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    I was trying to comprehend a paper last night, but it's been so long since I've studied particle physics, I don't remember how to convert Gev's to velocity. :cry:

    hmmm... Can the breaking up of atomic nuclei with a particle accelerator be referred to as "fission"?

    ps. I just found some equations on an old thread, but when I did the math, v came out to be zero. Naprawde, ja nic nie wiem.... :frown:
    Wait! I think I've figured out where I went wrong. :smile:
     
  17. Jul 22, 2012 #16

    PAllen

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    To underscore that this is the main point: in some, fairly short, distance, the KE of the ball will be dissipated. The amount of that KE (at gamma a little over 2 for .9c) is (assuming standard weight of baseball, 145+/-5 grams) is about 150 times the energy released by the Nagasiki nuclear bomb, or about the same as 3 megaton H bomb. This is without even considering possible fusion.
     
  18. Jul 22, 2012 #17

    pervect

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    I was thinking about this some more, and my best guess goes something like this. It seems pretty obvious that the incoming atoms would quickly ionize. Then you'd probably have some sort of rutherford scattering pinball going on as the heavy nitrogen nucleus (you'd have the usual assortment of elements, the majority would be nitrogen though) bounces around. I don't know if you'd need relatistic corrections to the Rutherford formula or not, you might. Exactly how much stuff gets knocked out of the baseball per incoming ion isn't at all clear, but I would guess you'd get more than one atom knocked out per incoming atom. There'd be a lot of ionizing radiation - ions recombining with electrons, Bhremsstrauling from various disturbed electrons, etc. I could imagine the occasional nuclear event happening, but I'm not sure how often.

    It'd be interesting to work out how many atoms there are in the baseball, and how many air atoms are in the path. If we could guess how many atoms got knocked out by the assumed Rutherford pinball per incomming atom, we could get a handle on how long before the baseball was totally disintegrated by that process.
     
    Last edited: Jul 22, 2012
  19. Jul 22, 2012 #18

    PeterDonis

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    These are pretty easy to estimate, at least to order of magnitude:

    Atoms in the baseball: average molecular weight around 10 (assuming mostly hydrogen, carbon, nitrogen, and oxygen, but hydrogen atoms will predominate because most atoms of the other types will have at least one and maybe more hydrogens attached). So 145 grams of baseball is about 14 moles, or about 14 times Avogadro's number of atoms. That works out to about 10^25 atoms.

    Air atoms in the path: the number we really want here is air atoms per second encountered by the baseball as it flies. A mole of gas at STP takes up 22.4 liters or 0.0224 cubic meters, or about 3 x 10^25 atoms per cubic meter. The standard diameter of a baseball is (on average) 7.4 cm, for a radius of 0.037 meters; so it sweeps out 0.9 x 3 x 10^8 m/s * pi * (3.7 x 10^-2)^2 m^2 = about 6 x 10^4 m^3/s. Multiplying this by 3 x 10^25 atoms per cubic meter gives about 2 x 10^30 atoms per second encountered.

    So if the number of baseball atoms disintegrated per air atom encountered is anything close to unity, the baseball will disintegrate in a fraction of a second.
     
  20. Jul 22, 2012 #19

    PAllen

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    But given its speed, a second is a long time. However, I get about 10^-7 seconds from pitcher to home plate, which is still order 10^23 atoms encountered. This is still enough, I think, to suggest it is mostly disintegrated by home plate, and that most of the 'magically appearing' KE has been released. With or without fusion, the mushroom cloud image looks not far off.
     
  21. Jul 22, 2012 #20

    PeterDonis

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    If each atom encountered causes approximately 1 baseball atom to disintegrate, then about 1% of the baseball atoms will be disintegrated when it reaches home plate. That's enough to be noticeable, certainly, but not necessarily enough to call the baseball "mostly disintegrated". If the baseball was just traveling through air, it would take about 100 times the distance to home plate to disintegrate every atom at this rate.

    Of course, if the baseball encounters any solid objects, that will drastically increase the rate of disintegration, since solid densities are about 1000 times the density of air. So if the event takes place in a stadium, for example, the baseball won't get far through the seats behind home plate. (Even leaving out, of course, the fact that the entire stadium is being obliterated.)
     
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