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Relative velocity inside a train

  1. May 7, 2012 #1
    Hello Everybody!

    I have a question -

    If I'm standing inside a train and I jump up in the air I will land in the same place, I think. Likewise, if I'm holding a pen in my hand and I throw it up in the air it will land again in my hand. But if I stood on top of the train, on the roof, and I jumped up in the air the train would carry on and I would land further back, I think. Same as with a skateboard - if I jump up in the air while on a skateboard the skateboard will carry on and I will land on the ground. Why then does that not happen when I'm inside the train.

    I'm very confused, I would appreciate your input. I'm not a physics student at any level, just curious.

  2. jcsd
  3. May 7, 2012 #2
    Every body in the universe has an innate property called inertia, which is due to its mass. Now this is what keeps you resting on your couch without you just randomly tumbling down. Its also that what keeps you moving when the car brakes are applied hard. (Ouch)

    So when you jump in a train, your innate velocity is the same as that of the train, so when you leave contact from the train's base, your inertia kicks in and keeps you moving at the same velocity. So you land just where you would be if you were standing, assuming the train does not accelerate in the meantime and your jump is humanely small to neglect air resistance :wink:

    This would also be the case even if you jump from the train's roof. It only changes if you already had a different velocity before jumping up, then it would be the vector sum of the velocity of 'you' plus the 'train' that would effect your motion.
  4. May 7, 2012 #3


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    The difference is aerodynamic drag.
  5. May 7, 2012 #4


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    If you jump straight up you will in fact land back on the skateboard.

    It's just that even being a little bit off will result in kicking the skateboard away from under you.

    Now, I don't have a skateboard, and I've never been on one, but the physics is straightforward. If you do have a skateboard then by all means try it!

    If you are running along and in mid-run you jump up then you don't come to a standstill. When you touch down again you either must resume running, or you use the air-time to brace for the sudden stop. Either way: if you run at full speed then there is no way you can stop effortlessly.

    Same thing when you are on a skateboard. Go up to the same velocity as a fast run. Then step of the skateboard. Same choice: either you start running to match your velocity, or you must brace for a sudden stop.

    Of course, to really feel it you must go as fast as running at full speed.
    Try it!
    Last edited: May 7, 2012
  6. May 7, 2012 #5
    Just adding the -why-is-it-so-,

    Since the skateboard is small compared to you, in terms of mass, the law of conservation of linear momentum will act here, which states that if no external force acts on a closed system of objects, the momentum of the closed system remains constant. So if you jump in a specific direction, instead of the normal vertical jump, you'd land a little away from the skateboard, as the skateboard will change its velocity to conserve the total momentum.

    And I did try out what Cleonis said, a couple years ago. Believe me, its fun! :biggrin:
  7. May 7, 2012 #6
    Someone get this kid a skateboard :-)
  8. May 7, 2012 #7


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    Considering the above: Is it possible to gain speed on a skateboard over level ground without touching the ground, or any other object other than the skateboard? (no aerodynamics involved, assume vacuum)
  9. May 8, 2012 #8
    You mean the skateboard on level ground and you not touching anything else? then no. Of course, you can jerk yourself backward a bit so that the skateboard moves forward shortly(probably making you slip off) but soon, you'll be back to your initial velocity as your momentum will definitely be conserved. In fact, try it out being stationary on the board!
  10. May 8, 2012 #9


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    You are thinking in 1 dimension. Try to see it in at least 2.
  11. May 8, 2012 #10
    Since you said so, I actually tried this out just now. I could jump on the skateboard and thats gaining velocity indeed, I could move about on the skateboard too, half a foot here and there, but i doubt thats what you are suggesting.

    Another thing that I did then was jump off in a northeast direction assuming the board was aligned north-south. That again would be me gaining velocity in the upward/eastern direction but the final momentum of north-south direction had to be conserved as the skateboard did move backward.

    But I didnt see any way to accelerate myself continuously without using anything else.
    Last edited: May 8, 2012
  12. May 8, 2012 #11


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    You almost have it.
  13. May 8, 2012 #12
    I lacked expertise! :shy:

    But yes, I do see now. Thanks a ton.

    Also, would a ground-friction free environment cause a difference? I believe it would, since the wheels wouldn't hold on to the ground as I turn...?
  14. May 8, 2012 #13


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    You're welcome. Snake boards allow you to do basically the same, without lifting the axle.


    Without ground-friction you don't even need wheels. They make no difference. And since you cannot transfer any horizontal momentum to the ground, you obviously cannot gain horizontal momentum yourself.
  15. May 8, 2012 #14
    Wow! I really want to try out one of these! :cool:

    Gotcha, thanks again.
  16. May 8, 2012 #15


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    You might also want to take a look at caster boards. I find them to be a bit more elegant than snake boards. It does take quite a bit more coordination to stay up on one, however. The propulsion method is identical for both.
  17. May 8, 2012 #16
    Surely, but skate(snake/caster)boarding just isn't the craze in this part of the earth, because it would be great if I could actually get someone around with one, just to try them out, before I go serious :biggrin:

    Thanks for the suggestion :smile:
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