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I Speed and kinetic energy in different inertial frames.

  1. Oct 26, 2016 #1
    From Chris' perspective Bob is travelling with 1.5*108 m/s in direction a. Angelica is also travelling with 2.4*108 m/s in direction a.

    From Bob's perspective Chris is travelling with 1.5*108 m/s in direction b (The opposite of x). Angelica is travelling with 1.5*108 m/s in direction a.

    They all have a mass of 1

    I am pretty sure these numbers are right. I used w = (u+v)/(1+(u*v)/(c2)) To calculate the relative speeds.



    I used the calculation in the picture to calculate the Ek of Bob. I also calculated the Ek of Angelica, all from chris' perspective. Now the outcome that I was expecting was that Bob's Ek would be half of Angelica's Ek when looking from Chris' perspective. Because Angelica is also travelling with 1.5*108 m/s when measured from Bob's perspective. Why does this not count up?

    I am sorry if a skipped a few vital steps. All of my special relativity knowledge comes from self-studying. We don't get this in school.

    Thank you in advance.
     
    Last edited: Oct 26, 2016
  2. jcsd
  3. Oct 26, 2016 #2
    Why would that be true? Even in the non relativistic domain, it makes no sense.
    Suppose you have an observer ##C## at the origin. An object ##B## moves with velocity ##v## in a particular direction. In the same direction, another object ##A## moves with velocity ##v## as seen by ##B##. The velocity of ##A## as seen by ##C## will be ##2v## ( since this is non relativistic, they simply add). The kinetic energy ( as observed by ##C##), of ##A## is not twice that of ##B##, rather it's four times .
    Likewise, in the relativistic domain, there is no reason for the results you expected.
     
    Last edited: Oct 26, 2016
  4. Oct 26, 2016 #3
    I see I made a few unnecessary mistakes there, also in the picture I posted with it. But my confusion is still there, let me try to explain it in another way.

    You have an observer ##C## at the origin. An object ##B## is moving with 1.5*108 m/s in a particular direction. Object ##B## has his buddy ##A## moving next to him, with the same velocity and direction as ##B##. Now object ##A## accelerates till he reaches a speed of 1.5*108 m/s, when looking from ##B##'s point of view, and a speed of 2.4*108 m/s viewed from the observers point of view.

    The Ek of ##B## viewed from ##C##'s point of view = 1,392*1016 J.
    The Ek of ##A## viewed from ##C##'s point of view = 6,00*1016 J.
    The Ek of ##A## viewed from ##B##'s point of view = 1,392*1016 J.

    Now from ##C##'s point of view, ##A## gained 4,606*1016 J.
    And from ##B## point of view, ##A## only gained 1,392*1016 J.

    Now my question is, how do you explain this?


    I used 3*108 m/s as the speed of light to make things easier.
    0ef9f8c42e.jpg
     
  5. Oct 26, 2016 #4
    Is your doubt something like this : The change in velocity for both A and B is the same, yet the change in their kinetic energies are different. How?
    If so, the answer is simple. The slope of the curve in ##K## vs ##v## graph is not a straight line. It keeps on increasing (the curve has an asymptote at ##v=c##). It means that as the value of ##v## increases, so does the slope. It means for a given ##\Delta v## , ##\Delta K## is greater for larger values of ##v##.
     
  6. Oct 26, 2016 #5
    The same thing is seen in non relativistic domain also. The change in kinetic energy of a body going from ##100 m/s## to ##101 m/s## is greater than the change in ##K## for a body going from ##0 m/s## to ##1m/s##.
    The reason is same here. The slope ##(\Delta K)/(\Delta v)## is not a straight line.
     
  7. Oct 26, 2016 #6
    That does come very close to what I ment, yes, thank you very much.
     
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