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Algebra in energy-momentum-mass relations

  1. Jan 24, 2015 #1
    <<Mentor note: Please always use descriptive thread titles.>>

    First of all, the title is such that it attracts most views.You see, in class our professor did some goofing around numbers and variables in the relativistic energy momentum relation:
    E2=(pc)2+m02c4
    Since the energy required to accelerate an object to a certain velocity is
    E=m0c2/√1-v2/c2,
    ∴E2=m02c4/1-v2/c2
    plug in the value of E2,
    p2c2+m02c4=m02c4/1-v2/c2
    cancel out the m02c4
    so p2c2=1/1-v2/c2
    since c2= E/m,
    ⇒Ep2/m=1/1-v2/c2\
    But, p2/m = 2* K.E and since E in E=mc2 implies any form of energy,and the object gains kinetic energy through it's motion, so Ek=E
    ⇒E(2E)=1/1-v2/c2
    ⇒2E2=1/1-v2/c2
    ⇒E2=1/2(1-v2/c2)
    ⇒E2=1/2-v2/c2
    ⇒E=1/√2-v2/c2
    and that's it.No one in the room could figure out what's wrong, but our prof. said that something is wrong, but it is our job to find it out, plus, immediately one notices that if v=c, E=1 J. WTH!
     
    Last edited by a moderator: Jan 24, 2015
  2. jcsd
  3. Jan 24, 2015 #2

    phinds

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    This might actually be readable if you put in some parentheses.
     
  4. Jan 24, 2015 #3

    Bandersnatch

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    That's... an interesting piece of algebra you did there.
     
  5. Jan 24, 2015 #4
    Thanks Bandersnatch, i finally find out the mistake he did, and sorry for sounding stupid
     
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