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Relativity and Equivalence of Mass and Energy

  1. Mar 16, 2017 #1
    1. The problem statement, all variables and given/known data
    An electron is accelerated to a speed that is 99 percent the speed of light, and is moving through a 2-km-long tunnel. The rest mass of the electron is 9.11*10^-31 kg. What is the mass of the electron at this speed?
    c= speed of light
    2. Relevant equations
    t= (tsubscript(o))/ root(1-(v^2/c^2)
    L= Lsubscript(o)* root(1-0)= Lsubscript(o)
    p= (mv)/ root(1-0) = mv
    KE= ((mc^2)/ root(1-(v^2/c^2))-mc^2
    3. The attempt at a solution
    I tried plugging the rest mass into the last equation on the top which gives me 9.11*10^-31/ root(1-((.99c)^2/c^2
    which calculates out to
    9.11*10^-31/ root(1-.9801)
    9.11*10^-31/root(0.0199)
    9.11*10^-31/0.14106736
    =6.458*10^-30

    I'm unsure if this is correct. It's listed as one of the answers but I don't know if I used the correct equation, so the fact that it's listed as an answer could be a trick. I also don't know how the 2km long tunnel plays into the equation. Please help!
     
  2. jcsd
  3. Mar 16, 2017 #2

    Doc Al

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    Staff: Mentor

    Looks fine to me. The length of the tunnel is irrelevant. (Note that "relativistic mass" is a rather antiquated concept nowadays.)
     
  4. Mar 16, 2017 #3
    So in a different equation using some of the same values, say,
    An electron is accelerated to a speed that is 99 percent the speed of light, and is moving through a 2-km-long tunnel.
    Could I calculate the length of the tunnel in the frame of reference of the electron or is that too irrelevant?
     
  5. Mar 16, 2017 #4

    Doc Al

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    Staff: Mentor

    Sure you can. For that problem, the "rest" length of the tunnel is very relevant.
     
  6. Mar 16, 2017 #5
    So how would I do that?
     
  7. Mar 16, 2017 #6

    Doc Al

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    Staff: Mentor

    Look up the formula for "length contraction" (one of the key relativistic effects).
     
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