Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proving one of Einsteins formulas (Kinetic energy of an object)

  1. Jan 11, 2004 #1
    My physics teacher is having me prove two of Einsteins formulas as a homework assignment. One is his formula for the relationship between the energy of an object and it's momentum, E = sqrt(p^2c^ + m(original)^2c^4), that one was no problem, insert m = m(original) * gamma into E = mc^2 and so on. The other one, his formula for the kinetic energy of an object, is a trickier thing. My book says that it's found by defining K as such:

    [tex]K = \int_{0}^{s} Fds = \int_{0}^{s} \frac{d(mv)}{dt}ds[/tex]

    Then it says it's possible to calculate this integer by inserting for the mass from equation 1.3 (Below) and do it by parts.

    [tex] m = \frac{m_o}{\sqrt(1 - v^2/c^2)} (1.3) [/tex]

    The end result being:

    [tex] K = mc^2 - m_oc^2 [/tex]

    I'm completely stuck. I'd really appreciate any piece of advice you might have on integrating this by parts, or other means. I've done a little algebraic manipulation to try to simplify it but with no succes. What I'd really like to know if you can treat gamma as a constant when integrating (or diffrentiating) for time or distance? It'd simplify things a lot, but I suspect it can't be done that way since gamma contains velocity which is a function of distance and time, and would then be affected.

    Any thoughts or hints?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Proving one of Einsteins formulas (Kinetic energy of an object)
  1. Einstein energy (Replies: 1)

  2. Einsteins formula (Replies: 2)

Loading...