1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Exercise 26 in Schutz's First course in GR

  1. Feb 13, 2016 #1

    MathematicalPhysicist

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    The question as follows:

    Calculate the energy that is required to accelerate a particle of rest mass ##m\ne 0## from speed ##v## to speed ##v+\delta v## (##\delta v \ll v##).
    Show that it would take an infinite amount of energy to accelerate the particle to the speed of light.




    2. Relevant equations


    3. The attempt at a solution

    Here's what I have done so far, the 4-momentum before is ##(m,mv)## and the 4-momentum after is: ##(E,m(v+\delta v))##, the square of the 4 momentum is conserved, i.e:
    $$E^2 - m^2(v+\delta v)^2 = m^2-m^2v^2$$

    After rearranging I get the following equation for the energy:

    $$E=mv\sqrt{1/v^2+2\delta v /v +(\delta v/v)^2}$$

    I think I have a mistake somewhere, since I don't know how to expand this in a Taylor series, I have the expansion ##\sqrt{1+x} \approx 1+1/2 x##, but here I have ##1/v^2## inside the sqrt.

    Perhaps I am wrong with the 4-momentum or something else, any tips?

    Thanks in advance.

     
  2. jcsd
  3. Feb 13, 2016 #2

    MathematicalPhysicist

    User Avatar
    Gold Member

    I think I got it wrong it should be ##E=\gamma(v+\delta v)mc^2##, and $$\gamma(v+\delta v) \approx 1+1/2 (v+\delta v)^2$$

    For ##v +\delta v = c$, we get the E diverges.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Exercise 26 in Schutz's First course in GR
  1. Jackson problemno. 26 (Replies: 4)

Loading...