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!

Homework Help: Length contraction numerical problem

  1. Jul 11, 2017 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    1) k.e. = (1/2)mv2, non- relatvistic

    2)K.E. = m0 c2 (ϒ -1), relativistic

    3) L=L0/ϒ , Length contraction

    3. The attempt at a solution
    (A) Taking 1019 eV to be the kinetic energy of the proton,
    Non- relativistic calculation
    (1/2)mv2 = 1019 eV = 1.6

    v = √[ (3.2/1.67)* 1027 ] = 4.3 * 1013 m/s

    How is kinetic energy defined relativistically?

    K.E. = m0 c2 (ϒ -1)

    We can't take 1019 eV as total energy of the proton as if we take so then we won't be able to calculate speed of the proton.

    So, for calculating speed of the proton, I have to take 1019 eV as the kinetic energy of proton.

    ϒ2 = [ {1019 eV/ m0 c2}+1]2

    m0 c2 = 939 MeV

    Solving it gives,
    1 - v2/c2 = [939 * 10-13]2

    v ≈ c

    Hence, w.r.t. galaxy frame the proton will take 105 years to cross the galaxy.


    W.r.t. the proton frame,
    the length of the galaxy is shortened to 105 [939 * 10-13] light years.

    Hence, the time taken = 105 [939 * 10-13] years

    Is this correct?
  2. jcsd
  3. Jul 11, 2017 #2

    Buzz Bloom

    User Avatar
    Gold Member

    Hi Pushoam:

    Your work looks OK to me. However, I suggest converting the (B) answer to seconds.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted