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!

Density change of an object with mass

  1. Sep 5, 2014 #1
    1. The problem statement, all variables and given/known data

    This is an introductory special theory of relativity short question from university question paper that carried 2marks.
    Does the density of an object change as its speed increases? if yes by what factor.

    2. Relevant equations

    m=m0/√[1- (v/c)2]

    3. The attempt at a solution
    My guess is yes .
    If 1/√[1-(v/c)2]=γ lorentz factor
    ρ=m/L3=m/volume(V)=(m0/V0) *γ4
    No text book has exclusively covered this problem except for one.
    There it is written for proper mass density
    ρ/ρ0=γ and it is γ2 for mass-energy density.
    And V=V0/γ.
    The author only mentioned the relations.Did not derive them either concisely or in detail.
    I am now confused.How come lorentz factor has the same power for both length and volume?
    Why and how does proper mass density and mass-energy density have different factor?
  2. jcsd
  3. Sep 5, 2014 #2


    User Avatar
    Science Advisor

    If an object has a velocity in the X-direction, are all three spatial dimensions Lorentz contracted?
  4. Sep 5, 2014 #3
    The answer to your question is no.But nobody said here about a velocity in x direction.What if for the most general case the object is travelling in an 3d space.Shouldn't all the components contract?
  5. Sep 5, 2014 #4


    User Avatar
    Science Advisor

    No, all components don't contract, only the component in the direction of motion. It doesn't matter what direction it is, I just used the X-direction to make the question simpler. If it is moving with a uniform velocity, I can always rotate my coordinate system and call the direction of motion the X-direction.
  6. Sep 5, 2014 #5
    Ok so that clears up the volume factor. Could you please explain the proper mass density and mass energy density factor difference?
  7. Sep 7, 2014 #6
    After thinking on my own question what I feel is in the case PROPER MASS DENSITY variation is only due to contraction in dimension of the body parallel to its direction of motion.Hence V=V0/γ.
    So ρ=ρ0γ.
    But for MASS-ENERGY DENSITY both the mass and volume change.
    Mass increases :m=m0γ
    Volume changes as above.
    So ρ=ρ0γ2.
    Am I right?
    Do you guys concur?
    If yes then what should be right answer to my first post?
    Should it be γ or γ2?
  8. Sep 7, 2014 #7


    User Avatar
    Science Advisor

    Your reasoning is correct. As to the answer to your first question, it depends on which they are asking about. I would think that the word density refers to the proper density, but I'm not really sure.
  9. Sep 7, 2014 #8
    What still makes my mind itch is my inability to explain the answer physically.
    My answer was clearly out of mathematical intuition.
    Can somebody explain PHYSICALLY why proper mass density varies by a factor γ while mass energy density by γ2?
    What could be the best possible QUALITATIVE explanation?
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: Density change of an object with mass
  1. Density mass (Replies: 1)

  2. Density of an Object (Replies: 13)

  3. Density and mass (Replies: 3)

  4. Density Of the Object (Replies: 13)