Results 1 to 2 of 2

Math Help - Einstein's Special Theory of Relativity Quesion

  1. #1
    Junior Member
    Joined
    Sep 2005
    Posts
    62

    Einstein's Special Theory of Relativity Quesion

    I have no idea how to start this problem, We barely learned alittle part of this in class today but the teacher just said read the book and it is easy to undertand. I read the book over and over but I don't know....

    Einstein's Special Theory of Relativity says that mass m is related to v velocity by the formula



    Here, m0 is the rest mass and c is the velocity of light. Use differentials to determine the percent increase in mass of an object
    when its velocity increases from 0.8c to 0.82c.

    Approximate percent increase:_______
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,885
    Thanks
    325
    Awards
    1
    Quote Originally Posted by killasnake View Post
    I have no idea how to start this problem, We barely learned alittle part of this in class today but the teacher just said read the book and it is easy to undertand. I read the book over and over but I don't know....

    m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

    I'm going to rewrite this as:

    m = m_0 \left ( 1 - \frac{v^2}{c^2} \right ) ^{-1/2}

    Now:

    dm = m_0 \cdot \frac{-1}{2} \left ( 1 - \frac{v^2}{c^2} \right ) ^{-3/2} \cdot \frac{-2v}{c^2} dv

    dm = m_0 \frac{v}{c^2} \left ( 1 - \frac{v^2}{c^2} \right ) ^{-3/2} dv

    We have v = 0.8c and dv = 0.02c, so

    dm = m_0 \frac{0.8c}{c^2} \left ( 1 - \frac{(0.8c)^2}{c^2} \right ) ^{-3/2} \cdot 0.02c

    dm = m_0(0.016) (1 - 0.64)^{-3/2}

    dm = 0.074074m_0

    Now, we need this as a percentage increase in mass:

    \frac{dm}{m_0} \times 100 %

    = \frac{0.074074m_0}{m_0} \times 100 %

    = (0.074074) \times 100 %

    = 7.4074 %

    -Dan
    Last edited by topsquark; October 27th 2006 at 05:39 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Was Einstein wrong about relativity?
    Posted in the Math Forum
    Replies: 5
    Last Post: November 20th 2011, 06:01 AM
  2. special Relativity #4
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: December 7th 2009, 02:04 PM
  3. Special Relativity #3
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: December 7th 2009, 01:51 PM
  4. Special Relativity #2
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: December 7th 2009, 01:47 PM
  5. re: Einstein's theory of relativity
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: February 28th 2009, 07:33 AM

Search Tags


/mathhelpforum @mathhelpforum