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Relativistic Momentum

  1. Aug 16, 2012 #1
    Hi,

    I was given a question in which I had to work out the speed of an object given its momentum and its mass.

    Now I had to answer what would be the new speed if the momentum doubled.

    So, from what I understand, the rest mass can't change, it is like a constant for a given body. So, in other words, in this case, it is the velocity that is going to change.

    In order to find by what factor v must be increased in order to yield an increase in momentum of two I tried to rearrange the following equation:

    v/√1-(v2/c2 = 2

    Is this what I should do?

    Can anyone please maybe give me a hint of what step I should take?
     
  2. jcsd
  3. Aug 16, 2012 #2

    Curious3141

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    Homework Helper

    The formula for the relativistic momentum is [itex]p = {\gamma}mv[/itex], where [itex]\gamma =\frac { 1 }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } }[/itex], which gives [itex]p = \frac { mv }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } }[/itex]

    You're given that [itex]p_{new} = 2p_{old}[/itex].

    So what you need to do is to solve this equation:

    [tex]\frac { mv }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } } = 2\frac { mu }{ \sqrt { 1-\frac { { u }^{ 2 } }{ { c }^{ 2 } } } }[/tex]

    where v is the new speed and u is the old speed (which you've already calculated). Solve for v.
     
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