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Homework Help: Relative momentum formula or not?

  1. Jan 26, 2010 #1
    1. The problem statement, all variables and given/known data
    In which of these situations is it reasonable to use the approximate formula for the momentum of an object, instead of the full relativistically correct formula?
    A car traveling on the interstate.
    A proton in outer space traveling at 2×108 m/s.
    A commercial jet plane flying between New York and Seattle.
    An electron in a vacuum tube traveling 6×106 m/s.
    A neutron traveling at 3600 meters per second.


    2. Relevant equations
    Velocities closer to the speed of light require a relativistic formula for momentum.

    3. The attempt at a solutionA car traveling on the interstate.
    A proton in outer space traveling at 2×108 m/s. (Relativistic)
    A commercial jet plane flying between New York and Seattle. (Approximate)
    An electron in a vacuum tube traveling 6×106 m/s. (Relativistic)
    A neutron traveling at 3600 meters per second. (Approximate)

    I am incorrect in these answers... however, what makes a velocity "close" to the speed of light. Would a neutron traveling 3600 m/s require a relativistic formula? 3600 m/s isn't very close to 3E8 m/s.

    Any help or insight would be greatly appreciated! Thanks!
     
  2. jcsd
  3. Jan 26, 2010 #2

    Andrew Mason

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    Homework Helper

    The electron in vacuum tube travelling at 6 x 10^6 m/s is travelling at .02c. So the relativistic calculation differs from the approximate by a factor of 1.0002. There is no need to use the relativistic calculation.

    To determine whether the relativistic calculation is needed you have to evaluate:

    [tex]\frac{1}{\sqrt{1 - v^2/c^2}}[/tex]

    AM
     
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