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F = ma doesn't work when aproaching c

  1. Aug 10, 2010 #1
    Hello all,

    Im only a student, taking physics in college in september, However I have read up on the level of physics I will be studying. One thing that I couldn't get my head round, Why when an object aproaches c does its mass increase? Am I right in saying this also makes it impossible from the object to reach c? Also why does this cancel out f = ma?

    Sorry if this seems like a stupid question, but it just sparked an interest in my mind and I couldn't find an explanation that actually fully explained it to me. Thanks all.
  2. jcsd
  3. Aug 10, 2010 #2


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    Welcome to Physics Forums!

    There are basically two ways of describing this in relativity.

    The more old-fashioned way is to write F=ma, and say that [itex]m=\gamma m_o[/itex], where [itex]m_o[/itex] is the mass the object has when it's at rest.

    More recently (roughly within the last 50 years), it's been more common to write [itex]F=m\gamma a[/itex], and treat m as a constant.

    So depending on which description you prefer, you can either say that mass increases or it doesn't increase, but either way the prediction is the same.

    It doesn't cancel out F=ma completely. At velocities that are small compared to the speed of light, [itex]\gamma[/itex] is very close to 1, so F=ma is approximately right. That's why people believed F=ma was exact for hundreds of years.

    Yes, this is one way of seeing that an object can't reach c. As its velocity gets close to c, [itex]\gamma[/itex] approaches infinity, so the force required in order to maintain the same acceleration also approaches infinity.

    For an explanation of why this happens: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html#Section1.3 [Broken]
    Last edited by a moderator: May 4, 2017
  4. Aug 10, 2010 #3
    The mass increases because m = e/c^2 and E = 1/2mv^2

    This means that if your velocity increases your energy increases your mass increases.

    You are correct, a massive object can't reach the speed c.

    Also f=ma does not work at speed c because the force would be infinite along with the mass which essentially states 1=1 since "a" now equals next to 0. Perhaps it works it is just not very interesting.
  5. Aug 12, 2010 #4
    Thanks for the reply, this sort of stuff doesn't get explained to you in Secondary school it was basically f=ma end of. But I understand now so thanks alot :)
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