F = ma doesn't work when aproaching c

1. Aug 10, 2010

Jacob_hull

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. Aug 10, 2010

bcrowell

Staff Emeritus
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 $m=\gamma m_o$, where $m_o$ 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 $F=m\gamma a$, 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, $\gamma$ 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, $\gamma$ 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
3. Aug 10, 2010

LostConjugate

The mass increases because m = e/c^2 and E = 1/2mv^2