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-   -   A dimensional problem in relativistic mechanics (http://www.physicsforums.com/showthread.php?t=488200)

Shyan Apr7-11 08:41 AM

A dimensional problem in relativistic mechanics
 
[tex]{F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a} [/tex]

You all know this equation.Relativistic newton's second law.
The problem is as follows:
As you know [tex]\gamma[/tex] is dimensionless.So the first term of the right side has dimension of mass.but it should have the dimension of force!
what's wrong here?
thanks

harrylin Apr7-11 09:25 AM

Re: A dimensional problem in relativistic mechanics
 
Quote:

Quote by Shyan (Post 3234207)
[tex]{F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a} [/tex]

You all know this equation.Relativistic newton's second law.
The problem is as follows:
As you know [tex]\gamma[/tex] is dimensionless.So the first term of the right side has dimension of mass.but it should have the dimension of force!
what's wrong here?
thanks

Hi Shyan. :smile:

F = dp/dt.

However, the equation that you write, I don't know it.
See http://en.wikipedia.org/wiki/Special_relativity (scroll down to the section on force).
It looks like you forgot a dv/dt term.

Harald

Bill_K Apr7-11 09:27 AM

Re: A dimensional problem in relativistic mechanics
 
You left out a factor. The first term is actually

γ3 m/c2 (v.a) v


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