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 Shyan Apr7-11 08:41 AM

A dimensional problem in relativistic mechanics

$${F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a}$$

You all know this equation.Relativistic newton's second law.
The problem is as follows:
As you know $$\gamma$$ 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) $${F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a}$$ You all know this equation.Relativistic newton's second law. The problem is as follows: As you know $$\gamma$$ 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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