# A dimensional problem in relativistic mechanics

1. ### Shyan

2,025
$${F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a}$$

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

2. ### harrylin

Hi Shyan.

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

3. ### Bill_K

4,159
You left out a factor. The first term is actually

γ3 m/c2 (v.a) v