Is the Use of F=γma Correct in Special Relativity Calculations?

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

Can I do it like this:
$F=γma$
$F=γm\frac{dv}{dt}$
$F=γm\frac{dv}{ds}\frac{ds}{dt}$
$v\frac{dv}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{F ds}{m}$

The finial answer will becom
v=$\frac{\sqrt{2c^2mFx-Fx}}{mc}$

What's wrong?

 

[K^2]

$$F=\frac{dp}{dt}$$
$$F=\frac{d}{dt}(\gamma mv)$$
$$F=\gamma m \frac{dv}{dt} + mv\frac{d\gamma}{dt}$$

Because gamma is a function of v and varies with time, you run into problems. You should still be able to solve it this way if you take the extra term into account, but it's a lot more work than energy conservation method.