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.