Special Relativity Forces and Energy

[jeffbarrington]

Homework Statement

Hi, I have this problem:

For motion under a pure (rest mass preserving) inverse square law force f = −αr/r3 , where α is a constant, derive the energy equation γmc² − α/r = constant.

Homework Equations

E = γmc²
dE/dt = f.u for a pure force

The Attempt at a Solution

I start by saying:

dE/dt = f.u = f.dr/dt

Next, I know f is independent of time, so I can just integrate this to get:

E = f.r +constant

So then you get:

γmc² = -α/r + constant

Which is painfully close to the result I'm meant to get but out by a minus sign. I don't know if I've made an error here or if the question is erroneous.

Thanks for any help.

 

[DuckAmuck]

Looks like there's some symbol-related confusion here.
You have 2 different variables both named "E".

 

[jeffbarrington]

Looks like there's some symbol-related confusion here.
You have 2 different variables both named "E".

Really? I don't understand how that's the case, they're both the particle's energy.

edit - I actually get something viable by considering dE/dt = grad(E) dot dr/dt, since r is a function of time and I forgot to chain rule it.