Oh come on, no physics thread is complete without it...
Also from the article: E=mc^2. Therefore m=E/c^2.
Question 1: Is this the same "m" in both equations?
Question 2: If so, does F/a = E/c^2? I would have thought not. In fact, I would have thought them to be many orders of magnitude apart.
(please forgive me. It's been 30 years since college physics, and I wasn't quite as inquisitive then.)
Your math is correct, but what are you trying to explain? The force on an object divided by the acceleration it's undergoing is equal to the total energy contained in that object's mass divided by the square of the speed of light?
1. The m is the same in both equations, yes. F is the force of interaction when a particle interacts with another. If particle 'b' perturbs the motion of particle 'a', then the amount of force 'b' exerts on 'a' is measured by F=ma. If you know the mass of 'b', the force exerted upon it by 'a', and the acceleration change from the interaction, you can determine the mass of particle 'a'.
E is the total amount of energy that could be released by converting all the mass of the particle to energy. Not a lot of ways to do this; a matter-antimatter collision of equivalent particles comes to mind. The total energy released by the destruction of the two particles would be their combined masses x c^2. If you know the total amount of energy released in such an instance, and divide by c^2, you get the total mass involved.
2. Yes. F/a is usually a small quantity over another small quantity. E/c^2 is a huge quantity over another huge quantity. It balances out.
And yes, I had to grab scratch paper to be sure :)