Why F=ma?

Because of Quora’s habit of applying answers to unrelated questions I need to clarify that the question I am responding to here is “Why is Newton’s second law written in the form F = ma, since a more accurate form based on the formula F = dp/dt should be F = m dv/dt + v dm/dt = ma + v dm/dt, since according to the theory of relativity, mass also changes, as does velocity?

Well first, Newton’s second law is written in the form F = ma because that is essentially the way he wrote it and if it wasn’t written that way it wouldn’t be Newton’s law. The form F=dp/dt (which is more general but not more “accurate”) was known to him but he didn’t need to use it because he was referring to the special basic case of an object of a fixed mass (as opposed to something like a rocket expelling massive exhaust) and he chose to take just the simpler special case as his starting point and deduce the more general as a consequence.

He did not write his laws in Lorentz covariant form because he was unaware of almost everything about electromagnetism and radiation, and so had no reason to expect that the correct laws of physics were not actually perfectly Galilean covariant. (But in any case, as described in more detail in other answers, both the Lorentz covariant laws of special relativity and those of General Relativity can be expressed in a form which includes an equation of the form F=ma for appropriate definitions of F,m, and a).

But your claim that “according to the theory of relativity, mass also changes, as does velocity” is based on a concept of “relativistic mass” which is not a well defined property of an object and has long been abandoned as misleading and not useful.

ce: (960) Alan Cooper’s answer to Why is Newton’s second law written in the form F = ma, since a more accurate form based on the formula F = dp/dt should be F = m dv/dt + v dm/dt = ma + v dm/dt, since according to the theory of relativity, mass also changes, as does velocity? – Quora

If energy (E) is equal to mass (m), then why is E = mc^2?

It is not true that “energy (E) is equal to mass (m)”. What is true is that the mass (m) of a system is equal to the special case of the time component of its 4-momentum in the “rest” frame (where the net spatial component of momentum is zero), and that the units we typically use to measure the time component as “energy” (E) are chosen in such a way that the extra “kinetic” energy as seen by a moving observer is given approximately by (1/2)mv^2 rather than (1/2)m(v/c)^2 with units of space and time chosen in such a way that the limiting speed c is very large (and so that speeds we actually experience do not have to be associated with very tiny numbers).

Source: (952) Alan Cooper’s answer to If energy (E) is equal to mass (m), then why did Einstein add the multiplier c^2? Recall the equation E = mc^2. – Quora