Can you justify force calculations using more than one of Newton's laws?

Question

If an object is at rest on a flat surface I remember my school teacher would say, "By Newton's 1st law the normal reaction, R, is mg (mass x g)". Ok, sure this is fine because the object is at constant velocity (velocity=zero) and so there are no net forces and so the two forces must balance. But what's wrong with saying "By Newton's 2nd law R-mg=0. Therefore R=mg." (The net force on the object is zero, therefore the acceleration on the object is zero) But can't you also say, "By Newton's 3rd law R=mg." (The object is pushing on the ground with a force of mg, therefore the ground is pushing on the object with a normal reaction of mg).

Is this correct or have I erred somewhere?

Answer 1

So Newton's first is inertia, Newton's second is for force and momentum F=d(mv)/dt and Newton's third is the equal/opposite thing, i.e., forces occur in pairs. You have not really erred, just used all three laws to characterize the situation and because Newton's Laws are all applicable, there must be a way to characterize the situation with all three. A couple of nits: Newton’s first only gets you the reaction because of the particular description of the problem; it is of course not true in general that the Law of Inertia really helps you determine particular forces in a given situation - that is the job of laws 2 and 3. I could also mention that we should be talking about the vector nature of forces, i.e., that they are directional in nature and that some of your dynamical quantities should have an algebraic sign e.g., it should be said above that R-mg=0 -> R = -mg but that would take us into some complexities about how your coordinate system was defined, etc.

Answer 2

There's no rule saying the behavior of a particular physical system can only be justified by one law. Actually that would be kind of silly because what you count as "one law" is completely arbitrary. :-P

However, when you use different laws to justify the same behavior, the results had better be consistent. If not, you're doing it wrong. (Or something is wrong with the laws, but that doesn't happen with Newtonian mechanics any more.)