# Force and Newton's Third Law

That Force is necessarily the result of interaction is made explicit with Newton's Third law.

The second law gives us an Operational (experimental) definition of Force, $\vec{F} \equiv m\vec{a}$. The experiment that I had come across while understanding the second law involved two masses being pulled equally (one at a time) on an air track. The experiment convinced me that the second law is not just a matter of definition because Force is the result of real physical interactions (pull on the masses by means of a band, for example). How does Newton's Third law make the concept of Force more evident?

Newton's Third law is essential if the second law is to be meaningful.

• The question is too vague. Can you be more specific? – D. Ennis Nov 26 '17 at 18:23
• What does "evident" mean in this context? – probably_someone Nov 26 '17 at 18:31
• It is not surprising that in the mentioned experiment the force seems to come from interactions:it is because in real life forces ARE the result of interactions. But the second law does not imply that, so you have to add it as a third law. In addition the third law limits the form of this interaction to equal and opposite forces. – user172184 Nov 26 '17 at 19:24
• Newton's laws don't define force. They assume a common awareness of the existence of forces as pushes or pulls, and a common awareness of the existence of objects. What they add is the rules that nature seems to abide by, based on all of the data and evidence so far, for the interactions of forces and objects. – D. Ennis Nov 26 '17 at 20:08

As some comments say, the problem is that Newton laws presume that the reader already HAS the concept of force and the concept of mass, and he just relates them with the formula.

However, a pure scientist would be so against these laws because they are too very badly done, and the third law comes to "fix" that fact.

If we know the mass, we can get the force by just measuring acceleration, that's okay. The thing is, how do we know the masses? That's the point. A complete set of dynamics rules would have had to include this, and Newton does not.

We cannot know the mass of an object, unless we are able to count all its particles, assigning a value of mass to every single particle and assuming linearity and isotropy. So this doesn't go well.

So we can only measure masses by the force they exert (their weight). But the formula says "F=ma" (with vectors). So the same formula contains two unkwowns... big fail. (Acceleration is measurable, you just need a ruler and a chrono)

Fortunately, the 3rd law kind of fixes that. If $F_{1\ to\ 2}=-F_{2\ to \ 1}$, then we can stablish

$m_1 a_1 = - m_2a_2 \Rightarrow m_2 = - m_1 \frac{a_1}{a_2}$

So if we set $m_1$ as the standard unit mass, then we can measure any other mass by just finding the ratio of accelerations in interactions. Now Newton rules CAN work, but they are assuming more thngs, like $m$ is constant, and son on.