Newton's second law of motion states that $F = ma$, where $F$ is the net force on some object with mass $m$ and acceleration $a$. This implies that an object with net force $F$ acting on it, may have two individual forces in opposite directions on it, $F_A$ and $F_B$, respectively, such that their vector sum is $F$. My question is: how are the values of $F_A$ and $F_B$ determined? I know that Newton's second law of motion can only be used to determine the difference between them.
For example, if we apply $2 N$ on an object in a direction and $4 N$ in the opposite direction, and in another case we apply $1000 N$ one a direction and $1002 N$ in the opposite direction, the acceleration of the object is identical in both the cases.
How do we distinguish between the two situations? How can we assign
one pair of values for the first case and another pair of values for
the second? Is this not arbitrary? How are these values assigned?
Best Answer
With context. Usually you will have some idea what forces you're working with. For instance, if you're told that you're lifting a boulder upwards with an acceleration of $a=2\ \rm m/s^2$ then you know there are at least 2 forces acting on the rock: gravity ($mg$) and the force you apply to lift it $F_A$. Therefore, $ma=F_{\rm A}-mg$, and you can solve for the force you apply, $F_{\rm A}$.
However, if all the information you're given that an object has some acceleration with no context as to its environment, then you can't find the forces acting on it. Of course, such a problem is rather useless, and you will always have the necessary information to figure out which forces may act on the object.
If you're told an object is falling down, then for sure gravity is acting on it. There would also be air resistance (which is often ignored in intro physics classes to simplify the calculations, but you would be explicitly told to ignore it). If you're dealing with a charged particle, then you know there are electric forces.
As you proceed to learn physics, you will learn about different types of forces and how they act on objects. But these forces are certainly not arbitrary.