![]() " $\mathbf F = m \mathbf a$." My understanding is that this is not a ![]() Insofar as whether or not it provides enough information it depends on what kind of information you are looking for. A force (push or pull) does not require that there is an influence. It's broader than using Newton's 2nd law since, as discussed below, Newton's 2nd law only addresses the influence of a net force. That is the most commonly cited qualitative definition. "A force is a push or pull." This seems to be a "correct" definitionīut it doesn't provide enough information. What the law truly means is that any time we have a force without an opposite force, the system we are analyzing is not truly a closed/isolated system. In many cases, we actually ignore this law (for example when we consider a spring attached to a wall, we simplify our scenario by ignoring the fact that the motion of the spring imparts some momentum to the Earth). Newton's third law is different from the other two laws, because unlike the first two laws the third law gives a constraint on what the possible force laws (which are the things that specify what the force is in a given scenario) there can be. The role of Newton's first and second laws are to relate force to the motion of objects, and in the process of doing this they elucidate what it means for a force to be "a push or a pull" or to be "an influence of one body on another." There is a subtle difference, because at no point do we say "a force is defined as blah-blah-blah" in either of the laws. Newton's first and second laws are not definitions of force so much as they are axiomatic characterizations of force. Of course, like I've said before, the force law can come from other theories such as electromagnetism where force is defined by the electric and magnetic fields. If you come across a new scenario that no one else has analyzed, you will have to guess the force law and empirically test whether or not your guess leads to correct predictions. You need to actually do and solve problems with Newtonian mechanics to understand exactly what this means.Īs I've said, what exactly is the force in a given scenario is specified by the relevant force law. The desired characterization that justifies force as the concretization of the notion of pushes and pulls is done through the axioms of Newtonian mechanics. The above options are the only two ways you can define anything rigorously, and force just happens to be a primitive concept in Newtonian mechanics, because it starts with force.Īlthough force itself is primitive, it is supposed to be the mathematical concretization of the intuitive (but vague) notion of pushes and pulls (and more generally influences between bodies). This is more evident with forces such as electricity and gravity. "A force is the influence of one body on another." This is not sufficient because as other people have pointed out to me, force is more so the relationship between two bodies as opposed to how one acts on another. "A force is a push or pull." This seems to be a "correct" definition but it doesn't provide enough information. As I pick up more physics I see that the definitions of force commonly provided in books and classrooms are misleading.
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