# Reactive force on two objects with central forces

I have a confusion with reactive forces, in how they act, and I hope to highlight my confusion with some (very) poorly drawn graphics by me.

From my understanding (likely false), a Newton's Third Law reactive force is the force vector equal in magnitude and opposite in direction of an applied force. In the case of an object undergoing circular motion, the pivot feels an outward force from the orbiting body. If I fire a gun, the force of the shot pushes me back (hence, kick). Cannons have wheels for a reason. My understanding is shown in a graphic I've butchered, but is that of a person punching someone's face, and the respective forces on either as a result: Now, I'm not actually sure if $F_{face}$ is the same as the normal force, but the forces should be balanced, as once contact is made the fist stops moving and experiences shock (in the same way punching a skull can break you hand). The normal force, or, just $F_{face}$ is a reactive force from the face upon the face as a result of the punch itself. That's my view, at least.

This understanding of reactive forces hurts me now, when I consider the following scenario: two objects feeling central forces as a result of eachother (let's let the central force be gravity). In my second bad graphic, I have $A$ and $B$ both exerting forces on eachother. $A$ feels force $F_{ab}$ (Force on $A$ as a result of $B$) while $B$ feels $F_{ba}$ (Force on $B$ as a result of $A$). Let $F_{ab} = -F_{ba}$.

The forces with "R" in front are reactive forces - and I've constructed them out of misguided necessity that I cannot refute rigorously. If $A$ pulls on $B$, then by Newton's Third Law, $B$ must pull on $A$, just as a face strikes a fist as a fist strikes a face. This assertion explains force $RF_{ba}$ on $A$, and the same faulty logic applies to $B$ and $RF_{ab}$. Can someone highlight the key misunderstandings that are causing me to have this odd train of thought?

• The forces $RF_{ba}$ and $RF_{ab}$ simply don't exist, you've made them up. $F_{ab}$ is equal and opposite $F_{ba}$ which satisfies Newton's third law. Sep 21 '17 at 23:39
• -1. No research effort. This site has many similar questions about Newton's 3rd Law. Have you read any of them? Sep 22 '17 at 23:31

The force $F_{ba}$ is the reactive force corresponding to $F_{ab}$ and vice versa. The forces you labeled with $R$ do not exist. It is perfectly normal for the forces on a single object to not balance. For example, the forces on $A$ and $B$ could be due to gravity. Both objects feel an unbalanced attractive force and begin to fall towards each other.
• Interesting. So, from what I gather from what you said in the first paragraph, even if the forces are due to gravity, where each object will exert a force on one another, each individual force is the reactive force of the other.. So, $F_{ba}$ is the reactive force of $F_{ab}$ even though $F_{ba}$ is the force $A$ exerts on $B$ due to gravity, and also the reactive force of $F_{ab}$, which is the reactive force of $F_{ba}$. I feel like there's some kind of never ending loop of consequence there. Sep 21 '17 at 23:59
• My view states that for each force $F$ there is a reactive force. There are two unique forces at play here, and as such need a reactive force to pair with them.. Sep 22 '17 at 0:00
• @sangstar I think what leads you astray is thinking that a force causes the reactive force, which would lead you to think that the reactive force appears after the original force. This is not so. Forces always occur in pairs. $F_{ab}$ and $F_{ba}$ arise simultaneously, no matter what the nature of the forces happen to be. Neither force precedes the other. Sep 22 '17 at 1:18
• But in the case of two objects feeling a gravitational force, which do you consider the reactive force if they each feel their own force? I would understand that if one object ONLY, like $A$, exerts a force on $B$ like in my graphic then $A$ would feel a reactive force, but they both have a force on eachother independent of eachother.. if that makes sense. I understand from what you said though that this explains the case of someone punching a face. The fist feels the reactive normal force, in that case. Sep 22 '17 at 11:38