# Equal and opposite reaction - forces coming in pairs - or just common sense?

I've never understood why the conservation of momentum law is taught in schools as "every force has an equal opposite reaction".

To me a gun's recoil is self explanatory; the explosion sits in-between the bullet and the back of the barrel and the gun and bullet fly in opposite directions (as would be expected). The bullet has a much higher velocity than the gun because of its lower comparative mass. Am I wrong here?

Same with stepping off a boat. You push against the boat and the mass differential between your body and the boat as well as the friction in the water enables you to jump off the boat onto the ground without falling on your face. The boat comparatively moves in the opposite direction minimally, but not because of some weird law, simply because you pushed it back!

To tell kids in school "every force has an equal and opposite force" is misleading I think. It makes it seem as if an equal mysterious force manifests out of thin air to keep the universe happy.

Just thinking - "direction of application" is only relevant to perspective, there really is no direction of application since the force and its counterpart occur simultaneously… so more accurately:

• The total force can never be propagated along a single vector?
• To future readers: the classic phrase "for every action there is an equal and opposite reaction" is extremely unhelpful, if not meaningless. I think it's a literal translation from the Latin. Mar 3, 2014 at 13:31
• Yes and also meaningless is telling kids in school that when you push on something it will push back at you. Well no, it doesn't push back at you it merely exhibits inertia and resistance to a change in acceleration right? Mar 4, 2014 at 0:49
• @MikeS As I mentioned in my other comment, you are wrong. The box really does exert a force on you. You simply don't gather a net force (friction force opposes your motion, cancelling it out), it doesn't mean the box doesn't push at you. In fact, it does push at you. Mar 4, 2014 at 2:12
• Please see our discussion below @garyp Mar 4, 2014 at 4:43

First of all, mathematical definitions of force and momentum aren't really very intuitive or common-sensical. Just ask Aristotle for his common sense laws of forces! The fact that momentum is conserved in closed systems is a highly non-trivial fact, as is the Third Law. The reason that these laws exist at all is because you can't really 'see' or' feel' exactly what forces and momentum are referring to: they are ONLY mathematical constructions to make sense of the world. So no, this isn't common sense. Honestly, even if it were, 'common sense' cannot account for quantitative aspects of physics at all, so formal mathematical constructions are still essential.

Now, "any force applied in one direction is split in the opposite direction" would be far more misleading. This is because forces are not 'split'. Instead, they are exactly what the Third law says they are: TWO different forces, acting on TWO different objects. Otherwise, I promise you, your math is wrong.

If you still have any questions, talk back and let me know.

• Yes I get what you're saying. There is no splitting - that makes complete sense. I edited my answer as you were writing this…does my last idea make sense? Mar 3, 2014 at 11:30
• Your last idea is valid only for closed systems. When an external force is present, the momentum of a system does change. So we have F=ma. Mar 3, 2014 at 11:32
• Yep you've helped me understand this concept more intuitively so thank you! Mar 3, 2014 at 11:37
• @MikeS You're always welcome. That's what SE is for! Mar 3, 2014 at 11:41
• Hmm.. just another quick question; if a person pushes on a box why do they talk about the box responding with the same force back? Isn't the box just exhibiting its mass and therefore its resistance to a change in acceleration (as well as any friction forces)? Mar 4, 2014 at 0:48

The forces act on BOTH the bodies involved, not on the same one! That's why the statement of Newton's third law is: The third law states that all forces exist in pairs: if one object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two forces are equal and opposite: FA = −FB Source:Wikipedia. So it isn't misleading if we mention that the two forces are opposite in direction and act on the two different bodies in picture.