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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?
Mike S
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    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. – garyp Mar 03 '14 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? – Mike S Mar 04 '14 at 00:49
  • @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. – resgh Mar 04 '14 at 02:12
  • Please see our discussion below @garyp – Mike S Mar 04 '14 at 04:43

2 Answers2

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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.

resgh
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  • 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? – Mike S Mar 03 '14 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. – resgh Mar 03 '14 at 11:32
  • Yep you've helped me understand this concept more intuitively so thank you! – Mike S Mar 03 '14 at 11:37
  • @MikeS You're always welcome. That's what SE is for! – resgh Mar 03 '14 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)? – Mike S Mar 04 '14 at 00:48
  • @MikeS Because, imagine you were pushing it in empty space, with nothing but you and the box. Then, after you push it, you will be flying backwards. The reason this doesn't usually happen is because of friction between you and the ground. – resgh Mar 04 '14 at 02:04
  • You'd only go backwards because the box resists a change in it's acceleration to a point directly proportional to its mass? If the box theoretically had zero mass you wouldn't go anywhere. – Mike S Mar 04 '14 at 02:26
  • @MikeS Your acceleration only depends on the net force upon you. Assuming the force you apply on the box is the same, then no matter how the mass of the box changes you fly backwards the same way. – resgh Mar 04 '14 at 03:08
  • my proposition is that the object's resistance to a change in momentum (its inertia - which is tied to its mass) is what causes you to be forced backwards if you were to (as an example) push off of the International Space Station when doing a space walk. Why must we say that it is a mysterious counter force that the universe decides to propagate "just because" when the properties of inertia could probably explain this? There are theories about how inertia could actually be an emerging property from space-time distortion. – Mike S Mar 04 '14 at 03:26
  • @MikeS Inertia only 'explains' why a force has to be applied to an object to cause it to accelerate, but does not account for the reaction force. The universe does not 'decide' to propagate any mysterious force. We, as physicists, only construct models that describe it. No one 'really' knows why the universe has this 'mysterious force'. – resgh Mar 04 '14 at 03:56
  • How do you know that it doesn't account for the reaction force? How would one construct an experiment to verify that it is separate to the inertia of the objects in the system? To my way of thinking the reaction force is as fictitious as centrifugal force is. – Mike S Mar 04 '14 at 04:18
  • @MikeS Quoting Wikipedia: 'Inertia is the resistance of any physical object to any change in its state of motion (including a change in direction). In other words, it is the tendency of objects to keep moving in a straight line at constant linear velocity' So the definition of inertia basically just says to accelerate an object, you must apply a force'. Though it may seem natural for some form of compensation to exist, you CANNOT directly deduce this compensation (Third Law) from inertia. Regarding your request for an experiment, here's a thought experiment: – resgh Mar 04 '14 at 04:27
  • We have two charged particles, one with +q, and another with +10q. They have different masses, and are not touching. By the Third Law, we CAN understand why the forces on both objects are of same magnitude. Inertia, however, doesn't even enter the picture. – resgh Mar 04 '14 at 04:29
  • @MikeS Centrifugal force is a fictions force because it does not exist in an inertial frame. This is not true for reaction forces. They exist in all frames of reference. – resgh Mar 04 '14 at 04:31
  • I'm saying either inertia or the "action/reaction" law must be fictitious unless they can be exhibited to not simply be an extrapolation of the other. To me its fictitiousness is inescapable within the very structure of the wording. An object's intension to collide with another obviously has no effect on the nature of the collision. A post collides with a car as much as a car collides with a post. Therefore, the phrases "equal/opposite" "action/reaction" call for an observer bias as to which is the originating action. Extract observer bias from the phrase and you aren't left with any words. – Mike S Mar 04 '14 at 05:00
  • let us continue this discussion in chat – resgh Mar 04 '14 at 05:02
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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.

sineman
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