Given Newton's third law, why is there motion at all? Should not all forces even themselves out, so nothing moves at all? When I push a table using my finger, the table applies the same force onto my finger like my finger does on the table just with an opposing direction, nothing happens except that I feel the opposing force. But why can I push a box on a table by applying force ( $F=ma$ ) on one side, obviously outbalancing the force the box has on my finger and at the same time outbalancing the friction the box has on the table? I obviously have the greater mass and acceleration as for example the matchbox on the table and thusly I can move it, but shouldn't the third law prevent that from even happening? Shouldn't the matchbox just accommodate to said force and applying the same force to me in opposing direction?
asked Dec 1, 2012 at 22:41 2,013 3 3 gold badges 13 13 silver badges 6 6 bronze badges$\begingroup$ There are excellent answers below. I wanted to add that on the system scale (i.e. all objects together) the forces DO cancel out---that's why momentum is conserved. $\endgroup$
Commented Dec 2, 2012 at 2:49 $\begingroup$ Duplicate of ? physics.stackexchange.com/q/2095 $\endgroup$ Commented Dec 2, 2012 at 14:23$\begingroup$ Here's a point of view that helped me to "get" this question: If the matchbox didn't push back on your finger with equal force, your finger would go right through it as if it were a ghost! $\endgroup$
Commented Dec 3, 2012 at 0:45$\begingroup$ Note that the acceleration of the object (i.e. matchbox) depends on its mass and the net sum of forces acting upon it. Crucially, it does not depend on forces which the object exerts upon other things (i.e. finger). $\endgroup$
Commented Dec 3, 2012 at 0:47$\begingroup$ There must be hundreds of questions similar to this one, all as a result of physics teachers forgetting to insert the words "..acting on different bodies" when explaining the 3rd law. $\endgroup$
Commented Dec 20, 2013 at 14:29I think it's a great question, and enjoyed it very much when I grappled with it myself.
Here's a picture of some of the forces in this scenario. $^\dagger$ The ones that are the same colour as each other are pairs of equal magnitude, opposite direction forces from Newton's third law. (W and R are of equal magnitude in opposite directions, but they're acting on the same object - that's Newton's first law in action.)
While $F_\text$ does press back on my finger with an equal magnitude to $F_\text$ , it's no match for $F_\text$ (even though I've not been to the gym in years).
At the matchbox, the forward force from my finger overcomes the friction force from the table. Each object has an imbalance of forces giving rise to acceleration leftwards.
The point of the diagram is to make clear that the third law makes matched pairs of forces that act on different objects. Equilibrium from Newton's first or second law is about the resultant force at a single object.
$\dagger$ (Sorry that the finger doesn't actually touch the matchbox in the diagram. If it had, I wouldn't have had space for the important safety notice on the matches. I wouldn't want any children to be harmed because of a misplaced force arrow. Come to think of it, the dagger on this footnote looks a bit sharp.)
617 1 1 gold badge 4 4 silver badges 16 16 bronze badges answered Dec 2, 2012 at 0:07 2,197 1 1 gold badge 13 13 silver badges 10 10 bronze badges$\begingroup$ This answer is completely awesome. My question to you is how on earth did you decide it that it was better to write in an entire warning label instead of removing the word "match"? $\endgroup$
Commented Dec 2, 2012 at 5:41$\begingroup$ Just a little thing: the reaction force from the table shouldn't be paired with the matchbox's weight. $\endgroup$
Commented Dec 2, 2012 at 7:54 $\begingroup$ @StevenLu because I found it funny, particularly "May cause fire.". $\endgroup$ Commented Dec 2, 2012 at 9:28$\begingroup$ @JavierBadia Fixed now. Thanks for pointing out my silly (and ironic) but key mistake. My answer is better now because of your comment. $\endgroup$
Commented Dec 2, 2012 at 21:20$\begingroup$ A nice exercise is to draw the table, matchbox, person and earth and find as many third law matched pairs you can (remember to make sure they're acting on different objects). There's an answer to be found in the revision history of my answer (click the link after the word edited), but I hid it because I feel it distracts from the main part of the answer. $\endgroup$
Commented Dec 2, 2012 at 21:32 $\begingroup$I had similar problem in understanding the 3rd law. I found the answer myself while sitting in my study chair which has wheels!
sitting in the chair, I folded my legs up so that they are not in touch with ground. Now I pushed the wall with my hands. Of course, wall didn't move but my chair and I moved backward! why? because wall pushed me back and wheels could overcome the friction.
I was mixing up things earlier : trying to cancel the forces where one cannot.
Movement of the matchbox is due to the force which you apply on it. period.
Now why you didn't move when matchbox applied the equal force on you is because of the friction. If you reduce the friction like I did sitting in the chair, you would also move in opposite direction.
Equilibrium can only establish itself when the forces are on the same object..
Alas, I am free from this confusion.. such a relief
answered Jan 20, 2015 at 13:06 941 1 1 gold badge 9 9 silver badges 13 13 bronze badges$\begingroup$ @wondering Maybe, but to the beginner, Fmuscles clearly act on my hand (which is in the picture), whereas the friction is on my feet or rear end (which are not). Also, since my hand and my body move independently of each other in this scenario, I feel that considering my entire body as a single particle in this instance is invalid. A force acts on my hand to move it forwards. It is not friction; friction always opposes motion rather than producing it. For all these reasons I conclude that calling it friction would cause more confusion for a beginner, not less. $\endgroup$
Commented Feb 20, 2020 at 15:32 $\begingroup$In any financial transaction the money given is equal to the money received. (If I give you \$ 10 I am \$ 10 poorer and you are \$ 10 better off.) So how does anyone get rich?
answered May 29, 2018 at 19:58 RogerJBarlow RogerJBarlow 10.1k 1 1 gold badge 21 21 silver badges 45 45 bronze badges$\begingroup$ This fantastic answer goes directly to the heart of the question. If we sum +\$10 and -\$10 we get \$0, but the mistake is in considering those two numbers as applying to the same person, whereas in reality they apply to different people. This is epically clear and deserves more prominence. $\endgroup$
Commented Feb 20, 2020 at 15:36 $\begingroup$ Just an amazing thought (: $\endgroup$ Commented Oct 5, 2021 at 18:01$\begingroup$ This might be the most intuitive approach to an answer to this question that I've ever seen. +1 $\endgroup$
Commented May 20, 2022 at 22:11 $\begingroup$Forces related to Newton's third law apply to different bodies, therefore they cannot cancel each other out.
For example, the reaction to Earth's gravitational pull on the Moon is the Moon's pull on Earth. That force won't have any relevance to the Moon.
answered Dec 1, 2012 at 22:46 564 3 3 silver badges 7 7 bronze badges $\begingroup$Good! This question implies that you're thinking hard and questioning the laws. It turns out that you are misunderstanding Newton's 2nd Law though. Motion of a body is due to an external force. F1 (force of finger on box) acts on your box, but not F2 (force of box on finger). An object can never act on itself.
answered Dec 1, 2012 at 22:55 Chris Gerig Chris Gerig 2,768 20 20 silver badges 28 28 bronze badges $\begingroup$ Think you mean "motion of a body". $\endgroup$ Commented Dec 1, 2012 at 23:48 $\begingroup$If I could only change one thing about physics education, it would be the phrasing of Newton's 3rd law. According to my copy of Magnificent Principia (by Colin Pask, Prometheus Books, 2013) the "To every action there is always opposed an equal reaction. " phrasing is Newton's. And it's been causing confusion ever since.
To get a sense of what Newton really meant, consider the universal gravitation equation: $$F=G\frac$$
Notice there are two masses specified, but there is no "source" mass and no "target" mass. And there is only one force produced by this equation. Now, you can look at it as two different forces: $m_1$ attracting $m_2$ and $m_2$ attracting $m_1$ . But that is misleading. It gives the impression that the forces somehow have independent existences. But they don't. They are completely, inextricably linked. So much so, that I think it makes much more sense to this of this as one attractive force between two masses.
Coulombs law follows the same format:
Again, you can think of this as two different forces. But I think the equation really hints at a single attractive force (different charge signs) or a single repulsive force (identical charge signs) between two charges.
That is what Newton meant by his third law. It's not possible for $m_1$ to attract $m_2$ without $m_1$ being caught up in the very same force of attraction between the two particles. And it's not possible for $q_1$ to attract or repel $q_2$ without $q_1$ being caught up in the very same force.
Newton's third law is traditionally taught as pairs of forces. I think it makes more sense to present it is as a single force that must always operate between pairs of bodies, as implied by Coulomb's law and the Universal Gravitation equation.
This is harder to see with contact forces. Part of the problem is that human muscles must constantly expend energy at a molecular level in order to stay contracted. So it's easy to confuse force exertion with expenditure of energy. And humans have cognition and agency. So to say, "The person pushes on the matchbox and the matchbox pushes on the person" feels wrong because the person is expending energy; the matchbox is not. The person has agency and initiates the push; the matchbox is inanimate.
To get a better feel for Newton's third law, consider yourself in a deep swimming pool where your feet are off the bottom. You're next to the wall. Now push on the wall. What happens? You push yourself away from the wall. The traditional explanation is that you push on the wall, and "the wall pushes back on you." And while that is technically true, it doesn't make intuitive sense because you know darn well that you're the one doing the pushing.
What's really happening is that you create a repulsive force between the wall and yourself. The wall is fixed to the earth and the earth is mighty big and hard to move. So the repulsive force manifests itself in you pushing yourself away from the wall.
When you "push the matchbox," you're really setting up a repulsive force between your finger and the matchbox. (At a molecular level, this is just the Coulomb repulsion, of course.) But you're much more massive than the matchbox. Your weight and the friction between your shoes and the floor essentially fix you to the floor and make you immovable. So the repulsive force manifests itself as the matchbox moving.
So many physics problems are expressed as "A attracts B" or "A repels B." That wording is misleading at best. What really happens is that "A and B attract each other" or "A and B repel each other." Always. That is Newton's 3rd law.
Finally, when dealing with forces where one mass (or one charge) is fixed in some way, or so much larger than the other (such as an apple falling towards the earth), it's very common to ignore that fact that the masses are attracting each other, and to phrase the interaction as if it were just the earth attracting the apple and nothing more. That is an oversimplification. But it's justified by the fact that the attractive force between the two masses is overwhelmingly manifested in the motion of the apple.
In fact, Newton phrased that part well in The Principia,
"The changes made by these actions are equal . . . if the bodies are not hindered by any other impediments . . . the changes of velocities made towards common parts are reciprocally proportional to the bodies [the masses]."
