# With Newton's third law, why are things capable of moving?

I've got a rather humiliating question considering newton's third law

"If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A" -> $F_1=-F_2$

Considering that, 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 same force to me in opposing direction?

I've found a lot of answers considering that question but none was satisfying to an extend that I had an epiphany solving my fundamental problem I've got understanding it.

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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. – DilithiumMatrix Dec 2 '12 at 2:49
Duplicate of ? physics.stackexchange.com/q/2095 – Hobo Dec 2 '12 at 14:23
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! – wim Dec 3 '12 at 0:45
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). – wim Dec 3 '12 at 0:47
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. – ja72 Dec 20 '13 at 14:29

I 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 $F_{matchbox}$ does press back on my finger with an equal magnitude to $F_{finger}$, it's no match for $F_{muscles}$ (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.)

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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"? – Steven Lu Dec 2 '12 at 5:41
@StevenLu because I found it funny, particularly "May cause fire.". – AndrewC Dec 2 '12 at 9:28
@JavierBadia Fixed now. Thanks for pointing out my silly (and ironic) but key mistake. My answer is better now because of your comment. – AndrewC Dec 2 '12 at 21:20
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. – AndrewC Dec 2 '12 at 21:32
+1 for the humour. – centralcharge Jul 1 '13 at 13:46

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 on a body is due to an external force. F1 acts on your box, but not F2. An object can never act on itself.

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Think you mean "motion of a body". – Eugene Seidel Dec 1 '12 at 23:48

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 relevante to the Moon.

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While considering 3rd law, forces act on different bodies , and not on same bodies. So the body which is hit is under the influence of applied external force only. The force which the hit body applies back to the hitting object is acting on the hitting object, so no point of cancelling of forces as they are acting on different objects.

I too used to think that way. Try this experiment : Ask your friend to stand in front of you and both of you try to push each other with approximately same strength, see what happens. Try this with friends of different masses.

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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

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You are using one law (third) that is true, to try to invalidate another unrelated law (second).

Using your own examples, the reason you are able to move the box, is because you apply a force larger that the force produced by friction of the box against the table. If you glue the box on the table, it will take a much larger force to move it! The equal but opposite force that the box exerts against your finger, can only be as large as the friction force (or the glue force), if you exceed it, the box will have to move.

Similarly, the table you mention, can only exert a force against your hand equal to the friction exerted by the table legs on the floor. If you exceed it, the table will definitively move! Just to make this clear, if you put rollers on the table legs, it will take little force to move it, but if you nail the legs to the floor, you might break the legs or nails before it moves. If the force is less that the required amount, nothing (no movement) happens.

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Think of the "a" in F=ma as the instantaneous rate of change in velocity - meaning, how quickly velocity changes at an instant. In calculus terms, a is the derivative of v(t), where t represents time and v(t) = at.

The moment you start moving that box, you are creating a force, because the velocity then is changing instantaneously. At any point, you can reduce the force to be equal to the opposing forces, at which time the "net force", the sum of the aforementioned forces, becomes zero.

So, if you are pushing that box, at some point you must have caused that box to accelerate. The acceleration may have been unnoticeable, but it must have been there, otherwise there would be no change in the velocity.

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action and reaction Depends on the frame eg: if you push matchbox with your fingers kept on a table, from matchbox's frame, we have to see for only those force acting ON the matchbox, not those forces that matchbox applies i.e the reaction force to your fingers So, from matchbox's frame, forces acting on matchbox are: your push, downward mg and normal reaction from table, that is why it moves

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Try to avoid abbreviations ("ur") and run-on sentences. It makes your answer hard to read. – Javier Dec 2 '12 at 7:55
Aside from that, you can "see" all forces from a reference frame, so this answer is wrong. The frames don't matter, it is just that an object moves only due to the forces acting on it. – Manishearth Dec 2 '12 at 14:16

## protected by Qmechanic♦Dec 20 '13 at 13:12

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