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Newton's third law of motion - why?

  1. Jul 17, 2011 #1
    Greetings everyone, I'm new here!

    I tried searching the forums for my problem, but most deal more with the common misconceptions, not the question why - if there is such a question. Lately, I've been trying to gain an in-depth look into Newton's work, moreover the third law which has been bugging me for quite a while.

    It states, that whenever an object exerts a force on another object, the second one will also exert a force on the first, equal in magnitude, collinear / opposite in direction.


    Why does the other object respond with an equal, opposite force? Is there a causality link I'm missing? I'd really like to understand this more. For example, I can understand that when a bird flaps its wings, the wings exert a force on the air, pushing it out of the way, but at the same time the air exerts a force on the wings, giving them an upward force, lift.

    Perhaps it sounds like a stupid question, but why and how does it happen... When you push on the air, how does it push back on your wings? Is it an intrinsic, observational fact or is there more to it?

    The more ambiguous case to me is the example of the gravitational interaction between our planet and the Sun. The Sun exerts a gravitational force on Earth and Earth returns the "favor", but considering the mass ratio, the center of rotation is pretty much in the Sun.

    Why? Why would Earth exert a force on the Sun, equal in magnitude, opposite in direction? Why wouldn't the Sun just push Earth around?

    Can anybody see what's bothering me? Can you give me a way of looking at this, to find a logical explanation to this... Any insight is helpful! I hope I am making some sense.

    Thanks everyone! You don't have to give me an answer, just point me in the right direction, books, web resources, anything. I am willing to learn, but sometimes stuff doesn't want to be learned by me.
  2. jcsd
  3. Jul 17, 2011 #2


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    Look at the topic historically:
    1. Tycho Brache made thousands of observations: at such date/time planets are seen in such positions, he never cared about any theory behind those observations;
    2. Kepler got confused by Ptolemeian/Copernican concept of epicycles, as he would have to complicate it even more in order to reflect accurate Tycho's observations. He looked for something simpler. He made a lot of calculations, concluding them: if planets obey Kepler laws, their positions are like Tycho spotted. And Kepler laws occured to be much simpler than multiple epicycle model, although it was hard to accept, as the circular motion was the heavenly perfect one, while ellipses were not so ellegant for 17th cent taste. Kepler just chose: better one non-ellegant ellipse with non-uniform motion, than ugly combination of 40+ perfectly circular epicycles.
    Kepler gave no justification for his laws. Or rather he gave: angels are pushing planets that way;
    3. Newton made next step: Kepler laws, but also other earthy phenomena, like falling apples, may be explained by his principles and his law of gravity. We don't need Kepler's angels any longer.

    But Newton gave no further justification. Neither for 3rd law, neither for 1st one. You may equally well ask why if the body is not a subject to external forces its velocity remain constant? Newton did not answer it. He just reduced experimental knowledge about our world to smaller number of simpler laws, treating them as fundamental.

    ``Can anybody see what's bothering me?''
    Not quite. You are either bothered why Newton stopped at that point on the way to find more fundamental causes, or you are asking us (21st century physicists) about thouse causes. I believe I answered you in the first case. If it is the second - I could direct you to Einstein's theories, going further on the way. But (unless you have some religious explanation) the path never ends - we are making just simpler and more ellegant theories, explaining how the world acts, but those theories always must start from some axioms or assumptions, which are taken arbitrarily, just to make our theory fitting to observations by Tycho (and MtPalomar).

    Sample of modern explanation of your question: if the forces wouldn't be balanced, the total momentum of Sun-Earth system wouldn't be conserved. That is not so painful by itself, but there is a correspondence between conservation laws and symmetries. Momentum conservation (thus Newton's 3rd law) is bound to translational symmetry. If 3rd law would be violated, the same experiments would give different results if performed at different places. It is something contrary to our common-sense experience and would destroy the very foundations of the whole physics.
    Last edited: Jul 17, 2011
  4. Jul 17, 2011 #3
    Yeah, I thought that was the case, I was just looking for a confirmation. I'd like to know more about the conservation of momentum (as I understand, it's a repercussion of the third law of motion), but I won't take anymore of your time, I'll try to find a good book and study it more in-depth. Thank you for the assist, it was helpful!

    Just one more question, why is conservation of momentum important?
  5. Jul 17, 2011 #4


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    Because it is equivalent to translational symmetry of our world...
    Could you imagine the world having different laws of physics acting in Berlin and different in London? That would be an implication of breaking translational symmetry (or breaking 3rd law of dynamics, as it is equivalent to translational symmetry)

    Regarding conservation laws <-> symmetry correspondence - try to read something about Noether's theorem, you may start from Wiki: http://en.wikipedia.org/wiki/Noether's_Theorem
  6. Jul 17, 2011 #5
    Thank you very much for the link, I'll try to delve deeper into the subject!
  7. Jul 17, 2011 #6
    @Ledgeknow : just keep in mind one thing in physics. When call something law in physics it simply means it is law . A law is not derived it is just abserved and accepted. We accept it just becoz it happens.A LAW CANT BE PROVED. A law might seem illogical to someone but it is just the truth. So we have to accept it. thats it.

    People do find logic and stories that WHY A LAW IS THERE. but its not correct. It will only take you to another LAW.

    for example i can prove NEWONS III LAW with the help of CONSERVATION OF LINEAR MOMENTUM but it is not a proof as it makes CONSERVATION OF LINEAR MOMENTUM a LAW.

    You see i tried to proove it but it took me to another law.

    Now someone told THE TRANSLATION SYMMETRY and u accepted it. WHY didnt u asked WHY TRANSLATION SYMMETRY. And not asking a 'WHY?' to a theory makes the theory LAW. Thats it. You tried to find a logic behind a LAW and it took you to a new LAW
    Last edited: Jul 17, 2011
  8. Jul 17, 2011 #7

    Philip Wood

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    Gold Member

    Try this informal argument...

    Suppose that two particles have a potential energy E, which is a function of their separation,s. This relies on translational symmetry: if both particles are translated through space by the same displacement, their mutual PE doesn't change.

    Choose a co-ordinate system such that both particles (1 and 2) lie on the x-axix, at x1 and x2 [x1 < x2].

    Then s = x2 - x1.

    Now, the force on particle 1 is F1 = -[itex]\partial[/itex]E/[itex]\partial[/itex]x1 = + dE/ds,

    whereas the force on particle 2 is F2 = -[itex]\partial[/itex]E/[itex]\partial[/itex]x2 = - dE/ds.

    So F1 = - F2
    Last edited: Jul 17, 2011
  9. Jul 17, 2011 #8


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    I see this question has received much attention already but I'll add a tidbit of intuitive logic.

    Think about what would happen if objects did not exert an equal and opposite force when a force is applied.

    It would mean that, if I tried to use my own strength to push on the sun, it would provide no resistance. I could toss the sun about like a basketball!
  10. Jul 18, 2011 #9

    Philip Wood

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    Gold Member

    Can't resist having another crack at this, trying to boil the argument in my last post down to its essentials...

    Suppose two particles, 1 and 2, attract each other with forces depending only on their separation. [This assumes translational symmetry: the forces stay the same even if we displace the particles, provided we keep their separation the same.]

    This means that the system has a certain potential energy. The energy belongs to the whole system and can't be separated into energy belonging to particle 1 and energy belonging to particle 2. For me, this notion of mutual energy is intuitively acceptable, and more 'obvious' than Newton's Third Law. But I'm not claiming that it's more basic than Newton's third law, just that I like it better as a starting point. That said, the argument goes like this...

    If we let particle 2 move by small distance [itex]\delta[/itex]s
    in a direction towards particle 1, particle 2 has work F2 [itex]\delta[/itex]s done on it by the attractive force from particle 1 and the system loses F2 [itex]\delta[/itex]s of potential energy.

    But If we let particle 1 move by the same small distance [itex]\delta[/itex]s
    in a direction towards particle 2, particle 1 has work F1 [itex]\delta[/itex]s done on it by the attractive force from particle 2 and the system loses F1 [itex]\delta[/itex]s of potential energy.

    But by our original postulate that the potential energy depends only on the separation of the particles, these energy changes are equal, so F1 = F2. [These are,of course, magnitudes of forces; their directions are opposite.]
  11. Jul 18, 2011 #10
    No need to be worried ledge :cry: , you see....

    ...You are simply forgetting that law #3 follows law #2 : F = ma

    The equality of the forces is only formal.When you apply the formulas
    F(s) = GMm / r^2 F(e) = GMm/ r^2

    You get the real values:
    F(s) = GM/ r^ 2
    F(e) = Gm/ r^ 2

    so F(s) / F (e) = 333,000

    cheer up! no more nightmares :zzz:
  12. Jul 18, 2011 #11

    Doc Al

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    Staff: Mentor

    What does that mean?

    Nope. You had it right the first time.

  13. Jul 18, 2011 #12


    Staff: Mentor

    The variables highlighted in red are all accelerations, not forces. The forces are equal and opposite, the accelerations are not.
  14. Jul 18, 2011 #13
    I just applied the same explanation given in all scientific textbooks to justify g ! . . (:blushing:)
    Is the force of an apple equal to the force of the earth?
    Doesn't earth give the same acceleration to a feather and a cannonball?

    So isn't F = a , disregarding mass (of the other body) ?

    (My source was Encyclopaedia Britannica)
    Last edited: Jul 18, 2011
  15. Jul 18, 2011 #14


    Staff: Mentor

    Yes, but you have severely misapplied the physical principle. In the absence of air, the earth gives the same acceleration a1 to a feather and a cannonball, and the sun gives the same acceleration a2 to a feather and a cannonball, but that in no way implies that the acceleration from the sun, a2, is equal to the acceleration from the earth, a1.

    You can derive this from the laws as follows:
    f = ma
    f = GMm/r²
    ma = GMm/r²
    a = GM/r²

    So the acceleration of one object depends on the mass of the other object. You can divide out the mass of one object, but you must do so from both sides leaving you an acceleration on the left, not a force. You cannot just willy nilly drop out terms for no reason as you did above. It is mathematically incorrect (illogical) and is inconsistent with experiment.

    No, they cannot possibly be equal. The units are not the same. Always check your units.

    Perhaps you should try a physics textbook instead.
    Last edited: Jul 18, 2011
  16. Jul 18, 2011 #15
    Here is how I understand it.

    When you push on an object, it moves because electrons have charge, the like electromagnetic charges repel each other and when you put them close the electrons push each other away. This force applies both ways. If you try to push a spring together with your fingers, it doesn't want to move and exerts a force, it just pushes in both directions. You can put pressure on with the top finger or the bottom finger, the spring just pushes the same way, meaning there is an equal force in both directions.

    So basically there is a force between any two objects pushing them apart when you try to push them together and this force just pushes, it doesn't matter which body is causing it.
  17. Jul 18, 2011 #16
    1) I never said that.Actually I did not even mention the Sun in that post

    2)That is what I said, but not exactly

    I said that the acc. of an object depends exclusively on the mass of the other object, and NOT on its own mass
    so a feather (in vacuum or not) receives exactly the same acc. of a cannonball, a plane ...
    is that correct?

    (P.S. I need to make an example, could you, kindly, give me some reliable data:
    1) a ball 1 kg is rolling at 1 m/s. what is the F(b) (push) it exerts on an obstacle?
    2) how do you calc F(e) (gravity pull) of earth?
    3)do they obey to exactly the same laws, can I compare freely Fb and Fe to explain my point?

    much obliged
    Last edited: Jul 18, 2011
  18. Jul 18, 2011 #17


    Staff: Mentor

    No, you said that the gravitational force on an object depends exclusively on the mass of the other object. That is not at all the same as saying that the accelerations do. If you had said "acceleration" instead of "force" then neither of us would have corrected you.

    That depends on the Young's modulus and mass of the obstacle.


    No. Fe obeys Newtons law of gravitation. Fb obeys Hookes law.
  19. Jul 18, 2011 #18
    Hi Dalespam, I owe you an explanation,
    and an apology for being too hasty
    ( when I said formal (DocAl) I meant the same as when I apparently dropped the unit.
    that is m = 1 (the same as you get when you reduce 6/8 to 3/4*2/2)
    so, when I say F = a, it is not through stupidity or ignorance but because I'm just meaning
    F / (m=1) = a

    I thought the feather and cannonbal had clarified this point

    at the end of the discussion, if appropriate, I'd be glad to apologize

    1) I know the formula: I want to see how you get your result
    2) you mean that F = ma does not apply here?
    could you please calculate F explicitly, and then calculate the acc. of a feather of 10 grams and a cannonball of 10 kilos?

    Much obliged
  20. Jul 18, 2011 #19


    Staff: Mentor

    That's fine, then you say something like "using units where m=1". However, what you wrote above is still incorrect even so, because there are no units where both the mass of the earth and the mass of the sun are 1.

    You could use two different systems of units for each formula, but again, you would need to say something like "now switching to a system of units where M=1".

    Furthermore, you would not be able to simply divide out the two expressions to obtain the ratio of the forces, since they are in different units. You would have to put in the conversion factor between the different units, which, had you done so, would have demonstrated that the ratio of forces was 1.

    I am travelling and posting on a mobile device, so I won't be doing any calculations. There is no mystery in plugging numbers into a formula.

    It certainly does apply, but what is a? Both f and a are unknown, so you have one equation in two unknowns. You need another equation, known as a force law (e.g. Newton's law of gravitation or Hooke's law), to determine the force.

    Also, note that the f in f=ma is a net force. So you can only set it equal to the force law expression in the situation where that is the only force acting on the object. That is fine for the earth and the sun, but not for a feather dropping in air, nor for a ball colliding with an obstacle.
    Last edited: Jul 18, 2011
  21. Jul 19, 2011 #20
    Hallo Doc,
    are you beginning,now, to see my point? It is a very strong point.

    When you say that a feather gets the same a of a cannonball, you are implicitly admitting that
    (a=k => ( a*m1 = F, a*m2 = F....) => (m1,m2...= 1) => (F = a)

    we can manipulate the formula balancing the two sides (or in any other way),
    but the gist will not change
    Force is acting on all masses in the same way. mass is irrelevant!. This is a hard fact

    You use 6/ 8, and you are right, because hou have the right to do so. And I know also why you have to do so
    I use 3/ 4 and I'm right, too. Maybe a little more. And not only because it is more elegant and simple, but because 3/ 4 means => a= F= G * M (/...) and this
    gives you a tremendous
    insight on what G is (beyond the mere konstant), and most of all
    of what the NATURE of F(G) is
    I DO NOT want to convince you. I'm asking you just to reflect a while on it.
    You, and my dear friend Dalespam, don't have to convince that it is as you say.
    They already convinced me way back in 1959, when they first taught me the formulas.
    I have reflected on it for half a century.I have just a little start

    Good bye Sir, I have been greatly honoured by the attention you have given me.

    I'll go on arguing ad libitum with Dalespam,
    because is an old friend and has more patience with me)
    Last edited: Jul 19, 2011
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