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Newton's third law

  1. Feb 7, 2009 #1
    Well i known this is a kinda fundamental property of mechanics but i always have a weird thinking about this law.

    Let me illustrate my trouble with an example.

    Let's say i kick a ball with force F? According to the Law the ball experience F force, and my leg experiences -F. My questions are:

    1. Where is the Force -F actually came from? Since i am the only one putting energy on the ball. How come the ball have energy to exert force -F to me?

    2. Let's say if the answer for question 1 is due to me too, does this imply i have to use twice the energy to produce F and -F??

    (Sorry i think i am kinda confused as well...I be very happy and glad if anyone with clear mind here can help me solve this dilemma. Thanks a lot)
  2. jcsd
  3. Feb 7, 2009 #2


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    1. Regard "force" as the rate of change of the quantity called "momentum" (an object's moment equals the product of its mass and its velocity). Essentially, that is what Newton's 2.law says it is!

    2. Think of a object's "momentum" as a COMMODITY. In particular, it can GIVE AWAY some of its own momentum to another object. Thus, THAT object is GAINING momentum at the rate the first object is giving it away, whereas that FIRST object is LOSING momentum, at exactly the rate it is giving it away!
    The two objects, therefore, can NEVER change the total amount of momentum they have at their disposal; rather, they can only change what portions of momentum
    belongs to one or the other.
    One object's loss is the other object's gain.
    The rate of gaining (i.e, the force acting upon the "beneficiary") must therefore balance the rate of losing (i.e, the "reaction" force action upon the "giver")

    Does that clarify the issue for you?
  4. Feb 7, 2009 #3
    Athough the net force on something is the rate of change of its momentum, Newton's third law also applies to some cases where the velocities are zero and therefore everything's momentum is zero.

    A cup sits motionless on a table. Gravity makes the cup pushes downward on the table, and the table pushes upward on the cup with an oppositely directed force of equal magnitude. The force of the cup pushing down has made the springy molecular bonds of the table become compressed, and now the cup experiences a compressed spring's restoring force pushing upwards on it.

    Until I meditated on the image of those springy molecular bonds, I had difficulty picturing what going on in the example of two people playing "tug of war" with a rope, each person pulling on the rope with 5 N of force, in opposite directions, for a net force of zero. What amazed me was learning the fact that the tension in that rope is exactly the same as if you were to have just one person pulling the rope with 5 N of force, and the other end of the rope were simply tied to the wall. In the latter case, the elastic molecular structure in the wall is the other "player" who is now pulling the other end of the rope with the necessary 5 N of force.

    Generalizing this now to a dynamic case, such as kicking the football. The elastic nature of a rubber ball is obvious. The elastic nature of a rock that's being kicked isn't so obvious, but it's there. The molecules in a rock are merely displaced much shorter distances than those of a rubber ball, to produce the same amount of elastic restoring force.
    Last edited: Feb 7, 2009
  5. Feb 7, 2009 #4
    1. Exerting a force doesn't necessarily require an expense of energy. You're pushing a wall attached to the earth. The wall is too heavy to have any significant energy gain and the friction prevents you from moving back. So though you've sweat droplets dotting your entire face as a result of this exertion, energy expenditure theoretically is, sorry, zero!

    2. But in this case yes, the energy from your body was used up to increase the individual K.Es of both you and the ball. Consider a "slightly" bigger ball, earth. You push it and you walk(or drive your honda). This time almost all the energy extracted from your calories would be used up in increasing your KE alone. The former doesn't consume much K.E and your walking is essentially energy-efficient.
  6. Feb 10, 2009 #5
    Thanks a lot! I think i get it now...so i shouldn't confuse the term energy and force...
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