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## Newton's third law of motion

Suppose, for the sake of argument, that there are only two bodies in the Universe. Let us label these bodies and . Suppose that body exerts a force on body . According to to Newton's third law of motion, body must exert an equal and opposite force on body . See Fig. 22. Thus, if we label the action'' then, in Newton's language, is the equal and opposed reaction''.

Suppose, now, that there are many objects in the Universe (as is, indeed, the case). According to Newton's third law, if object exerts a force on object then object must exert an equal and opposite force on object . It follows that all of the forces acting in the Universe can ultimately be grouped into equal and opposite action-reaction pairs. Note, incidentally, that an action and its associated reaction always act on different bodies.

Why do we need Newton's third law? Actually, it is almost a matter of common sense. Suppose that bodies and constitute an isolated system. If then this system exerts a non-zero net force on itself, without the aid of any external agency. It will, therefore, accelerate forever under its own steam. We know, from experience, that this sort of behaviour does not occur in real life. For instance, I cannot grab hold of my shoelaces and, thereby, pick myself up off the ground. In other words, I cannot self-generate a force which will spontaneously lift me into the air: I need to exert forces on other objects around me in order to achieve this. Thus, Newton's third law essentially acts as a guarantee against the absurdity of self-generated forces.

Next: Mass and weight Up: Newton's laws of motion Previous: Hooke's law
Richard Fitzpatrick 2006-02-02