Simple Nature - Light and Matter

As in the preceding example, we have F < 0 when x is positive,because the object is being attracted back toward x = 0.When x is negative, the relationship between r and x becomesr = −x, and the result for the force is the same as before, but witha minus sign. We can combine the two equations by writing|F| = Gm 1 m 2 /r 2 ,and this is the form traditionally known as Newton’s law of gravity.As in the preceding example, the U and F equations containequivalent information, and neither is more fundamental than theother.Equilibrium example 42I previously described the condition for equilibrium as a local maximumor minimum of U. A differentiable function has a zero derivativeat its extrema, and we can now relate this directly to force:zero force acts on an object when it is at equilibrium.170 Chapter 3 Conservation of Momentum