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731_Physics ProblemsTechnical Physics

# 731_Physics ProblemsTechnical Physics - 71 Chapter...

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Chapter 25 71 *P25.64 Take the illustration presented with the problem as an initial picture. No external horizontal forces act on the set of four balls, so its center of mass stays fixed at the location of the center of the square. As the charged balls 1 and 2 swing out and away from each other, balls 3 and 4 move up with equal y -components of velocity. The maximum-kinetic- energy point is illustrated. System energy is conserved: k q a k q a mv mv mv mv k q a mv v k q am e e e e 2 2 2 2 2 2 2 2 2 3 1 2 1 2 1 2 1 2 2 3 2 3 = + + + + = = v + 2 4 v 3 v v + 1 CM FIG. P25.64 P25.65 For the given charge distribution, V x y z k q r k q r e e , , b g b g b g = + 1 2 2 where r x R y z 1 2 2 2 = + + + a f and r x y z 2 2 2 2 = + + . The surface on which V x y z , , b g = 0 is given by k q r r e 1 2 0 1 2 F H G I K J = , or 2 1 2 r r = . This gives: 4 4 4 2 2 2 2 2 2 x R y z x y z + + + = + + a f which may be written in the form: x y z R x y z R 2 2 2 2 8 3 0 0 4 3 0 + + + F H G I K J + + + F H G I K J = a f a f . [1] The general equation for a sphere of radius a centered at
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