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Unformatted text preview: maldonado (om2892) Homework 2 Stone (13750) 1 This printout should have 7 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Two small metallic spheres, each of mass . 17 g are suspended as pendulums by light strings from a common point as shown. The spheres are given the same electric charge, and it is found that the two come to equilib rium when each string is at an angle of 6 . 8 with the vertical. 2 9 . 2 c m 6 . 8 . 17 g . 17 g If each string is 29 . 2 cm long, find the mag nitude of the charge on each sphere. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 and the acceleration of gravity is 9 . 81 m / s 2 . Correct answer: 10 . 2857 nC. Explanation: Let : L = 29 . 2 cm = 0 . 292 m , m = 0 . 17 g = 0 . 00017 kg , and = 6 . 8 . L a m m q q From the right triangle in the figure above, we see that sin = a L a = L sin , and the separation of the spheres is r = 2 a . Consider the forces acting on one of the spheres: F e mg T The sphere is in equilibrium horizontally summationdisplay F x = T sin F e = 0 T sin = F e , and vertically summationdisplay F y = T cos mg = 0 T cos = mg . tan = T sin T cos = F e mg F e = mg tan . From Coulombs law, the electric force be tween the charges has magnitude  F e  = k e  q  2 r 2 , where  q  is the magnitude of the charge on each sphere, so  q  = r radicalBigg  F e  k e = (2 a ) radicalbigg mg tan k e = (2 L sin ) radicalbigg mg tan k e = 2 (0 . 292 m) sin6 . 8 radicalBigg...
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 Summer '10
 Stone
 Mass, Work

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