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Unformatted text preview: maldonado (om2892) Homework 2 Stone (13750) 1 This print-out should have 7 questions. Multiple-choice 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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