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Unformatted text preview: Madrid (nm7736) HW#1 Sharma (21539) 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 identical small charged spheres hang in equilibrium with equal masses as shown in the figure. The length of the strings are equal and the angle (shown in the figure) with the vertical is identical. The acceleration of gravity is 9 . 8 m / s 2 and the value of Coulombs constant is 8 . 98755 10 9 N m 2 / C 2 . . 2 4 m 6 . 01 kg . 01 kg Find the magnitude of the charge on each sphere. Correct answer: 5 . 37129 10 8 C. Explanation: Let : L = 0 . 24 m , m = 0 . 01 kg , and = 6 . L a m m q q From the right triangle in the figure above, we see that sin = a L . Therefore a = L sin = (0 . 24 m) sin(6 ) = 0 . 0250868 m . The separation of the spheres is r = 2 a = . 0501737 m . The forces acting on one of the spheres are shown in the figure below. m g F T e T sin T cos Because the sphere is in equilibrium, the resultant of the forces in the horizontal and vertical directions must separately add up to zero: summationdisplay F x = T sin - F e = 0 summationdisplay F y = T cos - m g = 0 . From the second equation in the system above, we see that T = m g cos , so T can be eliminated from the first equation if we make this substitution. This gives a value F e = m g tan = (0 . 01 kg) ( 9 . 8 m / s 2 ) tan(6 ) = 0 . 0103002 N , for the electric force. 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....
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