turner old hw 2 - linares (jl36797) oldhomework 02 Turner...

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Unformatted text preview: linares (jl36797) oldhomework 02 Turner (56705) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Two identical positive charges exert a repul- sive force of 6 . 2 10 9 N when separated by a distance 3 . 6 10 10 m. Calculate the charge of each. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . Correct answer: 2 . 99004 10 19 C. Explanation: Let : F = 6 . 2 10 9 N , d = 3 . 6 10 10 m , and k e = 8 . 98755 10 9 N m 2 / C 2 . The electric force is F = k e q 1 q 2 d 2 d 2 F k e = q 2 q = radicalBigg d 2 F k e = radicalBigg (3 . 6 10 10 m) 2 (6 . 2 10 9 N) 8 . 98755 10 9 N m 2 / C 2 = 2 . 99004 10 19 C . 002 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. . 2 m 3 . 02 kg . 02 kg Find the magnitude of the charge on each sphere. 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 . Correct answer: 2 . 23803 10 8 C. Explanation: Let : L = 0 . 2 m , m = 0 . 02 kg , and = 3 . 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 . 2 m) sin(3 ) = 0 . 0104672 m . The separation of the spheres is r = 2 a = . 0209344 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 mg = 0 . linares (jl36797) oldhomework 02 Turner (56705) 2 F sin F cos = F e mg F e = mg tan = (0 . 02 kg) ( 9 . 8 m / s 2 ) tan(3 ) = 0 . 0102719 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 | q | = radicalBigg | F e | r 2 k e = radicalBigg (0 . 0102719 N) (0 . 0209344 m) 2 (8 . 98755 10 9 N m 2 / C 2 ) = 2 . 23803 10 8 C ....
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turner old hw 2 - linares (jl36797) oldhomework 02 Turner...

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