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Unformatted text preview: vo (ytv59) oldhomework 01 Turner (56705) 1 This printout should have 10 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Three identical point charges hang from three strings, as shown. 45 45 F g 12.0 cm 12.0 cm + + + +q +q +q 0.10 kg 0.10 kg 0.10 kg What is the value of q ? 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: 7 . 92912 10 7 C. Explanation: Let : m = 0 . 10 kg , L = 12 . 0 cm , = 45 , and k e = 8 . 98755 10 9 N m 2 / C 2 . r = 2 L sin = 2 L sin 45 = 2 L 2 2 = L 2 F T,x = F T sin F T,y = F T cos Each sphere is in equilibrium horizontally F electric F T,x = 0 F electric F T sin = 0 and vertically F T,y F g = 0 F T cos F g = 0 F T = F g cos . From the horizontal equilibrium, F electric = parenleftbigg F g cos parenrightbigg sin F electric = F g tan = F g (tan 45 ) = F g . For either of the end charges, F electric = k e q 2 r 2 + k e q 2 ( r 2 ) 2 = k e q 2 r 2 + 4 k e q 2 r 2 = 5 k e q 2 r 2 5 k e q 2 r 2 = mg . Thus  q  = radicalBigg r 2 mg 5 k e = radicalBigg ( L 2) 2 mg 5 k e = L radicalbigg 2 mg 5 k e = (12 cm) parenleftbigg 1 m 100 cm parenrightbigg radicalBigg 2(0 . 1 kg)(9 . 81 m / s 2 ) 5(8 . 98755 10 9 N m 2 / C 2 ) = 7 . 92912 10 7 C . 002 10.0 points There are two identical small metal spheres with charges 82 . 4 C and 50 . 9712 C. The distance between them is 6 cm. The spheres are placed in contact then set at their original distance. Calculate the magnitude of the force between the two spheres at the final position. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . Correct answer: 616 . 502 N. Explanation: vo (ytv59) oldhomework 01 Turner (56705) 2 Let : q A = 82 . 4 C = 8 . 24 10 5 C , q B = 50 . 9712 C = 5 . 09712 10 5 C , and d = 6 cm = 0 . 06 m . When the spheres are in contact, the charges will rearrange themselves until equi librium is reached. Each sphere will then have half of the original total charge: q = q A + q B 2 = 8 . 24 10 5 C 5 . 09712 10 5 C 2 = 1 . 57144 10 5 C . The force between the two spheres is F = k q 2 d 2 = ( 8 . 98755 10 9 N m 2 / C 2 ) (1 . 57144 10 5 C) 2 (0 . 06 m) 2 = 616 . 502 N . 003 10.0 points The diagram shows an isolated, positive charge Q , where point B is twice as far away from Q as point A . + Q A B 10 cm 20 cm The ratio of the electric field strength at point A to the electric field strength at point B is 1....
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 Fall '10
 turner
 Charge, Work

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