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Unformatted text preview: vo (ytv59) oldhomework 01 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 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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