oldhomework 01-solutions

# oldhomework 01-solutions - WANG(xw788 oldhomework 01...

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WANG (xw788) – oldhomework 01 – Turner – (59070) 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 uncharged metal balls, Z and X , stand on insulating glass rods. A third ball, carrying a positive charge, is brought near the ball X as shown in the figure. A conducting wire is then run between Z and X and then removed. Finally the third ball is removed. X Z + conducting wire When all this is finished 1. ball Z is positive and ball X is neutral. 2. ball Z is negative and ball X is neutral. 3. balls Z and X are both negative, but ball X carries more charge than ball Z . 4. balls Z and X are both negative, but ball Z carries more charge than ball X . 5. balls Z and X are both positive. 6. ball Z is negative and ball X is positive. 7. balls Z and X are still uncharged. 8. ball Z is neutral and ball X is positive. 9. ball Z is neutral and ball X is negative. 10. ball Z is positive and ball X is negative. correct Explanation: When the conducting wire is run between Z and X , some positive charge flows from X to Z under the influence of the positive charge of the third ball. Therefore, after the wire is removed, Z is charged positive and X is charged negative. 002 10.0 points Three identical point charges hang from three strings, as shown. The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 , and the acceleration of gravity is 9 . 81 m / s 2 . 45 45 F g 35.0 cm 35.0 cm + + + +q +q +q 0.10 kg 0.10 kg 0.10 kg What is the value of q ? Correct answer: 2 . 31266 × 10 6 C. Explanation: Let : m = 0 . 10 kg , L = 35 . 0 cm , θ = 45 , and k e = 8 . 98755 × 10 9 N · m 2 / C 2 . r = 2 L sin θ = 2 L sin 45 = 2 L 2 2 = L 2 F T,x = F T sin θ F T,y = F T cos θ Each sphere is in equilibrium horizontally F electric F T,x = 0 F electric F T sin θ = 0 and vertically F T,y F g = 0 F T cos θ F g = 0 F T = F g cos θ .

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WANG (xw788) – oldhomework 01 – Turner – (59070) 2 From the horizontal equilibrium, F electric = parenleftbigg F g cos θ parenrightbigg sin θ F electric = F g tan θ = 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 = m g . Thus | q | = radicalBigg r 2 m g 5 k e = radicalBigg ( L 2) 2 m g 5 k e = L · radicalbigg 2 m g 5 k e = (35 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 ) = 2 . 31266 × 10 6 C . 003 (part 1 of 2) 10.0 points Two identical small metal spheres with q 1 > 0 and | q 1 | > | q 2 | attract each other with a force of magnitude 74 . 6 mN, as shown in the figure below. F 21 F 12 bardbl vector F bardbl = 74 . 6 mN 4 . 18 m q 1 q 2 r 1 = 16 μ m r 2 = 16 μ m Figure 1: Before touching The spheres are then brought together until they are touching. At this point, the spheres are in electrical contact so that the charges can move from one sphere to the other until both spheres have the same final charge, q .
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