47130_hw1 - ragsdale(zdr82 HW1 ditmire(58335 This print-out...

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ragsdale (zdr82) – HW1 – ditmire – (58335) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Two spheres, fastened to “pucks”, are rid- ing on a frictionless airtrack. Sphere “1” is charged with 3 nC, and sphere “2” is charged with 6 nC. Both objects have the same mass. 1 nC is equal to 1 × 10 9 C. As they repel, 1. they do not accelerate at all, but rather separate at constant velocity. 2. sphere “2” accelerates 4 times as fast as sphere “1”. 3. sphere “1” accelerates 4 times as fast as sphere “2”. 4. sphere “1” accelerates 2 times as fast as sphere “2”. 5. they have the same magnitude of acceler- ation. correct 6. sphere “2” accelerates 2 times as fast as sphere “1”. Explanation: The force of repulsion exerted on each mass is determined by F = 1 4 π ǫ 0 Q 1 Q 2 r 2 = m a where r is the distance between the centers of the two spheres. bardbl vector F 12 bardbl = bardbl vector F 21 bardbl Since both spheres have the same mass and are subject to the same force, they have the same acceleration. 002 10.0 points A negatively charged balloon has 3 . 7 μ C of charge. How many excess electrons are on this bal- loon? Correct answer: 2 . 3125 × 10 13 electrons. Explanation: Let : q = 3 . 7 μ C and ρ = 1 . 60 × 10 19 C / electron . The charge density is ρ = q N N = q ρ = 3 . 7 × 10 6 C 1 . 6 × 10 19 C / electron = 2 . 3125 × 10 13 electrons . 003 10.0 points You have 2 . 6 kg of water. One mole of water has a mass of 17 . 9 g / mol and each molecule of water contains 10 electrons since water is H 2 O. What is the total electron charge contained in this volume of water? Correct answer: 1 . 39956 × 10 8 C. Explanation: Let : N A = 6 . 02214 × 10 23 molec / mol , q e = 1 . 6 × 10 19 C / electron , m = 2 . 6 kg , M = 17 . 9 g / mol = 0 . 0179 kg / mol , and Z = 10 electrons / molec . The mass is proportional to the number of molecules, so for m grams in n molecules and M grams in N A molecules, m M = n N A n = m M N A Since 10 electrons are in each molecule of water, then the total number of electrons n e in the coin is n e = Z n = Z m M N A
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ragsdale (zdr82) – HW1 – ditmire – (58335) 2 and the total charge q for the n e electrons is q = n e q e = Z m N A q e M = (10 electrons / molec) 2 . 6 kg 0 . 0179 kg / mol × ( 6 . 02214 × 10 23 molec / mol ) × ( 1 . 6 × 10 19 C / electron ) = 1 . 39956 × 10 8 C . 004 10.0 points Three identical point charges, each of mass 160 g and charge + q , hang from three strings, as in the figure. The acceleration of gravity is 9 . 8 m / s 2 , and the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . 9 . 8 m / s 2 10 . 5 cm 160 g + q 10 . 5 cm 160 g + q 40 160 g + q If the lengths of the left and right strings are each 10 . 5 cm, and each forms an angle of 40 with the vertical, determine the value of q . Correct answer: 0 . 7304 μ C.
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