hw1 - Lieu (vml232) HW #1 Antoniewicz (56490) 1 This...

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Unformatted text preview: Lieu (vml232) HW #1 Antoniewicz (56490) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A particle of mass 42 g and charge 84 C is released from rest when it is 42 cm from a second particle of charge 13 C. Determine the magnitude of the initial ac- celeration of the 42 g particle. Correct answer: 1324 . 69 m / s 2 . Explanation: Let : m = 42 g , q = 84 C = 8 . 4 10 5 C , d = 42 cm = 0 . 42 m , Q = 13 C = 1 . 3 10 5 C , and k e = 8 . 9875 10 9 . The force exerted on the particle is F = k e | q 1 || q 2 | r 2 = ma bardbl vectora bardbl = k e bardbl vectorq bardblbardbl vector Q bardbl md 2 = k e vextendsingle vextendsingle 8 . 4 10 5 C vextendsingle vextendsingle vextendsingle vextendsingle 1 . 3 10 5 C vextendsingle vextendsingle (0 . 042 kg) (0 . 42 m 2 ) = 1324 . 69 m / s 2 . 002 10.0 points Two small silver spheres, each with a mass of 57 g, are separated by 1 . 53 m. The num- ber of electrons per atom of silver is 47, and the number of atoms per gram is Avogadros number divided by the molar mass of silver, 107 . 87 g / mol. Calculate the fraction of the electrons in one sphere that must be transferred to the other in order to produce an attrac- tive force of 10000 N (about a ton) be- tween the spheres. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 and the Avogadros number is 6 . 02214 10 23 mol 1 . Correct answer: 6 . 735 10 10 . Explanation: Let : m = 57 g , r = 1 . 53 m , n Ag = 47 , M Ag = 107 . 87 g / mol , f = 10000 N , and k e = 8 . 98755 10 9 N m 2 / C 2 . The force between the spheres is F = k e q 2 r 2 q = r radicalbigg F k e . The total charge is q = nq e n transferred = q q e = r q e radicalbigg F k e = 1 . 53 m 1 . 60218 10 19 C radicalBigg 10000 N 8 . 98755 10 9 N m 2 / C 2 = 1 . 0073 10 16 where q e is the charge of one electron. There are n atoms = m M Ag N A atoms in each sphere, where N A is Avogadros number, so the total number of electrons is n electrons = n Ag n atoms = n Ag mN A M Ag = 47(57 g) 107 . 87 g / mol (6 . 02214 10 23 mol 1 ) = 1 . 49562 10 25 . Thus the ratio is R = n transferred n electrons = 1 . 0073 10 16 1 . 49562 10 25 = 6 . 735 10 10 . Lieu (vml232) HW #1 Antoniewicz (56490) 2 The fraction of electrons needed to create a significant force is very tiny. When we talk about the charge of macro- scopic objects (like the silver spheres in this problem), we generally mean the surplus charge, which corresponds to only a tiny frac- tion of the total number of electrons in the material....
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hw1 - Lieu (vml232) HW #1 Antoniewicz (56490) 1 This...

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