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Unformatted text preview: villarreal (mfv229) – HW #1 – Antoniewicz – (56495) 1 This printout should have 23 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A particle of mass 47 g and charge 23 μ C is released from rest when it is 31 cm from a second particle of charge − 10 μ C. Determine the magnitude of the initial ac celeration of the 47 g particle. Correct answer: 457 . 663 m / s 2 . Explanation: Let : m = 47 g , q = 23 μ C = 2 . 3 × 10 − 5 C , d = 31 cm = 0 . 31 m , Q = − 10 μ C = − 1 × 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 2 . 3 × 10 − 5 C vextendsingle vextendsingle vextendsingle vextendsingle − 1 × 10 − 5 C vextendsingle vextendsingle (0 . 047 kg) (0 . 31 m 2 ) = 457 . 663 m / s 2 . 002 10.0 points Two small silver spheres, each with a mass of 113 g, are separated by 0 . 46 m. The num ber of electrons per atom of silver is 47, and the number of atoms per gram is Avogadro’s 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 Avogadro’s number is 6 . 02214 × 10 23 mol − 1 . Correct answer: 1 . 02141 × 10 − 10 . Explanation: Let : m = 113 g , r = 0 . 46 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 = . 46 m 1 . 60218 × 10 − 19 C × radicalBigg 10000 N 8 . 98755 × 10 9 N · m 2 / C 2 = 3 . 02849 × 10 15 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 Avogadro’s number, so the total number of electrons is n electrons = n Ag n atoms = n Ag mN A M Ag = 47(113 g) 107 . 87 g / mol × (6 . 02214 × 10 23 mol − 1 ) = 2 . 96501 × 10 25 . Thus the ratio is R = n transferred n electrons = 3 . 02849 × 10 15 2 . 96501 × 10 25 = 1 . 02141 × 10 − 10 . villarreal (mfv229) – HW #1 – Antoniewicz – (56495) 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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 Spring '10
 Antoniewicz
 Physics, Charge, Mass, Electric charge, ea, Villarreal

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