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3 - Copy (2) - tang(nmt352 oldhomework 02 Turner(56705 This...

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tang (nmt352) – oldhomework 02 – 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 You have 1 . 8 kg of water. One mole of water has a mass of 18 . 1 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: 9 . 58218 × 10 7 C. Explanation: Let : N A = 6 . 02214 × 10 23 molec / mol , q e = 1 . 6 × 10 19 C / electron , m = 1 . 8 kg , M = 18 . 1 g / mol = 0 . 0181 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 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) 1 . 8 kg 0 . 0181 kg / mol × ( 6 . 02214 × 10 23 molec / mol ) × ( 1 . 6 × 10 19 C / electron ) = 9 . 58218 × 10 7 C . 002 10.0 points Two identical small charged spheres hang in equilibrium with equal masses as shown in the figure. The length of the strings are equal and the angle (shown in the figure) with the vertical is identical. 0 . 25 m 3 0 . 04 kg 0 . 04 kg Find the magnitude of the charge on each sphere. The acceleration of gravity is 9 . 8 m / s 2 and the value of Coulomb’s constant is 8 . 98755 × 10 9 N m 2 / C 2 . Correct answer: 3 . 95631 × 10 8 C. Explanation: Let : L = 0 . 25 m , m = 0 . 04 kg , and θ = 3 . L a θ m m q q From the right triangle in the figure above, we see that sin θ = a L . Therefore a = L sin θ = (0 . 25 m) sin(3 ) = 0 . 013084 m . The separation of the spheres is r = 2 a = 0 . 026168 m . The forces acting on one of the spheres are shown in the figure below.
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tang (nmt352) – oldhomework 02 – Turner – (56705) 2 θ θ m g F T e T sin θ T cos θ Because the sphere is in equilibrium, the resultant of the forces in the horizontal and vertical directions must separately add up to zero: summationdisplay F x = T sin θ F e = 0 summationdisplay F y = T cos θ m g = 0 . F sin θ F cos θ = F e m g F e = m g tan θ = (0 . 04 kg) ( 9 . 8 m / s 2 ) tan(3 ) = 0 . 0205439 N , for the electric force.
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