Midterm 1 (Solutions) - oldmidterm 01 KANUNGO ANIL Due...

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oldmidterm 01 – KANUNGO, ANIL – Due: Sep 18 2007, 11:00 pm 1 Question 1, chap 22, sect 2. part 1 of 1 10 points Two spheres fastened to “pucks” are rid- ing on a frictionless airtrack. Sphere “1” is charged with 1 nC, and sphere “2” is charged with 5 nC. Both objects have the same mass. 1 nC is equal to 1 × 10 9 C. As they repel, 1. sphere “2” accelerates 25 times as fast as sphere “1”. 2. sphere “1” accelerates 5 times as fast as sphere “2”. 3. sphere “2” accelerates 5 times as fast as sphere “1”. 4. sphere “1” accelerates 25 times as fast as sphere “2”. 5. they have the same magnitude of acceler- ation. correct 6. they do not accelerate at all, but rather separate at constant velocity. 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 m 1 a 1 = m 2 a 2 . Since both spheres have the same mass and are subject to the same force, they have the same acceleration. Question 2, chap 23, sect 1. part 1 of 1 10 points Three equal charges of 8 μ C are in the x - y plane. One is placed at the origin, another is placed at (0 . 0 , 16 cm), and the last is placed at (89 cm , 0 . 0). Calculate the magnitude of the force on the charge at the origin. The value of the Coulomb constant is 9 × 10 9 N m 2 / C 2 . Correct answer: 22 . 5117 N (tolerance ± 1 %). Explanation: Let : q = 8 μ C = 8 × 10 6 C , ( x 1 , y 1 ) = (0 , 16 cm) = (0 , 0 . 16 m) , ( x 2 , y 2 ) = (89 cm , 0) = (0 . 89 m , 0) , and ( x 0 , y 0 ) = (0 , 0) . The electric field along the y -axis is E y = k e q x 2 1 + y 2 1 = ( 9 × 10 9 N m 2 / C 2 )( 8 × 10 6 C ) 0 + (0 . 16 m) 2 = 2 . 8125 × 10 6 N / C , and along the x -axis E x = k e q x 2 2 + y 2 2 = ( 9 × 10 9 N m 2 / C 2 )( 8 × 10 6 C ) (0 . 89 m) 2 + 0 = 90897 . 6 N / C , so E = radicalBig E 2 x + E 2 y and F = q E = q radicalBig E 2 x + E 2 y = ( 8 × 10 6 C ) × radicalBig (2 . 8125 × 10 6 N / C) 2 + (90897 . 6 N / C) 2 = 22 . 5117 N . Question 3, chap 22, sect 2. part 1 of 1 10 points Two identical small charged spheres hang in equilibrium with equal masses as shown in
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oldmidterm 01 – KANUNGO, ANIL – Due: Sep 18 2007, 11:00 pm 2 the figure. The length of the strings are equal and the angles with the vertical are identical. 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 . 0 . 09 m 6 0 . 03 kg 0 . 03 kg Find the magnitude of the charge on each sphere. Correct answer: 3 . 48875 × 10 8 C (tolerance ± 1 %). Explanation: Let : L = 0 . 09 m , m = 0 . 03 kg , and θ = 6 . L a θ m m q q From the right triangle in the figure above, we see that sin θ = a L a = L sin θ = (0 . 09 m) sin(6 ) = 0 . 00940756 m . The separation of the spheres is r = 2 a = 0 . 0188151 m . Consider the forces acting on the left sphere: θ θ m g F T e T sin θ T cos θ Because the sphere is in equilibrium, summationdisplay F x = T sin θ F e = 0 T sin θ = F e and summationdisplay F y = T cos θ m g = 0 T cos θ = m g .
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