oldmidterm 01

# oldmidterm 01 - nguyen(jmn727 – oldmidterm 01 – Turner...

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Unformatted text preview: nguyen (jmn727) – oldmidterm 01 – Turner – (59070) 1 This print-out should have 19 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 15 nC. Both objects have the same mass. 1 nC is equal to 1 × 10 − 9 C. As they repel, 1. they have the same magnitude of acceler- ation. correct 2. sphere “1” accelerates 25 times as fast as sphere “2”. 3. sphere “2” accelerates 25 times as fast as sphere “1”. 4. sphere “2” accelerates 5 times as fast as sphere “1”. 5. sphere “1” accelerates 5 times as fast as sphere “2”. 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 Q 1 Q 2 r 2 = ma 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 Three equal charges of 9 μ C are in the x- y plane. One is placed at the origin, another is placed at (0.0, 23 cm), and the last is placed at (77 cm, 0.0). The Coulomb constant is 9 × 10 9 N m 2 / C 2 . Calculate the magnitude of the force on the charge at the origin. Correct answer: 13 . 8355 N. Explanation: Let : q = 9 μ C = 9 × 10 − 6 C , ( x 1 , y 1 ) = (0 , 23 cm) = (0 , . 23 m) , ( x 2 , y 2 ) = (77 cm , 0) = (0 . 77 m , 0) and ( x , y ) = (0 , 0) . The electric fields are E y = k e q x 2 1 + y 2 1 = ( 9 × 10 9 N m 2 / C 2 )( 9 × 10 − 6 C ) 0 + (0 . 23 m) 2 = 1 . 53119 × 10 6 N / C , and E x = k e q x 2 2 + y 2 2 = ( 9 × 10 9 N m 2 / C 2 )( 9 × 10 − 6 C ) (0 . 77 m) 2 + 0 = 1 . 36617 × 10 5 N / C , Thus E = radicalBig E 2 x + E 2 y and F = q E = q radicalBig E 2 x + E 2 y = ( 9 × 10 − 6 C ) · radicalBig (1 . 53119 × 10 6 N / C) 2 + (1 . 36617 × 10 5 N / C) 2 = 13 . 8355 N . 003 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. 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 . nguyen (jmn727) – oldmidterm 01 – Turner – (59070) 2 . 8 m 4 ◦ . 03 kg . 03 kg Find the magnitude of the charge on each sphere. Correct answer: 1 . 68803 × 10 − 8 C. Explanation: Let : L = 0 . 08 m , m = 0 . 03 kg , and θ = 4 ◦ . L a θ m m q q From the right triangle in the figure above, we see that sin θ = a L ....
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oldmidterm 01 - nguyen(jmn727 – oldmidterm 01 – Turner...

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