turner old hw 2

# turner old hw 2 - linares(jl36797 – oldhomework 02 –...

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Unformatted text preview: linares (jl36797) – 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 Two identical positive charges exert a repul- sive force of 6 . 2 × 10 − 9 N when separated by a distance 3 . 6 × 10 − 10 m. Calculate the charge of each. The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . Correct answer: 2 . 99004 × 10 − 19 C. Explanation: Let : F = 6 . 2 × 10 − 9 N , d = 3 . 6 × 10 − 10 m , and k e = 8 . 98755 × 10 9 N · m 2 / C 2 . The electric force is F = k e q 1 q 2 d 2 d 2 F k e = q 2 q = radicalBigg d 2 F k e = radicalBigg (3 . 6 × 10 − 10 m) 2 (6 . 2 × 10 − 9 N) 8 . 98755 × 10 9 N · m 2 / C 2 = 2 . 99004 × 10 − 19 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. . 2 m 3 ◦ . 02 kg . 02 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: 2 . 23803 × 10 − 8 C. Explanation: Let : L = 0 . 2 m , m = 0 . 02 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 . 2 m) sin(3 ◦ ) = 0 . 0104672 m . The separation of the spheres is r = 2 a = . 0209344 m . The forces acting on one of the spheres are shown in the figure below. 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 − mg = 0 . linares (jl36797) – oldhomework 02 – Turner – (56705) 2 F sin θ F cos θ = F e mg F e = mg tan θ = (0 . 02 kg) ( 9 . 8 m / s 2 ) tan(3 ◦ ) = 0 . 0102719 N , for the electric force. From Coulomb’s law, the electric force be- tween the charges has magnitude | F e | = k e | q | 2 r 2 | q | = radicalBigg | F e | r 2 k e = radicalBigg (0 . 0102719 N) (0 . 0209344 m) 2 (8 . 98755 × 10 9 N m 2 / C 2 ) = 2 . 23803 × 10 − 8 C ....
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turner old hw 2 - linares(jl36797 – oldhomework 02 –...

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