3 - roofner (bar784) Homework 3 Weathers (22202) 1 This...

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Unformatted text preview: roofner (bar784) Homework 3 Weathers (22202) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points A particle of mass 6 . 9 10 5 g and charge 58 mC moves in a region of space where the electric field is uniform and is 4 . 4 N / C in the x direction and zero in the y and z direction. If the initial velocity of the particle is given by v y = 2 . 7 10 6 m / s, v x = v z = 0, what is the speed of the particle at 0 . 8 s? Correct answer: 4 . 00559 10 6 m / s. Explanation: Let : m = 6 . 9 10 5 g = 6 . 9 10 8 kg , E x = 4 . 4 N / C , E y = E z = 0 , v y = 2 . 7 10 6 m / s , v x = v z = 0 , and t = 0 . 8 s . According to Newtons second law and the definition of an electric field, vector F = mvectora = q vector E . Since the electric field has only an x compo- nent, the particle accelerates only in the x direction a x = q E x m . To determine the x component of the final velocity, v xf , use the kinematic relation v xf = v xi + a ( t f- t i ) = a t f . Since t i = 0 and v xi = 0 , v xf = q E x t f m v xf = (0 . 058 C) (4 . 4 N / C)(0 . 8 s) (6 . 9 10 8 kg) = 2 . 95884 10 6 m / s . No external force acts on the particle in the y direction so v yi = v yf = 2 . 7 10 6 m / s. Hence the final speed is given by v f = radicalBig v 2 yf + v 2 xf = bracketleftbigg ( 2 . 7 10 6 m / s ) 2 + ( 2 . 95884 10 6 m / s ) 2 bracketrightbigg 1 / 2 = 4 . 00559 10 6 m / s . Note: This is analogous to a particle in a gravitational field with the coordinates ro- tated clockwise by 2 (90 )....
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3 - roofner (bar784) Homework 3 Weathers (22202) 1 This...

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