HW 3 solution

# HW 3 solution - song (shs546) – Homework 3 – weathers...

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Unformatted text preview: song (shs546) – 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 0 . 000109 g and charge 93 mC moves in a region of space where the electric field is uniform and is 3 . 6 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 = 4 . 9 × 10 5 m / s, v x = v z = 0, what is the speed of the particle at 0 . 4 s? Correct answer: 1 . 32273 × 10 6 m / s. Explanation: Let : m = 0 . 000109 g = 1 . 09 × 10 − 7 kg , E x = 3 . 6 N / C , E y = E z = 0 , v y = 4 . 9 × 10 5 m / s , v x = v z = 0 , and t = 0 . 4 s . According to Newton’s 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 . 093 C) (3 . 6 N / C)(0 . 4 s) (1 . 09 × 10 − 7 kg) = 1 . 22862 × 10 6 m / s . No external force acts on the particle in the y direction so v yi = v yf = 4 . 9 × 10 5 m / s. Hence the final speed is given by v f = radicalBig v 2 yf + v 2 xf = bracketleftbigg ( 4 . 9 × 10 5 m / s ) 2 + ( 1 . 22862 × 10 6 m / s ) 2 bracketrightbigg 1 / 2 = 1 . 32273 × 10 6 m / s . Note: This is analogous to a particle in a gravitational field with the coordinates ro- tated clockwise by π 2 (90 ◦ )....
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## This note was uploaded on 04/22/2011 for the course PHYS 2220 taught by Professor Littler during the Spring '00 term at North Texas.

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HW 3 solution - song (shs546) – Homework 3 – weathers...

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