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hw5 - Muraj Hamza Homework 5 Due Feb 1 2006 4:00 am Inst...

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Muraj, Hamza – Homework 5 – Due: Feb 1 2006, 4:00 am – Inst: Florin 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points Consider four vectors ~ F 1 , ~ F 2 , ~ F 3 , and ~ F 4 , where their magnitudes are F 1 = 38 N, F 2 = 24 N, F 3 = 25 N, and F 4 = 47 N. Let θ 1 = 120 , θ 2 = - 140 , θ 3 = 25 , and θ 4 = - 51 , measured from the positive x axis with the counter-clockwise angular direction as positive. What is the magnitude of the resultant vec- tor ~ F , where ~ F = ~ F 1 + ~ F 2 + ~ F 3 + ~ F 4 ? Correct answer: 17 . 1004 N. Explanation: Basic Concepts: Vector components fig- ure1 Solution: The x components of the forces ~ F 1 , ~ F 2 , and ~ F 3 are F 1 x = F 1 cos(120 ) = - 19 N F 2 x = F 2 cos( - 140 ) = - 18 . 3851 N F 3 x = F 3 cos(25 ) = 22 . 6577 N F 4 x = F 4 cos( - 51 ) = 29 . 578 N . and the y components are F 1 y = F 1 sin(120 ) = 32 . 909 N F 2 y = F 2 sin( - 140 ) = - 15 . 4269 N F 3 y = F 3 sin(25 ) = 10 . 5655 N F 4 y = F 4 sin( - 51 ) = - 36 . 5259 N . The x and y components of the resultant vec- tor ~ F are F x = F 1 x + F 2 x + F 3 x + F 4 x = ( - 19 N) + ( - 18 . 3851 N) + (22 . 6577 N) + (29 . 578 N) = 14 . 8506 N F y = F 1 y + F 2 y + F 3 y + F 4 y = (32 . 909 N) + ( - 15 . 4269 N) + (10 . 5655 N) + ( - 36 . 5259 N) = - 8 . 47835 N Hence the magnitude of the resultant vector k ~ F k is k ~ F k = q F 2 x + F 2 y = q (14 . 8506 N) 2 + ( - 8 . 47835 N) 2 = 17 . 1004 N 002 (part 2 of 2) 10 points What is the direction of this resultant vector ~ F ? Note: Give the angle in degrees, use coun- terclockwise as the positive angular direction, between the limits of - 180 and +180 from the positive x axis. Correct answer: - 29 . 7224 . Explanation: ( - 4, 7) ( - 3 . 9, - 3 . 3) (4 . 8, 2 . 2) (6 . 3, - 7 . 8) - 29 . 7 The angle is given by θ = arctan F y F x = tan - 1 - 8 . 47835 N 14 . 8506 N = - 29 . 7224 . The “arctan” function is defined between lim- its - 90 and +90 . Thus you must check to see in which quadrant your resultant vector lies.
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