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Unformatted text preview: Muraj, Hamza – Homework 5 – Due: Feb 1 2006, 4:00 am – Inst: Florin 1 This printout should have 10 questions. Multiplechoice 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 counterclockwise 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....
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This note was uploaded on 04/12/2010 for the course PHY 58195 taught by Professor Turner during the Spring '09 term at University of Texas at Austin.
 Spring '09
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