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Unformatted text preview: Gozick, Brandon Homework 3 Due: Sep 15 2006, 5:00 pm Inst: D Weathers 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 = 56 N, F 2 = 27 N, F 3 = 12 N, and F 4 = 60 N. Let 1 = 140 , 2 = 140 , 3 = 18 , and 4 = 54 , 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: 31 . 1721 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(140 ) = 42 . 8985 N F 2 x = F 2 cos( 140 ) = 20 . 6832 N F 3 x = F 3 cos(18 ) = 11 . 4127 N F 4 x = F 4 cos( 54 ) = 35 . 2671 N . and the y components are F 1 y = F 1 sin(140 ) = 35 . 9961 N F 2 y = F 2 sin( 140 ) = 17 . 3552 N F 3 y = F 3 sin(18 ) = 3 . 70821 N F 4 y = F 4 sin( 54 ) = 48 . 541 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 = ( 42 . 8985 N) + ( 20 . 6832 N) + (11 . 4127 N) + (35 . 2671 N) = 16 . 902 N F y = F 1 y + F 2 y + F 3 y + F 4 y = (35 . 9961 N) + ( 17 . 3552 N) + (3 . 70821 N) + ( 48 . 541 N) = 26 . 192 N Hence the magnitude of the resultant vector k ~ F k is k ~ F k = q F 2 x + F 2 y = q ( 16 . 902 N) 2 + ( 26 . 192 N) 2 = 31 . 1721 N 002 (part 2 of 2) 10 points What is the direction of this resultant vector...
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This note was uploaded on 09/12/2008 for the course PHYS 1710 taught by Professor Weathers during the Fall '08 term at North Texas.
 Fall '08
 Weathers
 mechanics, Work

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