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# 4 - roofner(bar784 Homework 4 Weathers(17104 This print-out...

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roofner (bar784) – Homework 4 – Weathers – (17104) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points Consider four vectors vector F 1 , vector F 2 , vector F 3 , and vector F 4 , where their magnitudes are F 1 = 41 N, F 2 = 34 N, F 3 = 23 N, and F 4 = 49 N. Let θ 1 = 150 , θ 2 = 150 , θ 3 = 16 , and θ 4 = 66 , measured from the positive x axis with the counter-clockwise angular direction as positive. What is the magnitude of the resultant vec- tor vector F , where vector F = vector F 1 + vector F 2 + vector F 3 + vector F 4 ? Correct answer: 41 . 7695 N. Explanation: Basic Concepts: Vector components fig- ure1 Solution: The x components of the forces vector F 1 , vector F 2 , and vector F 3 are F 1 x = F 1 cos(150 ) = 35 . 5071 N F 2 x = F 2 cos( 150 ) = 29 . 4449 N F 3 x = F 3 cos(16 ) = 22 . 109 N F 4 x = F 4 cos( 66 ) = 19 . 9301 N . and the y components are F 1 y = F 1 sin(150 ) = 20 . 5 N F 2 y = F 2 sin( 150 ) = 17 N F 3 y = F 3 sin(16 ) = 6 . 33966 N F 4 y = F 4 sin( 66 ) = 44 . 7637 N . The x and y components of the resultant vec- tor vector F are F x = F 1 x + F 2 x + F 3 x + F 4 x = ( 35 . 5071 N) + ( 29 . 4449 N) + (22 . 109 N) + (19 . 9301 N) = 22 . 9129 N F y = F 1 y + F 2 y + F 3 y + F 4 y = (20 . 5 N) + ( 17 N) + (6 . 33966 N) + ( 44 . 7637 N) = 34 . 9241 N Hence the magnitude of the resultant vector bardbl vector F bardbl is bardbl vector F bardbl = radicalBig F 2 x + F 2 y = radicalBig ( 22 . 9129 N) 2 + ( 34 . 9241 N) 2 = 41 . 7695 N 002 (part 2 of 2) 10.0 points What is the direction of this resultant vector 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: 123 . 268 . Explanation: ( 7 . 2, 4 . 2) ( 6, 3 . 5) (4 . 5, 1 . 3) (4 . 1, 9 . 1) 123 The angle is given by θ = arctan parenleftbigg F y F x parenrightbigg = tan 1 parenleftbigg 34 . 9241 N 22 . 9129 N parenrightbigg =

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4 - roofner(bar784 Homework 4 Weathers(17104 This print-out...

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