Homework 4-preview-3

Homework 4-preview-3 - Version PREVIEW – Homework 4 –...

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Unformatted text preview: Version PREVIEW – Homework 4 – rostovtsev – (17102) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Sum of Four Vectors 001 (part 1 of 2) 10.0 points Consider four vectors vector F 1 , vector F 2 , vector F 3 , and vector F 4 with magnitudes F 1 = 39 N, F 2 = 31 N, F 3 = 12 N, and F 4 = 57 N, θ 1 = 140 ◦ , θ 2 = − 150 ◦ , θ 3 = 17 ◦ , and θ 4 = − 62 ◦ , measured from the positive x axis with counterclockwise positive. What is the magnitude of the resultant vec- tor vector F = vector F 1 + vector F 2 + vector F 3 + vector F 4 ? Correct answer: 41 . 586 N. Explanation: The x components are F x = F cos θ , so F 1 x = (39 N) cos(140 ◦ ) = − 29 . 8758 N F 2 x = (31 N) cos( − 150 ◦ ) = − 26 . 8468 N F 3 x = (12 N) cos(17 ◦ ) = 11 . 4757 N F 4 x = (57 N) cos( − 62 ◦ ) = 26 . 7599 N and the y components are F y = F sin θ , so F 1 y = (39 N) sin(140 ◦ ) = 25 . 0687 N F 2 y = (31 N) sin( − 150 ◦ ) = − 15 . 5 N F 3 y = (12 N) sin(17 ◦ ) = 3 . 50846 N F 4 y = (57 N) sin( − 62 ◦ ) = − 50 . 328 N . The components of the resultant vector are F x = F 1 x + F 2 x + F 3 x + F 4 x = ( − 29 . 8758 N) + ( − 26 . 8468 N) + (11 . 4757 N) + (26 . 7599 N) = − 18 . 487 N and F y = F 1 y + F 2 y + F 3 y + F 4 y = (25 . 0687 N) + ( − 15 . 5 N) + (3 . 50846 N) + ( − 50 . 328 N) = − 37 . 2508 N , so the magnitude of the resultant vector is bardbl vector F bardbl = radicalBig F 2 x + F 2 y = radicalBig ( − 18 . 487 N) 2 + ( − 37 . 2508 N) 2 = 41 . 586 N . 002 (part 2 of 2) 10.0 points What is the direction of this resultant vec- tor vector F , within the limits of − 180 ◦ and 180 ◦ as measured from the positive x axis with coun- terclockwise positive ?...
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This note was uploaded on 10/19/2010 for the course CSCI 2342 taught by Professor Meg during the Spring '10 term at Tarrant County.

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Homework 4-preview-3 - Version PREVIEW – Homework 4 –...

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