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Unformatted text preview: lim (kl9356) Homework 4 Weathers (17104) 1 This printout should have 11 questions. Multiplechoice 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 = 31 N, F 2 = 27 N, F 3 = 28 N, and F 4 = 58 N. Let 1 = 140 , 2 = 140 , 3 = 34 , and 4 = 63 , measured from the positive x axis with the counterclockwise 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: 33 . 8385 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(140 ) = 23 . 7474 N F 2 x = F 2 cos( 140 ) = 20 . 6832 N F 3 x = F 3 cos(34 ) = 23 . 213 N F 4 x = F 4 cos( 63 ) = 26 . 3314 N . and the y components are F 1 y = F 1 sin(140 ) = 19 . 9264 N F 2 y = F 2 sin( 140 ) = 17 . 3552 N F 3 y = F 3 sin(34 ) = 15 . 6574 N F 4 y = F 4 sin( 63 ) = 51 . 6784 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 = ( 23 . 7474 N) + ( 20 . 6832 N) + (23 . 213 N) + (26 . 3314 N) = 5 . 11386 N F y = F 1 y + F 2 y + F 3 y + F 4 y = (19 . 9264 N) + ( 17 . 3552 N) + (15 . 6574 N) + ( 51 . 6784 N) = 33 . 4498 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 (5 . 11386 N) 2 + ( 33 . 4498 N) 2 = 33 . 8385 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....
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 Fall '08
 Weathers
 Magnetism, Work

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