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Unformatted text preview: sanchez (ds28677) – homework 06 – Turner – (58220) 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 = 35 N, F 2 = 37 N, F 3 = 14 N, and F 4 = 43 N. Let θ 1 = 120 ◦ , θ 2 = − 130 ◦ , θ 3 = 21 ◦ , and θ 4 = − 72 ◦ , 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: 37 . 0503 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(120 ◦ ) = − 17 . 5 N F 2 x = F 2 cos( − 130 ◦ ) = − 23 . 7832 N F 3 x = F 3 cos(21 ◦ ) = 13 . 0701 N F 4 x = F 4 cos( − 72 ◦ ) = 13 . 2877 N . and the y components are F 1 y = F 1 sin(120 ◦ ) = 30 . 3109 N F 2 y = F 2 sin( − 130 ◦ ) = − 28 . 3436 N F 3 y = F 3 sin(21 ◦ ) = 5 . 01715 N F 4 y = F 4 sin( − 72 ◦ ) = − 40 . 8954 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 = ( − 17 . 5 N) + ( − 23 . 7832 N) + (13 . 0701 N) + (13 . 2877 N) = − 14 . 9254 N F y = F 1 y + F 2 y + F 3 y + F 4 y = (30 . 3109 N) + ( − 28 . 3436 N) + (5 . 01715 N) + ( − 40 . 8954 N) = − 33 . 911 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 ( − 14 . 9254 N) 2 + ( − 33 . 911 N) 2 = 37 . 0503 N 002 (part 2 of 2) 10.0 points What is the direction of this resultant vector vector F ?...
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 Spring '08
 Turner
 Physics, Vector Space, Acceleration, Work, Correct Answer, Vector Motors, Sanchez

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