Homework 4 Solutions

# Homework 4 Solutions - lim(kl9356 – Homework 4 –...

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Unformatted text preview: lim (kl9356) – 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 = 31 N, F 2 = 27 N, F 3 = 28 N, and F 4 = 58 N. Let θ 1 = 140 ◦ , θ 2 = − 140 ◦ , θ 3 = 34 ◦ , and θ 4 = − 63 ◦ , 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: 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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## This note was uploaded on 09/07/2010 for the course PHYS 1710 taught by Professor Weathers during the Fall '08 term at North Texas.

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Homework 4 Solutions - lim(kl9356 – Homework 4 –...

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