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# 2-4 - Create assignment 00223 Homework 4 Sep 15 at 9:06 pm...

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Create assignment, 00223, Homework 4, Sep 15 at 9:06 pm 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Perpendicular Vectors 02 05:01, trigonometry, numeric, > 1 min, nor- mal. 001 Two vectors of magnitudes 10 N and 20 N act at right angles to each other. What is the magnitude of their resultant? Correct answer: 22 . 3607 N. Explanation: The resultant of two vectors acting at right angles to each other is the hypotenuse of a right triangle, so f = q f 2 1 + f 2 2 = q (10 N) 2 + (20 N) 2 = 22 . 3607 N Hanging Weight 04 05:07, trigonometry, numeric, > 1 min, wording-variable. 002 Consider the 700 N weight held by two cables shown below. The left-hand cable had tension T 2 and makes an angle of θ 2 with the ceiling. The right-hand cable had tension 570 N and makes an angle of 55 with the ceiling. The right-hand cable makes an angle of 55 with the ceiling and has a tension of 570 N . 700 N T 2 570 N 55 θ 2 a) What is the tension T 2 in the left-hand cable slanted at an angle of θ 2 with respect to the wall? Correct answer: 401 . 518 N. Explanation: Observe the free-body diagram below. F 2 F 1 θ 1 θ 2 W g Note: The sum of the x - and y -components of F 1 , F 2 , and W g are equal to zero. Given : W g = 700 N , F 1 = 570 N , θ 1 = 55 , and θ 2 = 90 - θ . Basic Concept: Vertically and Horizontally, we have F x net = F x 1 - F x 2 = 0 = F 1 cos θ 1 - F 2 cos θ 2 = 0 (1) F y net = F y 1 + F y 2 - W g = 0 = F 1 sin θ 1 + F 2 sin θ 2 - W g = 0 (2) Solution: Using Eqs. 1 and 2, we have F x 2 = F 1 cos θ 1 (1) = (570 N) cos 55 = 326 . 939 N , and F y 2 = F 3 - F 1 sin θ 1 (2) = 700 N - (570 N) sin 55 = 700 N - 466 . 917 N = 233 . 083 N , so F 2 = q ( F x 2 ) 2 + ( F y 2 ) 2 = q (326 . 939 N) 2 + (233 . 083 N) 2 = 401 . 518 N .

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Create assignment, 00223, Homework 4, Sep 15 at 9:06 pm 2 003 b) What is the angle θ 2 which the left-hand cable makes with respect to the ceiling? Correct answer: 35 . 4861 . Explanation: Using Eq. 2, we have θ 2 = arctan F y 1 F x 1 = arctan 466 . 917 N 326 . 939 N = 35 . 4861 . Three Forces 05:07, trigonometry, numeric, > 1 min, nor- mal. 004 An object in equilibrium has three forces ex- erted on it. A(n) 33 N force acts at 80 , and a(n) 44 N force acts at 60 . What is the direction of the third force? (Consider all angles to be measured counter- clockwise from the positive x -axis.) Correct answer: 248 . 557 . Explanation: Basic Concepts: Choose a coordinate system with the pos- itive x -axis representing 0 and the positive y-axis representing 90 . Any force F has an x -component of F x = F cos θ and a y -component of F y = F sin θ where θ is measured from the x -axis.
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2-4 - Create assignment 00223 Homework 4 Sep 15 at 9:06 pm...

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