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Problem 2.48 The bracket must support the two forces shown, where |F₁| = |F₂| = 2 kN. An engineer deter- mines that the bracket will safely support a total force of magnitude 3.5 kN in any direction. Assume that 0 ≤ a ≤ 90°. What is the safe range of the angle a?

Problem 2.48 The bracket must support the two forces shown, where |F₁| = |F₂| = 2 kN. An engineer deter- mines that the bracket will safely support a total force of magnitude 3.5 kN in any direction. Assume that 0 ≤ a ≤ 90°. What is the safe range of the angle a?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
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Problem 2.48 The bracket must support the two forces shown, where |F₁| = |F₂| = 2 kN. An engineer deter- mines that the bracket will safely support a total force of magnitude 3.5 kN in any direction. Assume that 0 ≤ a ≤ 90°. What is the safe range of the angle a? 14~ = 24 = Zcoszł + 2 sind j | F₁+F₂ | = √√ (2+2 coza)² + Zsind NTIL ≤ 3.5 F2 F ₁²+ F²₂²₂ = (2+2 coad) —² + 2 sidj F₁ x = 58° 4 + 8 cos 2 + 4 coz²2 +4 sin? d ≤ 3.5² 8+8 cod ≤ 12.25 Coz α = 4.25 8 I note the flip because cosa ↓ as a ↑ for 02 22 90°.
Transcribed Image Text:Problem 2.48 The bracket must support the two forces shown, where |F₁| = |F₂| = 2 kN. An engineer deter- mines that the bracket will safely support a total force of magnitude 3.5 kN in any direction. Assume that 0 ≤ a ≤ 90°. What is the safe range of the angle a? 14~ = 24 = Zcoszł + 2 sind j | F₁+F₂ | = √√ (2+2 coza)² + Zsind NTIL ≤ 3.5 F2 F ₁²+ F²₂²₂ = (2+2 coad) —² + 2 sidj F₁ x = 58° 4 + 8 cos 2 + 4 coz²2 +4 sin? d ≤ 3.5² 8+8 cod ≤ 12.25 Coz α = 4.25 8 I note the flip because cosa ↓ as a ↑ for 02 22 90°.
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