Meriam, Kraige & Bolton — Statics of Particles: Problem 2_82

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/82 A commercial airliner with four jet engines, each producing 90 kN of forward thrust, is in a steady, level cruise when engine number 3 suddenly fails. Determine and locate the resultant of the three remaining engine thrust vectors. Treat this as a two-dimensional problem. Problem 2/82 (a) Magnitude and Direction of the Resultant Force ● Calculation Process 1. Present Final Formula: Since all thrust vectors are parallel and acting in the same forward direction, the magnitude of the resultant force is the algebraic sum of the individual thrust magnitudes. 2. Substitute Values: According to the problem, engine 3 fails, so its thrust . The other three engines each produce of thrust. 3. Final Calculation: ● Final Conclusion: The resultant force has a magnitude of and is directed in the forward direction of the aircraft's travel. (b) Location of the Resultant Force ● Calculation Process 1. Establish Coordinate System: Let the centerline of the aircraft be the -axis (). From the diagram, we define distances perpendicular to the centerline (starboard side R R=F = ∑T + 1 T + 2 T + 3 T 4 T = 3 0 90 kN R=90 kN+90 kN+0+90 kN R=270 kN R=270 kN xy=0 positive, port side negative): Engine 4: Engine 3: (FAILED) Engine 2: Engine 1: 2. Apply Principle of Moments (Varignon's Theorem): The moment of the resultant force about the centerline must equal the sum of the moments of the individual thrust forces about the same axis. 3. Substitute Values: