Meriam, Kraige & Bolton — Statics of Particles: Problem 2_118

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/118 A helicopter is shown here with certain three-dimensional geometry given. During a ground test, a 400-N aerodynamic force is applied to the tail rotor at P as shown. Determine the moment of this force about point O of the airframe. Problem 2/118 ● Step 1: Identify the Position Vector From the provided diagram, we establish a right-handed orthogonal coordinate system with the origin at point (the main rotor hub). The position of the tail rotor application point is determined by the given dimensions: The distance along the -axis (aft along the tail boom) is . The distance along the -axis (vertically upward) is . The distance along the -axis (transverse to the fuselage) is . Thus, the position vector from point to point is: ● Step 2: Identify the Force Vector The aerodynamic force has a magnitude of . The red arrow in the diagram indicates that this force is applied at point and acts parallel to the -axis in the positive direction. The force vector is expressed as: ● Step 3: Calculate the Moment The moment of the force about point is given by the cross product of the position vector and the force vector: r OP OP yy=6 m zz=1.2 m xx=0.8 m OP r = OP 0.8i+6j+1.2k [m] F 400 N Px F=400i [N] M O FO M = O r× OP F M = O (0.8i+6j+1.2k)×(400i) Applying the properties of the cross product for unit vectors (, , ): 1. 2. 3. Combining these components, we get: To find the magnitude of the moment: ● Final Conclusion: The moment of the 400-N fo