Meriam, Kraige & Bolton — Statics of Particles: Problem 2_121

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/121 Two 1.2-lb thrusters on the nonrotating satellite are simultaneously fired as shown. Compute the moment associated with this couple and state about which satellite axes rotations will begin to occur. Problem 2/121 1. Analysis of Force and Position Vectors The two thrusters exert forces of equal magnitude and opposite direction, thus forming a couple. We first identify the position vectors and force vectors for each thruster relative to the center of gravity (origin ) based on the provided diagram. Let the top thruster be and the bottom thruster be : Top Thruster (): Position: , , (assumed based on symmetry and diagram alignment). Position Vector: Force: Magnitude , pointing in the negative -direction. Force Vector: Bottom Thruster (): Position: , , . Position Vector: Force: Magnitude , pointing in the positive -direction. Force Vector: 2. Calculation of the Couple Moment Vector The moment of a couple is the same about any point and can be calculated by summing the moments of the individual forces about the origin: GO T 1 T 2 T 1 y = 1 20 inz = 1 25 inx = 1 0 r = 1 20j+25k in 1.2 lbx F = 1 −1.2i lb T 2 y = 2 −20 inz = 2 −25 inx = 2 0 r = 2 −20j−25k in 1.2 lbx F = 2 1.2i lb M M=r × 1 F + 1 r × 2 F 2 Substituting the values: Perform the cross products using unit vector identities ( and ): 1. First term: 2. Second term: Summing them together: 3. Magnitude of the Moment and Determination of Rotation Axes ● Magnitude: ● Rotation A