Meriam, Kraige & Bolton — Statics of Particles: Problem 2_114

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/114 The system of Prob. 2/98 is repeated here, and the tension in cable is . Consider the force which this cable exerts on point and determine its moment about point . Problem 2/114 1. Identify the Coordinates of Points and By observing the dimensions provided in the diagram for Problem 2/98 (repeated in 2/114), we can establish the position vectors for point (where the force is applied) and point (toward which the force is directed) relative to the origin . Point : Starting from the origin , we move up the -axis, then parallel to the -axis, and finally parallel to the -axis. Point : Starting from the origin , we move along the -axis, then parallel to the -axis. Point lies in the - plane (). 2. Express the Force as a Vector The force has a magnitude and acts from point toward point . We first find the displacement vector and its magnitude: The unit vector in the direction of the force is: The force vector is then: CDT=675 lb CO CD CD O(0,0,0) CO6 ftz12 ft x9 fty r = C 12i+9j+6k ft DO12 fty14 ft xDxyz=0 r = D 14i+12j+0k ft F FT=675 lbCD r CD r = CD r − D r= C (14−12)i+(12−9)j+(0−6)k=2i+3j−6k ft ∣r ∣= CD = 2+3+(−6) 222 = 4+9+36 = 497 ft u = CD = ∣r ∣ CD r CD (2i+ 7 1 3j−6k) 3. Calculate the Moment about Point The moment of force about point is given by the cross product of the position vector and the force vector : Expanding the determinant: component: component: component: Calculating the scalar components: The moment of the forc