Meriam, Kraige & Bolton — Statics of Particles: Problem 2_11

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/11 The guy cables AB and AC are attached to the top of the transmission tower. The tension in cable AB is 8 kN. Determine the required tension T in cable AC such that the net effect of the two cable tensions is a downward force at point A. Determine the magnitude R of this downward force. Problem 2/11 1. Coordinate System and Position Vectors First, we establish a Cartesian coordinate system with the origin at the base of the transmission tower. Based on the provided diagram, the positions of points and are identified as follows: The height of the hill at point is . Point is above the level of point , making its total height . Point is at ground level, to the left of the tower: . Point is on the hill, to the right of the tower: . Point is at the top of the tower: . The position vectors from point to the anchor points and are: The magnitudes of these vectors are: 2. Force Vector Expressions The force exerted by cable on point is given by its magnitude times its unit vector: O(0,0) A,B,C C20 m A30 mCy = A 20 m+ 30 m=50 m B40 mB(−40,0) C50 mC(50,20) AA(0,50) ABC = AB(x − B x )i+ A (y − B y )j= A (−40−0)i+(0−50)j={−40i−50j = AC(x − C x )i+ A (y − C y )j= A (50−0)i+(20−50)j={50i−30j} m AB= = (−40)+(−50) 22 = 1600+2500 = 4100 10 m≈ 4164.0 AC= = 50+(−30) 22 = 2500+900 = 3400 10 m≈ 3458.31 m ABA The force exerted by cable on point is: (a) Required tension T in cable AC ● Calculation Process 1. Equilibrium condition: The net force is pur