Meriam, Kraige & Bolton — Statics of Particles: Problem 2_40

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/40 The cable carries a tension of . Determine the moment about of this tension as applied to point of the slender bar. Problem 2/40 1. Identify the coordinates of the key points First, we establish a coordinate system with the origin at the pivot point . From the given diagram: Point is at . Point is located on the vertical axis at a height of . Thus, . Point is at the end of the slender bar of length , which is inclined at an angle of with the horizontal. Its coordinates are: So, . 2. Express the tension force as a vector The tension force acts along the line from point toward point . We first find the vector : The length of the cable segment is: The unit vector along the line of action is: AB400 NO A O O(0,0) B650 mmB= (0,650) mm AL=500 mm 30 ∘ x = A 500cos30= ∘ 500⋅ ≈ 2 3 433.01 mm y = A 500sin30= ∘ 500⋅0.5=250 mm A=(433.01,250) mm T TAB AB = AB(x − B x )i+ A (y − B y )j A = AB(0−433.01)i+(650−250)j=−433.01i+400j mm AB L = AB = (−433.01)+400 22 = 187500+160000 ≈ 347500589.49 u AB Given the tension magnitude , the force vector is: 3. Calculate the moment about point The moment is defined as . We can use the position vector to any point on the line of action of the force. Using point is mathematically simpler because its -coordinate is zero: Converting to standard units (): Alternatively, using Varignon's Theorem at point : The positive result indicates a counter-clockwise (CCW) direction. The moment of the tension force about