Meriam, Kraige & Bolton — Statics of Particles: Problem 2_27

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/27 The 4-kN force F is applied at point A. Compute the moment of F about point O, expressing it both as a scalar and as a vector quantity. Determine the coordinates of the points on the x- and y-axes about which the moment of F is zero. Problem 2/27 1. Analysis of the Force Vector From the problem diagram, the force has a magnitude of and is applied at point . The direction is defined by a slope triangle with a horizontal run of 5 and a vertical rise of 3. Based on the arrow direction (pointing toward the third quadrant), both components are negative. ● Calculation of Force Components 1. Hypotenuse of the slope triangle: 2. x-component (): 3. y-component (): 2. Moment of about Point The moment about the origin for a force applied at point is given by the formula , where counter-clockwise (CCW) is positive. ● Calculation Process 1. Present Final Formula: F F4 kN A(1.2,1.5) m L= = 5+3 22 ≈ 345.831 F x F = x − F = ( 34 5 )−4⋅ = 34 5 − kN≈ 34 20 −3.430 kN F y F = y − F = ( 34 3 )−4⋅ = 34 3 − kN≈ 34 12 −2.058 kN FO O(0,0)(x,y) M = O xF − y yF x M = O x F − Ay y F Ax 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: Since the value is positive, the sense is counter-clockwise. ● Vector Representation: In a standard right-hand coordinate system, a CCW moment is in the positive -direction ( ). Scalar: (CCW) Vector: 3. Points on axes where moment is zero The moment of a force about a point is zero if the line of action of