Meriam, Kraige & Bolton — Statics of Particles: Problem 2_79

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/79 Four people are attempting to move a stage platform across the floor. If they exert the horizontal forces shown, determine (a) the equivalent force–couple system at O and (b) the points on the x- and y-axes through which the line of action of the single resultant force R passes. Given values from the diagram: Platform dimensions: width , height . Point is at . Force at : to the right ( direction). Force at point : to the right ( direction). Force at point : at angle (upper-right quadrant). Force at point : upward ( direction). Problem 2/79 (a) Equivalent force–couple system at O ● Calculation Process 1. Decompose individual forces into and components: 2. Determine the resultant force : w=88 ′′ h=66 ′′ O(0,0) O80 lb+x A(0,66) ′′ 90 lb+x B(88,66) ′′′′ 70 lb45 ∘ C(88,0) ′′ 35 lb+y xy F = O 80i+0j lb F = A 90i+0j lb F = B 70cos(45)i+ ∘ 70sin(45)j= ∘ 49.50i+49.50j lb F = C 0i+35j lb R R = x F = ∑ x 80+90+49.50=219.5 lb R = y F = ∑ y 0+0+49.50+35=84.5 lb R=219.5i+84.5j lb 3. Calculate the resultant moment about point (): Using with counter-clockwise as positive: ● Final Conclusion: The equivalent force-couple system at consists of: Resultant force: (Magnitude at above the axis) Resultant moment: (clockwise) (b) Points on the x- and y-axes through which the line of action passes ● Calculation Process 1. Equation for the line of action: The equation of the line of action of the resultant force is given by . 2. Find the -axis intercep