Meriam, Kraige & Bolton — Statics of Particles: Problem 2_56

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/56 The top view of a revolving entrance door is shown. Two persons simultaneously approach the door and exert forces of equal magnitudes as shown. If the resulting moment about the door pivot axis at O is 25 N·m, determine the force magnitude F. Problem 2/56 (a) Determination of Force Magnitude F ● Calculation Process The total moment about the pivot axis is the sum of the moments produced by each of the two forces. According to the diagram, both forces have the same magnitude and are applied at a distance from the center. Each force is directed at an angle with respect to the line perpendicular to the door wing (the tangential direction). Only the tangential component of each force contributes to the moment about . 1. Present Final Formula: The resultant moment about point is given by: Solving for the force magnitude : 2. Substitute Values: Substitute the given values , , and : 3. Partial Operations: Calculate the denominator terms: M O O F r=0.8 mθ= 15 ∘ O O M = O 2⋅(Fcosθ⋅r) F F= 2rcosθ M O M = O 25 N⋅mr=0.8 m θ=15 ∘ F= 2⋅0.8⋅cos15 ∘ 25 2⋅0.8=1.6 cos15≈ ∘ 0.9659 1.6⋅0.9659≈1.5455 4. Final Calculation: ● Final Conclusion: The magnitude of the force exerted by each person is . Both forces act in a way that creates a counter-clockwise moment, and their combined effect yields the specified resultant moment. ✨ Final Answer Summary (a) Force magnitude Mecademy AI Solution · ENGProblem 2/56 F= ≈ 1.5455 25 16.176 N F=16.18 N F=16.18