Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_14

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The wall-mounted 2.5-kg light fixture has its mass center at G. Determine the reactions at A and B and also calculate the moment supported by the adjustment thumbscrew at C. (Note that the lightweight frame ABC has about 250 mm of horizontal tubing, directed into and out of the paper, at both A and B.) Problem 3/14 (a) Reactions at supports A and B 1. Formula: We use the equations of equilibrium for a rigid body in 2D: Let be the weight of the fixture. We assume point is a pin support (resisting horizontal and vertical motion) and point is a smooth contact (resisting only horizontal motion against the rod). 2. Substitution: Mass , Weight Horizontal distance from the rod (line ) to : Vertical distance between and : Summing moments about point : 3. Calculation: From : From : F = ∑ x 0, F = ∑ y 0, M = ∑ A 0 W=mgA B m=2.5 kgg= 9.81 m/s 2 W=2.5×9.81=24.525 N ABGd = x 200 mm+ 100 mm=300 mm=0.3 m ABh=230 mm=0.23 m A M = ∑ A W⋅d − x B ⋅ x h=0 24.525⋅0.3−B ⋅ x 0.23=0 B = x = 0.23 24.525⋅0.3 ≈ 0.23 7.3575 31.989 N F =∑ x 0A + x B = x 0⟹A = x −31.989 N F =∑ y 0A − y W=0⟹A = y 24.525 N Magnitude of reaction at : Magnitude of reaction at : 4. Result: , ● Final Conclusion: The reaction at support has a magnitude of , and the reaction at support is a horizontal force of . (b) Moment at the adjustment thumbscrew C 1. Formula: The moment supported by the thumbscrew at must balance the moment caused by the weight of the lamp portion acting at relat