Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_103

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The figure shows a side view of a tilting table. The left support controls the tilt angle of the table by means of a threaded shaft between pins and that raises and lowers the scissor mechanism. The table is pinned on the right to two vertical support posts. The scissor mechanism is located along the centerline of the table, which lies midway between the right- side support posts. If the tabletop is horizontal and a uniform 50-kg crate is placed along the centerline at the position shown, determine the magnitudes of the forces induced in pin and in the threaded shaft between pins and . The length and . Problem 4/103 (a) Magnitude of the force induced in the threaded shaft between pins C and D 1. Formula: First, we determine the total upward force required from the scissor mechanism to maintain the tabletop in horizontal equilibrium. By summing moments about the right- side pin support : Where is the weight of the crate, is the horizontal distance from to the crate's center, and is the horizontal distance from to the center of the scissor mechanism . Once is found, the force in the threaded shaft for a standard scissor mechanism is given by: 2. Substitution: Mass of crate , so . Distance from to pin : . Distance from to crate center : . Horizontal distance from to crate center: . CD E CDb=180 mmθ=15 ∘ F s G M = ∑ G 0⇒W⋅d − OG F ⋅ s d = EG 0 Wd OG G d EG G EF s F shaft F = shaft tanθ F s m=50 kgW=50×9.81=490.5 N GBd = BG 640 mm=0.64