Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_106

⚡ Mecademy AIENG정역학 · ch4 To solve for the compression force exerted on the can, we will analyze the equilibrium of the handle and the slider separately.  Problem Statement Determine the compression force exerted on the can for an applied force when the can crusher is in the position shown. Point is centered on the bottom of the can. Problem 4/106 (a) Determination of the compression force C ● Calculation Process 1. Equilibrium of the Handle (OBA): First, we determine the force in link , denoted as . Since is a two-force member, the force it exerts acts along the line . We take the sum of moments about the pivot for the handle. where is the total length of the handle and is the perpendicular distance (moment arm) from to the line of action of . 2. Substitute Values for Handle Equilibrium: Applied force . Total handle length . Moment arm , where (handle angle) and (link angle) are both measured from the vertical. . Substituting into the moment equation: 3. Calculate Link Force : C CP=50 N B AB F AB AB ABO M = ∑ O 0⟹P⋅L − total F ⋅ AB d=0 L total d OF AB P=50 N L = total 72 mm+225 mm=297 mm= 0.297 m d=L ⋅ OA sin(θ−φ)θ=30 ∘ φ=10 ∘ d=72 mm⋅sin(30− ∘ 10)= ∘ 72⋅sin(20)≈ ∘ 72⋅0.3420= 24.626 mm=0.024626 m 50 N⋅0.297 m=F ⋅ AB 0.024626 m F AB 14.85 N⋅m=F ⋅ AB 0.024626 m The link is in compression, pushing down on the slider . 4. Equilibrium of the Slider (B): The compression force on the can is the vertical reaction force required to maintain the equilibrium of the slider. Neglecting