Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_100

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A vertical force on the foot pedal of the bell crank is required to produce a tension of 400 N in the vertical control rod. Determine the corresponding bearing reactions at and . Problem 3/100 (a) Determination of the force and bearing reactions ● Calculation Process 1. Present Final Formula: First, we apply the moment equilibrium equation about the axis of the shaft (-axis) to find the required force . Next, we use force and moment equilibrium for the entire rigid body to find the reactions at and . Let and be the vertical reactions at the bearings. where: (lever arm for ) (horizontal moment arm for ) (distance from to the pedal along the shaft) (distance from to the control rod arm along the shaft) (total distance between bearings and ) 2. Substitute Values: Solve for : Solve for : PT AB P yP M = ∑ y 0⇒P⋅d − P T⋅d = T 0 ABA z B z F = ∑ z 0⇒A + z B − z P−T=0 M = ∑ A 0⇒B ⋅ z L−P⋅y − P T⋅y = T 0 d = P 200 mmP d = T 100sin30= ∘ 50 mmT y = P 120 mmA y = T 120+100=220 mmA L=120+100+60=280 mmA B P P(200)=400(50) B z B (280)= z P(120)+T(220) Substitute : Solve for : 3. Partial Operations: Find : Find : Find : 4. Final Calculation: Rounding to three significant figures: Since the applied forces and are purely vertical and their moment arms are along the -axis, the moments about the -axis are zero, which implies the -components of the bearing reactions are zero (). ● Final Conclusion: The bearing reactions are and , both acting vertically