Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_56

⚡ Mecademy AIENG정역학 · ch3  Problem Statement An 80-lb sheet of plywood rests on two small wooden blocks as shown. It is allowed to lean 20° from the vertical under the action of a force P which is perpendicular to the sheet. Friction at all surfaces of blocks A and B is sufficient to prevent slipping. Determine the magnitude P and the vertical reaction forces at A and B. Problem 3/56 (a) Magnitude of the force 1. Formula: Sum moments about the axis of rotation formed by the contact of the sheet with the floor (the -axis). For equilibrium: Taking the moment about the bottom edge (on the -axis), the moment of the weight must be balanced by the moment of force . The weight acts at the geometric center . where is the height of the sheet and is the angle with the vertical. 2. Substitution: 3. Calculation: 4. Result: ● Final Conclusion: The magnitude of the force required for equilibrium is . P x M = ∑ x 0 x PG P⋅h−W⋅ sinθ = ( 2 h )0 hθ=20 ∘ P⋅(4 ft)−(80 lb)⋅ sin20 = ( 2 4 ft ∘ )0 4P=160sin20 ∘ P=40sin20 ∘ P=40×0.34202=13.6808 P≈13.68 lb P13.68 lb (b) Vertical reaction forces at A and B 1. Formula: Use moment equilibrium about the -axis passing through point and the force equilibrium in the vertical () direction. For moment equilibrium about (along the -axis): where is the vertical component of . For vertical force equilibrium: 2. Substitution: Distance from to : Distance from to : Distance from to : Vertical component of : Substituting into the moment equation: 3. Calculation: Fi