Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_88

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The mass of the uniform right-triangular tabletop is 30 kg, and that of each of the vertical legs is 2 kg. Determine the normal reaction force exerted by the floor on each leg. The mass center of a right-triangular body can be obtained from Table D/3 in Appendix D. Problem 3/88 (a) Calculation of the normal reaction forces for each leg ● Calculation Process 1. Present Final Formula: We consider the equilibrium of the entire table system. Let the vertices of the right-triangular tabletop be , , and , where is at the right- angle corner. We set up a coordinate system with the origin at , leg at , and leg at . The mass center of the uniform right- triangular tabletop is located at its centroid: The total vertical equilibrium and moment equilibrium equations for the parallel force system are: ABCA A(0,0)B (0,0.6) mC(1.2,0) mG t =xˉ , = 3 b yˉ 3 h F = ∑ z 0:N + A N + B N − C (m + t 3m )g= L 0 M = ∑ x 0:N (h)− B m g(h)− L m g = t ( 3 h )0 M = ∑ y 0:−N (b)+ C m g(b)+ L m g = t ( 3 b )0 2. Substitute Values: Given: , , , , and . From moment about -axis (line ): From moment about -axis (line ): 3. Partial Operations: Calculate : Calculate : Calculate using vertical force balance: 4. Final Calculation: The reaction forces for all three legs are identical due to the symmetry of the mass distribution relative to the support triangle's centroid. ● Final Conclusion: The normal reaction force exerted by the floor on each of the three legs is . ✨