Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_24

⚡ Mecademy AIENG정역학 · ch7  Problem Statement Determine the force exerted on the log by each jaw of the fireplace tongs shown. Problem 7/24 (a) Calculation of the force in terms of the applied force ● Calculation Process 1. Present Final Formula: We will use the principle of virtual work to relate the applied force at the handles to the resulting force at the jaws. The total virtual work done by all external forces during an infinitesimal displacement must be zero: By symmetry, we can consider the upper half of the tongs. Let be the vertical coordinate of the upper handle where force is applied, and be the vertical coordinate of the upper jaw contact point. From the geometry of the bars, we can express these coordinates in terms of the angle that the links make with the horizontal: The virtual work equation for the squeezing action is: 2. Substitute Values: Taking the variations of the vertical coordinates: Substituting these into the virtual work equilibrium equation: N NP PN δW=F ⋅ ∑ i δr = i 0 y P Py jaw θ y = P 8tanθ,y = jaw 5tanθ 2Pδy − P 2Nδy = jaw 0⟹Pδy = P Nδy jaw δy = P (8tan θ ) δθ = dθ d 8secθδθ 2 δy = jaw (5tan θ ) δθ = dθ d 5secθδθ 2 P(8secθδθ)= 2 N(5secθδθ) 2 3. Partial Operations: Divide both sides by the common factor : 4. Final Calculation: Solve for : ● Final Conclusion: The force exerted on the log by each jaw is . This indicates that the mechanism provides a mechanical advantage, magnifying the input squeezing force by 60%. ✨ Final Answer Summary (a) Mecad