Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_155

⚡ Mecademy AIENG정역학 · ch5  Problem Statement A beaker of fresh water is in place on the scale when the 1-lb stainless-steel cylinder is added to the beaker. What is the normal force which the cylinder exerts on the bottom of the beaker? By how much does the scale reading increase as the cylinder is added? Explain your answer. Problem 5/155 (a) Normal force on the bottom of the beaker ● Calculation Process 1. Present Final Formula: Consider the equilibrium of the cylinder resting on the bottom of the beaker. The forces acting on it are its weight , the buoyant force from the water, and the normal force from the bottom. The buoyant force is given by , and the volume of the cylinder is . Thus: 2. Substitute Values: From standard tables (e.g., Table D/1), the specific weights are: Weight of cylinder, Specific weight of fresh water, Specific weight of stainless steel, 3. Partial Operations: Calculate the buoyant force: WB N F = ∑ y 0⇒N+B−W=0⇒N=W−B B=γ V watercyl V = cyl γ steel W N=W1− ( γ steel γ water ) W=1 lb γ = water 62.4 lb/ft 3 γ = steel 489 lb/ft 3 N=1 lb×1− ( 489 62.4 ) B= ≈ 489 62.4 0.1276 lb 4. Final Calculation: ● Final Conclusion: The normal force exerted by the cylinder on the bottom of the beaker is (upward on the cylinder, and downward on the beaker floor). (b) Increase in scale reading and explanation ● Calculation Process 1. Present Final Formula: Consider the entire system (beaker + water + cylinder) as a single free body. The scale reading must balance the tot