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Problem 3.104 - Problem 3.104[Difficulty 2 Given Geometry...

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Problem 3.104 [Difficulty: 2] ( L + c )/2 L c F BR W R L /2 a θ Given: Geometry of rod Find: How much of rod is submerged; force to lift rod out of water Solution: Basic equations Σ M Hinge 0 = F B ρ g V = (Buoyancy) The free body diagram is as shown. F BR is the buoyancy of the rod; c is the (unknown) exposed length of the rod Taking moments about the hinge F BR Lc + () 2 cos θ W R L 2 cos θ + 0 = with F BR ρ g A = W R M R g = Hence ρ A + 2 M R L 2 + 0 = We can solve for c ρ A L 2 c 2 M R L = cL 2 LM R ρ A = c5 m 2 5m m 3 1000 kg
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