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Problem 3.5

# Problem 3.5 - Problem 3.5 Given Data on system...

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Problem 3.5 [Difficulty: 2] Given: Data on system Find: Force on bottom of cube; tension in tether Solution: Basic equation dp dy ρ g = or, for constant ρ Δ p ρ g h = where h is measured downwards The absolute pressure at the interface is p interface p atm SG oil ρ g h oil + = Then the pressure on the lower surface is p L p interface ρ g h L + = p atm ρ g SG oil h oil h L + ( ) + = For the cube V 125 mL = V 1.25 10 4 × m 3 = Then the size of the cube is d V 1 3 = d 0.05m = and the depth in water to the upper surface is h U 0.3 m = Hence h L h U d + = h L 0.35m = where h L is the depth in water to the lower surface The force on the lower surface is F L p L A = where A d 2 = A 0.0025m 2 = F L p atm ρ g SG oil h oil h L + ( ) + A = F L 101 10 3 × N m 2 1000 kg m 3 9.81 × m s 2 0.8 0.5 × m 0.35 m + ( ) × N s 2 kg m × + 0.0025 × m 2 = F L 270.894N = Note: Extra decimals needed for computing T later! For the tension in the tether, an FBD gives Σ F y 0 = F L F U W T

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