Buoyancy

Float Your Boat Assume that you have a tub just barely large enough to hold an ocean liner. If you place water in the tub, will the ship float? A) Yes, if there is enough water to go all around it. B) Yes, if the water is swirling fast enough. C) No, the ship weighs more than the water. D) No, the surface tension of the water is too low.

Fluid Volume Within a fluid, any volume is at equilibrium. The pressure force on the sides of the volume balances the weight. Fg = -mg

Buoyant Force The force remains even without the original fluid. It must balance the weight that would have been there. This is the buoyant force. Equals the fluid weight Directed upward Acts on the volume Fb = mg

Sinking and Rising An object in a fluid displaces a volume that had some mass. If the object is heavier than the fluid it sinks. If the object is lighter it rises. Fb = rVg Fb = rVg W = mg W = mg

Archimedes’ Principle An object suspended in a fluid has less apparent weight due to buoyancy. FT = mg - rVg Fb = rVg W = mg

Iceberg An iceberg has an average density of 86% of seawater. What fraction of the iceberg is underwater? The buoyant force is the weight of water displaced by the iceberg: Fb = rwaterVsubg. The weight is the total weight of the ice: Wi = riceViceg. Find the ratio of Vsub/ Vice We know the ratio rice/rwater rwaterVsubg = riceViceg Vsub/ Vice = rice/rwater = 0.86

Center of Buoyancy The force of buoyancy acts at the center of mass of the missing fluid. The displacing object has a center of gravity at its center of mass. The two forces may not act at the same point.

Tippy Canoe If a forces on an object act at different points there is a torque. Buoyant force above the center of mass is stable. The torque moves it back to the center Buoyant force below the center of mass is unstable. The torque moves it away from the center next