Fluid Mechanics – Buoyancy AP Physics 2

Volume Displacement When the object is placed in fluid is DISPLACES a certain amount of fluid. If the object is completely submerged, the VOLUME of the OBJECT is EQUAL to the VOLUME of FLUID it displaces.

Buoyancy When an object is immersed in a fluid, such as a liquid, it is buoyed UPWARD by a force called the BUOYANT FORCE.

Buoyant Force The physical cause of the buoyant force is the pressure difference between the top and the bottom of the object The buoyant force is exerted by the fluid Whether an object sinks or floats depends on the relationship between the buoyant force and the weight

Archimedes' Principle Any object completely or partially submerged in a fluid experiences an upward buoyant force whose magnitude is equal to the weight of the fluid displaced by the object. The buoyant force is due to the displaced fluid. The block material does not matter. 2 kg 2 kg

Archimedes's Principle " An object is buoyed up by a force equal to the weight of the fluid displaced." In the figure, we see that the difference between the weight in AIR and the weight in WATER is 3 lbs. This is the buoyant force that acts upward to cancel out part of the force. If you were to weight the water displaced it also would weigh 3 lbs.

Archimedes's Principle

Calculating Buoyant Force The buoyant force FB is due to the difference of pressure P between the top and bottom surfaces of the submerged block.

Calculating Buoyant Force ∆𝑃= 𝐹 𝐵 𝐴 = 𝑃 2 − 𝑃 1 𝐹 𝐵 =𝐴 𝑃 2 − 𝑃 1 =𝐴( 𝜌 𝑓 𝑔 ℎ 2 − 𝜌 𝑓 𝑔 ℎ 1 ) 𝐹 𝐵 = 𝜌 𝑓 𝑔 𝐴 ℎ 2 − ℎ 1 𝑉 𝑓 =𝐴( ℎ 2 − ℎ 1 ) Vf is the volume of the displaced fluid Therefore, 𝐹 𝐵 = 𝜌 𝑓 𝑔 𝑉 𝑓

Buoyant Force The magnitude of the buoyant force always equals the weight of the displaced fluid The buoyant force is the same for a totally submerged object of any size, shape, or density

Archimedes’ Principle: Floating Object When an object floats, partially submerged, the buoyant force exactly balances the weight of the object. The object is in static equilibrium Volume of the fluid displaced corresponds to the volume of the object beneath the fluid level 𝜌 𝑓 𝑉 𝑓 = 𝜌 𝑥 𝑉 𝑥

Problem Solving Strategy 1. Draw a figure. Identify givens and what is to be found. Use consistent units for P, V, A, and found. 2.Use absolute pressure Pabs unless problem involves a difference of pressure P. 3.The difference in pressure P is determined by P is determined by the density and depth of the fluid:

Problem Solving Strategy 4. Archimedes’ Principle: A submerged or floating object experiences an buoyant force equal to the weight of the displaced fluid: 5. Remember: m, r and V refer to the displaced fluid. The buoyant force has nothing to do with the mass or density of the object in the fluid. (If the object is completely submerged, then its volume is equal to that of the fluid displaced.)

Problem Solving Strategy 6. For a floating object, FB is equal to the weight of that object; i.e., the weight of the object is equal to the weight of the displaced fluid:

Archimedes’ Principle: Totally Submerged Object The upward buoyant force is B=fluidgVobj The downward gravitational force is w=mg= objgVobj The net force is B-w=(fluid- obj)gVobj

Totally Submerged Object The object is less dense than the fluid The object experiences a net upward force

Totally Submerged Object The object is more dense than the fluid The net force is downward The object accelerates downward