Buoyancy Net upward force is called the Buoyant force… It is easier to lift a rock in water…

Archimedes Principle FB = Wfluid A fluid applies a buoyant force to an object that is partially or totally immersed in it: FB = Wfluid The Buoyant Force The Weight of the displaced fluid The amount of water displaced is equal to the volume of the rock. FB = Weight © Laura Fellman, PCC Rock Creek Campus

For a floating object: FB FB = mg mg Force 2

A floating object displaces a weight of fluid equal to its own weight. Object sinks Object floats Full objects volume Displaced volume Helpful Hint: Notation is important!

The Weight of the displaced fluid FB = Wfluid The Buoyant Force The Weight of the displaced fluid

7. 4 An aluminum object has a mass of 27 kg and a density of 2 7.4 An aluminum object has a mass of 27 kg and a density of 2.70x103 kg/m3. The object is attached to a string and immersed in a tank of water. a. Determine the volume of the object m = 27 kg ρAl = 2700 kg/m3 ρwater = 1000 kg/m3 = 0.01 m3

ΣF = FT + FB - (FG )Al = 0 FT = (FG )Al - FB FB = (FG )water b. Determine the tension in the string when it is completely immersed. ΣF = FT + FB - (FG )Al = 0 FB = (FG )water and Vwater = VAl FB = ρwVw g = 1000(0.01)(9.8) = 98 N FT = (FG )Al - FB = 27(9.8) - 98 = 166.6 N N1L FT FB FG

FB = FG - (FG )app = 0.8428 - 0.7154 = 0.1274 N AP FB = ρwVw g 7.5 A piece of alloy has a weight of 0.8428 N in air and 0.7154 N when immersed in water. Find its volume and its density. FB = FG - (FG )app = 0.8428 - 0.7154 = 0.1274 N AP FG = 0.8428 N (FG )app= 0.7154 N ρwater = 1000 kg/m3 FB = ρwVw g = 1.3x10-5 m3 = 6.6x103 kg/m3

“Equal Volumes give Equal Buoyant Forces” [1] A soccer ball floats in a bathtub of water. The ball has a mass of 0.5 kg and a diameter of 22 cm. (a) What is the buoyant force? (b) What is the volume of water displaced by the ball? (c) What is the average density of the soccer ball?

fluid  object In general, an object will float in a fluid if helium in air ice in water hot air balloons An object surrounded by air is buoyed up by a force equal to the weight of the air displaced. If the buoyant force is greater than the weight of the object, it will rise in the air © Laura Fellman, PCC Rock Creek Campus

[2] A geologist finds that a moon rock whose mass is 8 [2] A geologist finds that a moon rock whose mass is 8.20 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock? Ans: 4060 kg/m3 [3] An iron anchor of density 7900 kg/m3 submerged in water appears 200 N lighter in water than in air. a) What is the volume of the anchor? b) How much does it weigh in air? a) The buoyant force on the anchor is 200 N, so the weight of the displaced water is 200 N. The mass of the displaced water is 200/9.8 or 20.4 kg. The volume of the displaced water is M / ρ or 20.4 kg / 1000 kg/m3 = 0.0204 m3. b) The volume of the anchor equals the volume of the displaced water. The anchor’s mass is equal to ρ V = (7900 kg/m3)(0.0204 m3) = 161 kg. The weight of the anchor is equal to m g = 1580 N.

What percentage of a floating chunk of ice projects above the level of the water if the density of ice is 917 kg/m3? AP ρice = 917 kg/m3 ρwater = 1000 kg/m3 = 0.917 Vabove = 1 - 0.917 = 0.083(100) = 8.3%