Density and Buoyancy

Thank you to Robin Paul for sharing many of these slides!

Density: Density of a fluid is its mass per unit of volume. It’s the amount of mass (stuff) in a given space.

Density = mass d = m volume v

The units for density are grams/ml or grams/cm3

Comparing Densities: Each substance has a particular density that is characteristic of that substance.

•The density of water is 1gram per cubic centimeter (1g/cm3)•A substance with a density greater than 1g/cm3 will sink in water.•A substance with a density less than 1g/cm3 will float in water.•A substance with a density equal to 1g/cm3 will float at a constant depth in water.

Buoyancy: This is the ability to float. Fluids exert an upward force, called the buoyant force, on submerged objects.

At rest, the gravitational force and the buoyant force are equal and opposite. The net force on the surfer plus the board is zero.

•The buoyant force acts in a direction opposite to gravity (weight) and thus makes an object feel lighter.

•Fluid exerts pressure on all surfaces of a submerged object. Since pressure increases with depth, however, there is greater pressure on the bottom of an object than at the top. (The pressures on each side cancel out.) The greater bottom pressure creates a net upward force called the buoyant force.

Archimedes’ Principle: the buoyant force acting on an object that is submerged is equal to the weight of the volume of fluid the object displaces.

•When an object is placed in a fluid, it takes up space and takes the place of some of the particles of the fluid.

•The submerged object displaces (takes the place of) a volume of liquid equal to its own volume.

•If you measure the weight of the displaced liquid it will be equal to the buoyant force acting on the object.

“just the tip of the iceberg”

• This iceberg weighs 100,000 pounds. The weight of the water displaced by the submerged section of the iceberg weighs 100,000 pounds. The iceberg will sink until 100,000 pounds of water has been displaced.

•Submarines: By changing the level of water in its flotation tanks, the sub changes its weight. When its weight is greater than the buoyant force it sinks. It rises when its weight is equal to the buoyant force.

•Balloons: A balloon filled with air is denser than the surrounding air because it is under pressure. Because it is denser it sinks. If you heat the air in the balloon, it becomes less dense and rises.

•Ships: Since the buoyant force is equal to the amount of fluid displaced, a large object, like a ship, will have a greater buoyant force than a smaller object of the same weight. If you had a block of steel the same weight as a ships hull, the ship would displace more fluid and float while the block would sink.