1.5 Buoyancy

1.5 Buoyancy

What is Buoyancy?

Buoyancy is the upward force exerted on an object submerged in a fluid, caused by the difference in pressure at the object’s top and bottom. Since pressure increases with depth, the greater upward pressure results in a net upward force called the buoyant force. 🏄‍♂️

Archimedes’ Principle

The buoyant force is equal to the weight of the displaced fluid. This fundamental principle can be understood with a simple example:

Imagine placing a baseball into a bucket of water. As the baseball displaces some water, the weight of the displaced water equals the buoyant force acting on the baseball. 🚣‍♀️

Formula for Buoyant Force:

Where:

• : Buoyant force (N)

• : Volume of the object (m³)

• : Density of the fluid (kg/m³)

• : Acceleration due to gravity (m/s²)

Example Problem:

Find the net force on a box weighing 15 kg and with a volume of 0.2 m³ when fully submerged in water.

1. Calculate Buoyant Force:

2. Calculate Gravitational Force:

3. Net Force:

Key Points About Buoyancy

• Definition: Buoyancy is the upward force acting on an object submerged in a fluid.

• Floating or Sinking:

  • If , the object floats.

  • If , the object sinks.

• Factors Affecting Buoyancy:

  • Density of the fluid

  • Volume of the object

Apparent Weight

The apparent weight of an object in a fluid is the effective weight experienced when buoyant force acts against gravity. For example, lifting a person in a swimming pool feels easier than lifting them in the air because the buoyant force reduces the force needed to lift them. 😝

Formula for Apparent Weight:

Where:

• : Apparent weight (N)

• : True weight (N)

• : Buoyant force (N)

Key Points About Apparent Weight:

• Apparent weight is the force an object exerts on a measuring device in a fluid.

• If , the object floats, and .

• If , the object sinks, and .

• Apparent weight depends on the fluid’s density and the object’s volume.

Understanding buoyancy and apparent weight is crucial for solving problems involving submerged or floating objects. Archimedes’ principle not only explains everyday phenomena but also forms the foundation for applications in engineering and science. 👑