Buoyancy in Physics

Buoyancy Definition

• Buoyancy is the ability of an object to float, which occurs when an object is acted upon by an upward buoyant force equal to the weight of the fluid it displaces.

Buoyant Force

• The buoyant force is a net upward force acting on a submerged or partially submerged object.
• It is caused by the pressure increase with depth in fluids, resulting in a greater pressure on the bottom of the object than on the top.
• The buoyant force is fundamentally tied to gravity and does not exist in space.

Archimedes' Principle

• Archimedes' principle states that when an object is placed in water, an upward force (buoyant force) will act on the object that is equal to the weight of water (mass of displaced fluid) the object displaces.
• This principle can be surmised in the following equation:
• If an object is partially submerged, the volume of water displaced equals the volume partially submerged.
• If the object is fully submerged, the volume of water displaced equals the volume of the object.

Buoyancy Formula

• The buoyancy formula is used to solve for buoyant force (Fb) and includes:
  • Acceleration due to gravity (g) of 9.8 meters per second squared
  • Density of the fluid (ρ)
  • Volume of the displaced fluid (V)
• The formula is:

Using the Buoyancy Equation

• The buoyancy formula can be used to solve a variety of problems, taking into account whether the object is partially or fully submerged.
• Example 1: Determining the buoyant force when a cube with an edge length of one meter is fully submerged in water.
• Example 2: Calculating the buoyant force when a cube with volume is half submerged in water.

Buoyancy Examples

• Ice cubes in water: floats because it is less dense than water
• Birthday balloon in air: rises because it is less dense than air
• A person in water: floats or sinks depending on their relative density

Concepts of Weight, Density, and Buoyancy

• Density is the primary factor for determining buoyancy.
• If an object is less dense than the fluid it is placed in, it will float.
• Density is mass divided by volume.
• Weight is the mass of an object multiplied by the acceleration due to gravity (g).
• Buoyant force counteracts weight when an object is submerged.

Specific Gravity

• Specific gravity is the ratio of an object's density (ρobject) to the density of water (ρwater).
• The formula for specific gravity is:
• If the object's specific gravity is:
  • Greater than one, the object will sink (negative buoyancy)
  • Equal to one, the object will neither sink nor float (neutral buoyancy)
  • Less than one, the object will float (positive buoyancy)

Flotation

• Flotation refers to a situation where the buoyant force on a submerged object is greater than the object's weight.
• The net force on the object will be upwards, causing it to rise.
• The object will stop moving when the gravitational force (weight) and the upward force (buoyant force) are balanced.