Buoyant force is the upward force exerted by a fluid on an object submerged in it. This force is responsible for making objects float or sink in water or any other liquid. Understanding how to calculate buoyant force is essential in physics, engineering, and everyday life, especially in designing ships, submarines, and floating structures.
This topic explains the concept of buoyant force, Archimedes’ principle, the formula for calculating buoyant force, and practical examples to make it easy to understand.
What is Buoyant Force?
Buoyant force is the upward force that a fluid exerts on an object immersed in it. This force opposes gravity, which pulls objects downward. If the buoyant force is greater than or equal to the object’s weight, the object floats; otherwise, it sinks.
For example:
- A wooden log floats on water because the buoyant force is greater than its weight.
- A stone sinks because its weight is greater than the buoyant force.
Archimedes’ Principle
The buoyant force acting on an object is determined by Archimedes’ Principle, which states:
“An object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.“
This principle helps in calculating the buoyant force and determining whether an object will float or sink.
Formula for Buoyant Force
The formula to calculate buoyant force ( ) is:
F_b = rho cdot g cdot V
Where:
- = Buoyant force (Newton, N)
- = Density of the fluid (kg/m³)
- = Acceleration due to gravity (9.81 m/s²)
- = Volume of the fluid displaced (m³)
Understanding the Formula
- The greater the density of the fluid, the higher the buoyant force.
- The larger the volume displaced, the greater the buoyant force.
- The force is always directed upwards, opposing gravity.
How to Calculate Buoyant Force Step by Step
Step 1: Identify the Given Values
- Determine the density of the fluid (e.g., water = 1000 kg/m³).
- Measure the volume of the object submerged (for floating objects, this equals the volume of fluid displaced).
- Use the standard value for gravity (9.81 m/s²).
Step 2: Apply the Buoyant Force Formula
Substitute the values into the equation:
F_b = rho cdot g cdot V
Step 3: Compare Buoyant Force and Object’s Weight
- If is greater than or equal to the object’s weight, the object will float.
- If is less than the object’s weight, the object will sink.
Example Calculations
Example 1: A Floating Wooden Cube
A wooden cube with a volume of 0.02 m³ is floating on water. What is the buoyant force?
Given:
- (density of water) = 1000 kg/m³
- (volume of fluid displaced) = 0.02 m³
- = 9.81 m/s²
Solution:
F_b = (1000) times (9.81) times (0.02)
F_b = 196.2 N
Since the cube is floating, this force is equal to the cube’s weight.
Example 2: A Sinking Metal Object
A metal block with a volume of 0.01 m³ and a weight of 300 N is placed in water. Will it float or sink?
Step 1: Calculate Buoyant Force
F_b = (1000) times (9.81) times (0.01)
F_b = 98.1 N
Step 2: Compare with Object’s Weight
- Buoyant force = 98.1 N
- Object’s weight = 300 N
Since the object’s weight is greater than the buoyant force, the object sinks.
Factors Affecting Buoyant Force
1. Density of the Fluid
- Objects float more easily in denser fluids.
- Example: A person floats better in the Dead Sea than in a swimming pool because saltwater is denser.
2. Volume of Fluid Displaced
- The larger the object, the greater the volume displaced, leading to a higher buoyant force.
3. Gravity
- Since buoyant force depends on gravity, it varies in different locations (e.g., lower on the Moon, higher on Jupiter).
Real-Life Applications of Buoyant Force
1. Ship and Boat Design
Ships are designed with hollow hulls to displace enough water and generate sufficient buoyant force to stay afloat.
2. Submarines
Submarines control their buoyancy by adjusting the amount of water in their ballast tanks.
3. Hot Air Balloons
Hot air inside the balloon reduces air density, creating a buoyant force that lifts the balloon.
4. Swimming and Floating
Humans can increase buoyancy by taking deep breaths and expanding their lung volume.
Common Misconceptions About Buoyant Force
1. “Heavier Objects Always Sink”
Not necessarily! A large, lightweight object like a ship can float, while a small, dense object like a rock sinks.
2. “Objects Must Be Fully Submerged to Experience Buoyancy”
Even partially submerged objects experience buoyant force, as seen with floating boats.
3. “Buoyant Force is the Same in All Fluids”
The force depends on fluid density—an object experiences more buoyant force in denser liquids.
Calculating buoyant force is essential in understanding why objects float or sink. By applying Archimedes’ Principle and the buoyant force formula, we can determine the upward force exerted on an object in a fluid.
This knowledge is widely used in engineering, marine navigation, swimming, and even space exploration. Whether designing ships, submarines, or balloons, understanding buoyancy helps us navigate and manipulate the physical world effectively.