Understanding buoyancy force is crucial in various fields, from engineering to everyday life. The buoyancy force (\(F_b\)) is the upward force exerted by a fluid that opposes the weight of an object immersed in it. This can be calculated using the formula:
\[ F_b = \rho \cdot g \cdot V \]
Where:
- \(F_b\) is the buoyancy force (in newtons, N)
- \(\rho\) is the density of the liquid (in kilograms per cubic meter, kg/m³)
- \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\))
- \(V\) is the displaced volume of the liquid (in cubic meters, m³)
Example 1: Buoyancy Force on a Submerged Ball
Problem: A ball with a volume of \(0.05 \, \text{m}^3\) is completely submerged in water. The density of water is \(1000 \, \text{kg/m}^3\). What is the buoyancy force acting on the ball?
Calculation:
Given:
- \(\rho = 1000 \, \text{kg/m}^3\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(V = 0.05 \, \text{m}^3\)
Using the formula:
\[ F_b = \rho \cdot g \cdot V = 1000 \cdot 9.8 \cdot 0.05 = 490 \, \text{N} \]
Answer: The buoyancy force acting on the ball is 490 newtons.
Example 2: Buoyancy Force on a Wooden Log
Problem: A wooden log with a volume of \(0.2 \, \text{m}^3\) is floating in a lake. The density of the lake water is \(997 \, \text{kg/m}^3\). What is the buoyancy force acting on the log?
Calculation:
Given:
- \(\rho = 997 \, \text{kg/m}^3\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(V = 0.2 \, \text{m}^3\)
Using the formula:
\[ F_b = \rho \cdot g \cdot V = 997 \cdot 9.8 \cdot 0.2 = 1956.04 \, \text{N} \]
Answer: The buoyancy force acting on the log is 1956.04 newtons.
Example 3: Buoyancy Force on a Submarine
Problem: A submarine with a volume of \(2000 \, \text{m}^3\) is submerged in seawater. The density of seawater is \(1025 \, \text{kg/m}^3\). What is the buoyancy force acting on the submarine?
Calculation:
Given:
- \(\rho = 1025 \, \text{kg/m}^3\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(V = 2000 \, \text{m}^3\)
Using the formula:
\[ F_b = \rho \cdot g \cdot V = 1025 \cdot 9.8 \cdot 2000 = 20090000 \, \text{N} \]
Answer: The buoyancy force acting on the submarine is 20,090,000 newtons.
