Buoyancy Force Visualizer
Buoyancy Force Visualizer calculates the buoyant force on an object in a fluid using its volume, fluid density, and gravity, with plots for analysis.
Buoyancy Force Overview
Buoyancy force arises from the displacement of a fluid by an object, governed by Archimedes’ principle. The force is given by:
Archimedes’ Principle: \( F_b = \rho g V \)
Where:
- \(F_b\): Buoyant force (N)
- \(\rho\): Fluid density (kg/m³)
- \(g\): Acceleration due to gravity (m/s²)
- \(V\): Volume of displaced fluid (m³)
Net force (considering object weight): \( F_{\text{net}} = F_b – \rho_{\text{obj}} g V \)
Positive \(F_{\text{net}}\) indicates the object floats, negative indicates it sinks.
Example Calculations
Example 1: Wood in Water
\(V = 0.001 \, \text{m}^3\), \(\rho = 1000 \, \text{kg/m}^3\), \(g = 9.81 \, \text{m/s}^2\), \(\rho_{\text{obj}} = 500 \, \text{kg/m}^3\)
Buoyant Force: \( F_b = 1000 \times 9.81 \times 0.001 \approx 9.81 \, \text{N} \)
Net Force: \( F_{\text{net}} = 9.81 – (500 \times 9.81 \times 0.001) \approx 4.905 \, \text{N} \) (floats)
Example 2: Steel in Water
\(V = 0.001 \, \text{m}^3\), \(\rho = 1000 \, \text{kg/m}^3\), \(g = 9.81 \, \text{m/s}^2\), \(\rho_{\text{obj}} = 7850 \, \text{kg/m}^3\)
Buoyant Force: \( F_b = 1000 \times 9.81 \times 0.001 \approx 9.81 \, \text{N} \)
Net Force: \( F_{\text{net}} = 9.81 – (7850 \times 9.81 \times 0.001) \approx -67.1085 \, \text{N} \) (sinks)
Example 3: Wood in Seawater
\(V = 0.001 \, \text{m}^3\), \(\rho = 1025 \, \text{kg/m}^3\), \(g = 9.81 \, \text{m/s}^2\), \(\rho_{\text{obj}} = 500 \, \text{kg/m}^3\)
Buoyant Force: \( F_b = 1025 \times 9.81 \times 0.001 \approx 10.05525 \, \text{N} \)
Net Force: \( F_{\text{net}} = 10.05525 – (500 \times 9.81 \times 0.001) \approx 5.15025 \, \text{N} \) (floats)
Example 4: Aluminum in Mercury
\(V = 0.001 \, \text{m}^3\), \(\rho = 13534 \, \text{kg/m}^3\), \(g = 9.81 \, \text{m/s}^2\), \(\rho_{\text{obj}} = 2700 \, \text{kg/m}^3\)
Buoyant Force: \( F_b = 13534 \times 9.81 \times 0.001 \approx 132.76854 \, \text{N} \)
Net Force: \( F_{\text{net}} = 132.76854 – (2700 \times 9.81 \times 0.001) \approx 106.27854 \, \text{N} \) (floats)