Problem Statement
A wooden block of dimensions:
- Width: 2m
- Depth: 1.5m
- Length: 4m
- Specific gravity: 0.7
The block floats horizontally in water. Determine:
- The volume of water displaced.
- The position of the center of buoyancy.
Solution
1. Calculate Volume of Water Displaced
2. Calculate Depth of Immersion (\( h \))
3. Position of Center of Buoyancy
- Volume of water displaced: 8.4 m³
- Position of center of buoyancy: 0.525 m from the bottom
Explanation
1. Buoyancy Principle:
A floating body displaces a volume of liquid equal to its weight. Since the block is in equilibrium, the weight of the block is equal to the weight of the displaced water.
2. Depth of Immersion Calculation:
The total volume of the wooden block is known, and since it has a specific gravity of 0.7, only 70% of its volume needs to be submerged to balance the weight.
3. Center of Buoyancy:
The center of buoyancy is the centroid of the submerged portion of the block. Since the block is uniformly submerged, the center of buoyancy lies at half the submerged depth.
Physical Meaning
1. Floating Stability:
The position of the center of buoyancy plays a crucial role in determining the stability of a floating body. If the center of gravity is above the center of buoyancy, the body may tip over.
2. Archimedes’ Principle in Application:
This principle governs how ships and floating objects remain stable in water. Engineers use similar calculations to design floating structures, boats, and ships.
3. Use in Marine Engineering:
Ships are designed so that their center of buoyancy shifts with loading conditions, ensuring stability under different weights.
