Why is a force needed to keep a block of wood inside water?

Answer

To understand why a force is needed to keep a block of wood submerged in water, we can analyze the forces acting on the block:

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Block**:
- The block of wood experiences two main forces when submerged in water:
- The **weight of the wood** acting downwards (due to gravity).
- The **buoyant force** acting upwards (due to the displacement of water).

2. **Calculate the Weight of the Wood**:
- The weight of the wooden block can be calculated using the formula:
\[ \text{Weight of wood} = \rho_{\text{wood}} \times V \times g \]
where:
- \(\rho_{\text{wood}}\) is the density of the wood,
- \(V\) is the volume of the wood,
- \(g\) is the acceleration due to gravity.

3. **Calculate the Buoyant Force**:
- The buoyant force acting on the wood can be calculated using Archimedes' principle:
\[ \text{Buoyant force} = \rho_{\text{water}} \times V \times g \]
where:
- \(\rho_{\text{water}}\) is the density of water.

4. **Determine the Net Force**:
- The net force acting on the block can be expressed as:
\[ F_{\text{net}} = \text{Weight of wood} - \text{Buoyant force} \]
- Substituting the expressions from steps 2 and 3:
\[ F_{\text{net}} = (\rho_{\text{wood}} \times V \times g) - (\rho_{\text{water}} \times V \times g) \]
- This simplifies to:
\[ F_{\text{net}} = (\rho_{\text{wood}} - \rho_{\text{water}}) \times V \times g \]

5. **Analyze the Sign of the Net Force**:
- Since the density of wood (\(\rho_{\text{wood}}\)) is less than the density of water (\(\rho_{\text{water}}\)), the term \((\rho_{\text{wood}} - \rho_{\text{water}})\) will be negative.
- This indicates that the net force \(F_{\text{net}}\) is directed upwards, meaning the buoyant force is greater than the weight of the wood.

6. **Conclusion**:
- To keep the block of wood submerged in water, an additional downward force must be applied to counteract the upward buoyant force. This is why a force is needed to keep the block of wood inside the water.