A rectangular block of wood, 11 cm
×
18 cm
×
41 cm, has a specific gravity of 0.6 Determine the buoyant force that acts on the block when it is placed in a pool of fresh water. Hint: Draw a free-body diagram labeling all of the forces on the block. (Express your answer to two significant figures.)

To determine the buoyant force on the rectangular block of wood when it is submerged in water, let's start with understanding the principles involved.

### Given Data
- Dimensions of the block: \( 11 \, \text{cm} \times 18 \, \text{cm} \times 41 \, \text{cm} \)
- Specific gravity of the wood, \( SG = 0.6 \)

### Step-by-Step Solution

1. **Calculate the Volume of the Block:**

   Since the block is a rectangular prism, the volume \( V \) can be calculated by multiplying its dimensions:
   \[
   V = \text{Length} \times \text{Width} \times \text{Height}
   \]
   Converting dimensions to meters for standard units (1 cm = 0.01 m):
   \[
   V = (0.11 \, \text{m}) \times (0.18 \, \text{m}) \times (0.41 \, \text{m}) = 0.008118 \, \text{m}^3
   \]

2. **Determine the Buoyant Force:**

   The buoyant force, \( F_b \), is given by Archimedes’ principle:
   \[
   F_b = \rho_{\text{water}} \cdot V \cdot g
   \]
   where:
   - \( \rho_{\text{water}} \) is the density of water (approximately \( 1000 \, \text{kg/m}^3 \) for fresh water),
   - \( g \) is the acceleration due to gravity, \( 9.81 \, \text{m/s}^2 \),
   - \( V \) is the volume of the block.

   Substituting the values:
   \[
   F_b = 1000 \, \text{kg/m}^3 \times 0.008118 \, \text{m}^3 \times 9.81 \, \text{m/s}^2
   \]
   \[
   F_b = 79.6 \, \text{N}
   \]

### Answer

The buoyant force acting on the block when it is placed in fresh water is approximately:
\[
F_b = 80 \, \text{N} \quad (\text{to two significant figures})
\]

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What would happen to the buoyant force if the block's specific gravity increased?
2. How would the buoyant force change if the block were placed in salt water instead of fresh water?
3. If the block were completely submerged, how would we calculate its weight in water?
4. How does the buoyant force compare to the block's weight, given its specific gravity?
5. What factors determine whether the block will float or sink in water?

**Tip:** Specific gravity less than 1 indicates that an object will generally float in water, as it has a lower density than water.

A rectangular block of wood, 11 cm × 18 cm × 41 cm, has a specific gravity of 0.6. Determine the buoyant force that acts on the block when it is placed in a pool of fresh water. Hint: Draw a free-body diagram labeling all of the forces on the block. (Express your answer to two significant figures.)

Learn how to calculate the buoyant force acting on a rectangular block of wood in a pool of fresh water. With dimensions of 11 cm × 18 cm × 41 cm and a specific gravity of 0.6, the solution demonstrates how to apply Archimedes' Principle and volume calculation to find the buoyant force of approximately 80 N.

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