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When dealing with problems involving springs, it is important to understand spring compression. A spring compresses when a force is applied to it, like when the 8 kg block of wood rests on top of the spring at the bottom of the pool. Compression means the spring is squeezed smaller than its relaxed position. The amount of compression can be related to the force applied using Hooke's Law, expressed as \[ F = kx \]where:

• \( F \) is the force applied (in Newtons),
• \( k \) is the spring constant (a measure of the spring's stiffness),
• \( x \) is the displacement from the equilibrium (the amount the spring is stretched or compressed).

When the pool fills with water, buoyant forces decrease the compression and then stretch the spring beyond its original compression. The block's weight compresses the spring, and as water adds buoyant force, it affects how the spring reacts. Understanding this balance is key to solving problems involving forces and heir interactions.

Density is a crucial concept in physics, important for understanding buoyancy. The density of an object determines whether it floats or sinks. It's defined as mass per unit volume, given by the formula:\[ \rho = \frac{m}{V} \]where:

• \( \rho \) is the density,
• \( m \) is the mass of the object,
• \( V \) is the volume.

In our problem, the block has a density of 840 kg/m³, indicating that it's less dense than water (1000 kg/m³). This means the block will experience a buoyant force when submerged. Calculating the block's density helps predict how it will behave in water and how much of its volume is truly solid or hollow. Keeping an eye on the density lets us determine the buoyancy force that stretches the spring.

Calculating volume is fundamental to solving the problem, especially when determining how objects interact with forces like buoyancy. The total volume \( V \) of the block can be found using changes in the forces applied when submerged. In this problem, the total volume was determined to be \( 0.024 \ m^3 \), while the actual solid volume, derived from mass and density \( V_s = \frac{m}{\rho} \),was found to be \( 0.00952 \ m^3 \).Understanding how to calculate and compare these volumes lets you uncover the block's overall size and its components, leading to insights into the percentage of hollowness.

The calculation of hollow percentage is vital in determining how much of the block is not solid. This percentage considers the block's solid and total volumes. Here's how it unfolds:1. **Determine Total Volume**: Use equations involving buoyancy to find the complete volume when submerged.2. **Calculate Solid Volume**: Use density to compute the volume that is actually wood.3. **Find Hollow Volume**: Subtract the solid volume from the total volume.4. **Calculate Hollow Percentage**: \[ \text{Hollow Percentage} = \frac{V_h}{V} \times 100\% \]where:

• \( V_h \) is the hollow volume,
• \( V \) is the total volume of the block in water.

In this problem, the hollow percentage was determined to be approximately \( 60.33\% \), indicating a significant portion of the block is hollow. Understanding this helps us interpret the block's structure and how it interacts with forces like buoyancy and compression.