To compare the mass, volume, and density of the wood and aluminum blocks, we can analyze the properties of each material based on the observations and principles of physics.
1. Mass:
- Wood Block: The mass of the wood block is relatively low because wood is less dense than aluminum. Therefore, for blocks of the same size, the wood will have a smaller mass.
- Aluminum Block: The mass of the aluminum block is higher. Aluminum has a higher density than wood, so for blocks of equal dimensions, the mass of the aluminum block is greater than that of the wood block.
2. Volume:
- Both blocks are stated to have the same length and width, which means they occupy the same volume.
- Volume (\( V \)) can be calculated using the formula for the volume of a rectangular prism: \[ V = \text{length} \times \text{width} \times \text{height} \]
- Since both blocks have the same dimensions, their volumes are equal.
3. Density:
- Density (\( \rho \)) is defined as mass per unit volume, described by the formula: \[ \rho = \frac{\text{mass}}{\text{volume}} \]
- Wood Block: Since the mass of the wood block is lower than that of the aluminum block while both have the same volume, the density of the wood block will be lower than that of aluminum. This lower density explains why the wood block floats in water.
- Aluminum Block: The density of the aluminum block is higher because it has a greater mass for the same volume. This higher density is what causes the aluminum block to sink in water.
Summary Comparison:
- Mass: The aluminum block has a greater mass than the wood block.
- Volume: Both blocks have the same volume.
- Density: The density of the aluminum block is greater than the density of the wood block, explaining the different behaviors in water (aluminum sinks; wood floats).
In conclusion, the differences in mass and density between the two blocks illustrate fundamental principles of buoyancy as well as the properties of the materials themselves.
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