To calculate the mass of water displaced, you multiply the volume of the object submerged in the water by the density of water.
Here's a breakdown:
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Understanding the Principle: This calculation is based on Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
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Formula:
Mass of water displaced = Volume of object submerged × Density of water
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Density of Water: The density of fresh water is approximately 1000 kg/m³ (kilograms per cubic meter) or 1 g/cm³ (grams per cubic centimeter). For saltwater, the density is slightly higher, around 1025 kg/m³, due to the dissolved salt.
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Steps for Calculation:
- Determine the Volume: Find the volume of the object that is submerged in the water. This might be given directly or require calculation based on the object's dimensions. If the object is floating, the volume displaced is equal to the volume of the part of the object below the waterline.
- Identify the Density: Use the appropriate density for the water (freshwater or saltwater).
- Multiply: Multiply the submerged volume by the density of the water.
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Example:
Let's say you have a rock with a submerged volume of 0.05 m³ in freshwater. To calculate the mass of water displaced:
Mass = 0.05 m³ × 1000 kg/m³ = 50 kg
Therefore, the mass of water displaced is 50 kg.
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Units: Ensure that your units are consistent. If the volume is in cubic meters (m³) and the density is in kilograms per cubic meter (kg/m³), the mass will be in kilograms (kg). If the volume is in cubic centimeters (cm³) and the density is in grams per cubic centimeter (g/cm³), the mass will be in grams (g).
By following these steps, you can accurately calculate the mass of water displaced by an object.
