Upthrust, also known as buoyant force, can be calculated using different methods depending on the information available. The most common and direct method involves using Archimedes' principle.
Understanding Upthrust
Upthrust is the upward force exerted by a fluid (liquid or gas) on an object that is partially or fully submerged in it. This force is what makes objects appear lighter in water.
Methods for Calculating Upthrust
Here are the primary methods for calculating upthrust:
1. Using Archimedes' Principle:
Archimedes' principle states that the upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This is the most common and generally applicable method.
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Formula:
Upthrust (U) = Weight of displaced fluid -
Expanded Formula:
U = V * ρ * gWhere:
U= Upthrust (measured in Newtons, N)V= Volume of fluid displaced by the object (measured in cubic meters, m³)ρ(rho) = Density of the fluid (measured in kilograms per cubic meter, kg/m³)g= Acceleration due to gravity (approximately 9.81 m/s²)
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Example: A rock with a volume of 0.01 m³ is submerged in water (density = 1000 kg/m³). Calculate the upthrust.
U = 0.01 m³ * 1000 kg/m³ * 9.81 m/s² = 98.1 N
2. Using the Difference in Weight:
You can also calculate upthrust by measuring the weight of an object in air and its apparent weight when submerged in a fluid.
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Formula:
Upthrust (U) = Weight in air - Weight in fluid -
Example: A metal block weighs 50 N in air and 40 N when fully submerged in water. The upthrust is:
U = 50 N - 40 N = 10 N
3. Relating to Mass of Displaced Fluid:
As the upthrust equals the weight of the displaced fluid, you can also use the mass of the displaced fluid directly.
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Formula:
Upthrust (U) = m * gWhere:
m= mass of the fluid displaced (in kg)g= acceleration due to gravity (approximately 9.81 m/s²)
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Example: If a submerged object displaces 2 kg of water, the upthrust is:
U = 2 kg * 9.81 m/s² = 19.62 N
Important Considerations:
- Density: The density of the fluid is crucial. Different fluids (e.g., water, oil, air) have different densities, leading to different upthrust values for the same object.
- Volume Displaced: It's the volume of fluid displaced by the object that matters, not the object's total volume unless it's fully submerged.
- Units: Ensure you use consistent units (SI units are generally preferred) for accurate calculations.
Summary
Calculating upthrust involves determining the weight of the fluid displaced by a submerged object. This can be achieved directly using the volume and density of the fluid, or indirectly by measuring the apparent weight loss of the object when submerged. Understanding these methods allows you to accurately quantify the buoyant force acting on an object in a fluid.
