Upthrust, also known as buoyant force, can be determined by calculating the weight of the fluid displaced by the object. Here's a breakdown of how to find it:
Understanding Upthrust
Upthrust is an upward force exerted by a fluid (liquid or gas) that opposes the weight of an immersed object. It's the reason why objects float or appear lighter in water. Archimedes' principle states that the upthrust on a submerged object is equal to the weight of the fluid displaced by the object.
Formula for Upthrust
The formula to calculate upthrust is:
Upthrust = Volume of fluid displaced × Density of fluid × Acceleration due to gravity
Which can also be written as:
Upthrust (Fu) = V × ρ × g
Where:
- Fu is the upthrust (measured in Newtons, N)
- V is the volume of fluid displaced (which is equal to the volume of the object submerged, measured in cubic meters, m3)
- ρ (rho) is the density of the fluid (measured in kilograms per cubic meter, kg/m3)
- g is the acceleration due to gravity (approximately 9.81 m/s2 on Earth)
Steps to Calculate Upthrust:
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Determine the volume of fluid displaced: This is often the trickiest part. If the object is fully submerged, the volume of fluid displaced is equal to the volume of the object. If the object is only partially submerged, you need to determine the volume of the object that is below the surface of the fluid. This may be given in the problem or need to be calculated using geometry.
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Find the density of the fluid: The density of the fluid needs to be known or provided. Common densities (at room temperature) include:
- Water: 1000 kg/m3
- Seawater: Approximately 1025 kg/m3
- Air: Approximately 1.225 kg/m3
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Use the acceleration due to gravity: Unless stated otherwise, assume the acceleration due to gravity (g) is 9.81 m/s2.
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Apply the formula: Plug the values of V, ρ, and g into the formula Fu = V × ρ × g to calculate the upthrust.
Example:
A stone with a volume of 0.005 m3 is fully submerged in water. What is the upthrust on the stone?
- Volume of fluid displaced (V) = 0.005 m3
- Density of water (ρ) = 1000 kg/m3
- Acceleration due to gravity (g) = 9.81 m/s2
Upthrust (Fu) = 0.005 m3 × 1000 kg/m3 × 9.81 m/s2 = 49.05 N
Therefore, the upthrust on the stone is 49.05 N.
Key Considerations:
- Units: Ensure all values are in the correct units (meters, kilograms, seconds) before performing the calculation.
- Partial Submersion: For partially submerged objects, accurately determining the submerged volume is crucial.
- Density Variations: The density of fluids can vary with temperature and pressure, so use the correct density value for the specific conditions.
In summary, upthrust is calculated by multiplying the volume of the displaced fluid by its density and the acceleration due to gravity. This principle is based on Archimedes' principle and helps explain buoyancy.
