The thrust (upthrust or buoyant force) on a body immersed in a liquid depends on three key factors: the acceleration due to gravity, the density of the liquid, and the volume of the body immersed in the liquid.
Factors Affecting Upthrust
The upthrust, also known as buoyant force, is the upward force exerted by a fluid that opposes the weight of an immersed object. This force is responsible for why objects appear lighter in water and why some objects float.
Here's a breakdown of the factors:
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Density of the Liquid (ρ): A denser liquid will exert a greater upthrust. This is because a denser liquid contains more mass per unit volume. Consequently, it displaces a greater weight of fluid, resulting in a larger upward force. For example, an object will experience a greater upthrust in saltwater than in freshwater because saltwater is denser.
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Volume of the Body Immersed (V): The larger the volume of the object immersed in the liquid, the greater the upthrust. This is because a larger immersed volume displaces a larger volume of the liquid. The upthrust is equal to the weight of the fluid displaced. If only part of the object is submerged, only the submerged volume contributes to the upthrust.
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Acceleration Due to Gravity (g): The value of 'g' determines the weight of the fluid displaced, which is directly proportional to the upthrust. On a planet with a stronger gravitational field, the upthrust will be greater (assuming the same liquid density and immersed volume). While 'g' is relatively constant on Earth's surface, it's important to remember that it is a factor in determining upthrust.
The Buoyant Force Formula
These factors are mathematically expressed by the following formula:
Fb = Vρg
Where:
- Fb is the buoyant force (upthrust)
- V is the volume of the fluid displaced (equal to the volume of the body immersed)
- ρ (rho) is the density of the liquid
- g is the acceleration due to gravity
Example
Consider a wooden block submerged in water. The upthrust acting on the block depends on:
- The density of the water: Denser water (e.g., saltwater) will exert a greater upthrust.
- The volume of the block that's submerged: If the block is fully submerged, the entire volume of the block is considered. If only partially submerged, only the submerged portion's volume matters.
- The acceleration due to gravity: Though largely constant, variations in 'g' would slightly affect the upthrust.
Conclusion
In summary, the upthrust experienced by an object submerged in a liquid is directly determined by the density of the liquid, the volume of the object immersed, and the acceleration due to gravity. Understanding these factors is crucial for predicting and explaining buoyancy phenomena.
