Have you ever noticed that objects feel lighter in water? This happens because of upthrust, also known as buoyant force. It is the force exerted by a fluid (liquid or gas) that pushes an object upwards, counteracting the force of gravity.
The magnitude of upthrust acting on a body depends on several factors, including the density of the fluid, volume of the displaced fluid, gravitational acceleration, and shape of the object. Understanding these factors helps explain why ships float, balloons rise, and objects behave differently in different fluids.
This topic will explore what upthrust is, how it is calculated, and the factors that influence its magnitude.
What Is Upthrust?
Definition of Upthrust
Upthrust, or buoyant force, is an upward force exerted by a fluid that opposes the weight of an object immersed in it. This force allows objects to float or feel lighter in water.
Archimedes’ Principle states:
The upthrust acting on an object is equal to the weight of the fluid displaced by that object.
This means that if an object displaces more fluid, it experiences greater upthrust.
Formula for Upthrust
Upthrust ( F_b ) is calculated using the equation:
where:
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F_b = Buoyant force (Newtons, N)
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rho = Density of the fluid (kg/m³)
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g = Acceleration due to gravity (9.81 m/s²)
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V = Volume of the displaced fluid (m³)
From this formula, we can see that the upthrust depends on fluid density, gravity, and displaced volume.
Factors Affecting Upthrust
1. Density of the Fluid ( rho )
The denser the fluid, the greater the upthrust. This is because a denser fluid has more mass per unit volume, meaning the displaced fluid weighs more, generating a stronger upward force.
For example:
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Seawater provides more upthrust than freshwater because it contains dissolved salts, making it denser.
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Oil provides less upthrust than water because it has a lower density.
This is why swimming in the ocean is easier than swimming in a freshwater lake-the increased density of seawater provides more buoyancy.
2. Volume of the Displaced Fluid ( V )
The larger the volume of fluid displaced, the greater the upthrust. This is why:
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A large ship floats, even though it is made of metal, because its shape allows it to displace a large amount of water.
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A small, dense object like a metal cube sinks because it displaces very little fluid.
If an object is fully submerged, the displaced volume is equal to the object’s volume. If the object is partially submerged, only a portion of its volume contributes to the displaced fluid.
Example:
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A wooden block floating on water is partially submerged, displacing just enough water to balance its weight.
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A submarine controls its buoyancy by adjusting its ballast tanks, which change the volume of water displaced.
3. Acceleration Due to Gravity ( g )
Gravity plays a role in determining how much upthrust is exerted on an object. The force of upthrust depends on the weight of the displaced fluid, which is affected by the value of g .
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On Earth, gravity is 9.81 m/s², which provides a certain amount of upthrust.
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On the Moon, where gravity is weaker (1.62 m/s²), the upthrust in a liquid would also be weaker.
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On Jupiter, where gravity is stronger (24.79 m/s²), upthrust would be much greater.
This means that the same object in the same fluid would experience different upthrust forces on different planets due to varying gravitational acceleration.
4. Shape and Orientation of the Object
The shape of an object affects how much fluid it displaces, influencing the upthrust it experiences.
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A flat or hollow object (like a ship) can displace more fluid and experience greater upthrust, allowing it to float.
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A compact, dense object (like a metal ball) displaces little fluid and sinks.
For example:
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A hollow metal boat floats, while a solid metal block sinks.
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A wide raft stays on the surface, but if the same material is shaped into a compact sphere, it might sink.
The orientation of the object also matters. A horizontal plate may displace more water than a vertical one, changing the upthrust.
Real-Life Applications of Upthrust
1. Ships and Boats
Ships are designed to displace enough water to generate an upthrust equal to their weight, allowing them to float.
2. Submarines
Submarines adjust their buoyancy by controlling their ballast tanks, allowing them to float, sink, or remain at a fixed depth.
3. Hot Air Balloons
Buoyant force also exists in gases. A hot air balloon rises because warm air is less dense than the surrounding cold air, generating an upward force.
4. Icebergs Floating in Water
Icebergs float because ice is less dense than liquid water. However, about 90% of an iceberg is submerged, with only a small portion visible above water.
5. Swimming and Floating in Water
A swimmer experiences upthrust from water, which helps them stay afloat. When a person inhales, their body becomes less dense, making floating easier.
Example Calculation of Upthrust
Problem: Calculating Upthrust on a Fully Submerged Object
A wooden block with a volume of 0.02 m³ is completely submerged in water. If the density of water is 1000 kg/m³, what is the upthrust acting on the block?
Solution:
Using the formula:
So, the upthrust acting on the wooden block is 196.2 N.
Common Misconceptions About Upthrust
1. Objects That Sink Do Not Experience Upthrust
Even if an object sinks, it still experiences upthrust. However, it sinks because its weight is greater than the upthrust acting on it.
2. Heavy Objects Cannot Float
The ability to float is not just about weight; it depends on displaced fluid volume and density. Ships, despite their weight, float because they displace enough water to generate sufficient upthrust.
3. Only Liquids Provide Upthrust
Upthrust occurs in all fluids, including gases. This is why hot air balloons rise in the atmosphere.
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Upthrust is an upward force exerted by a fluid that counteracts an object’s weight.
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The upthrust on a body depends on the density of the fluid, the volume of displaced fluid, gravity, and the object’s shape.
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Objects float if upthrust equals or exceeds their weight and sink if the upthrust is smaller.
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Real-world applications include ships, submarines, hot air balloons, and swimming.
Understanding upthrust is essential for engineering, science, and daily life. Whether designing floating structures, exploring the ocean, or understanding how we swim, the principles of buoyancy and upthrust play a crucial role in our world.