Upthrust: The Invisible Lifting Hand
The Core Principles of Buoyancy
Imagine pushing an empty plastic bottle into a bucket of water. You can feel an upward push against your hand. This push is the upthrust. It is not a magical force; it is a direct and predictable result of how fluids (liquids and gases) behave. Every fluid exerts pressure, and this pressure increases with depth. Think about diving to the bottom of a swimming pool – your ears feel more pressure the deeper you go.
When an object is submerged, its bottom surface is at a greater depth than its top surface. Therefore, the pressure pushing upwards on the bottom of the object is greater than the pressure pushing downwards on the top. It is this difference in pressure that creates a net upward force – the upthrust.
Archimedes' Principle: The Golden Rule
The story goes that the ancient Greek scientist Archimedes discovered this principle while taking a bath. He was so excited he ran naked through the streets shouting "Eureka!" (I have found it!). Archimedes' Principle gives us a simple way to calculate the upthrust without needing to know the pressure at every point on the object.
Formula: $ F_b = \rho_{fluid} \times V_{displaced} \times g $
Where:
$ F_b $ = Buoyant Force (Upthrust) in Newtons (N)
$ \rho_{fluid} $ = Density of the fluid in kg/m³
$ V_{displaced} $ = Volume of fluid displaced in m³
$ g $ = Acceleration due to gravity (approx. 9.8 m/s²)
For example, if you submerge a brick that displaces 2 liters (0.002 m³) of water, the upthrust on the brick is the weight of that 2 liters of water. Since the density of water is 1000 kg/m³, the mass of displaced water is 2 kg, and its weight is about 19.6 N. So, the upthrust force on the brick is 19.6 N.
To Float or Not to Float: Density is the Key
The fate of an object in a fluid – whether it sinks, floats, or remains suspended – is determined by the battle between two forces: the object's weight (acting downwards) and the upthrust (acting upwards). The secret weapon in this battle is density.
| Condition | Comparison of Densities | Result | Example |
|---|---|---|---|
| Upthrust > Weight | $ \rho_{object} < \rho_{fluid} $ | The object will float and rise to the surface. | A cork in water, a helium balloon in air. |
| Upthrust = Weight | $ \rho_{object} = \rho_{fluid} $ | The object will remain suspended at any depth (neutral buoyancy). | A submarine maintaining its depth, a fish with a swim bladder. |
| Upthrust < Weight | $ \rho_{object} > \rho_{fluid} $ | The object will sink to the bottom. | A stone in water, a metal ball in air. |
This is why a massive, heavy aircraft carrier floats. It is not made of a material less dense than water; steel is much denser. However, the ship is designed to displace a huge volume of water. The shape of the hull pushes aside a weight of water equal to the entire weight of the ship. According to Archimedes' Principle, the upthrust is then equal to the ship's weight, allowing it to float.
Upthrust in Action: From Ships to Balloons
The principles of upthrust are not confined to laboratories; they are at work all around us, enabling technologies and natural phenomena we often take for granted.
1. Shipbuilding and Flotation: A solid block of steel sinks because it cannot displace enough water to generate an upthrust matching its weight. But when the same steel is shaped into a hollow hull, its overall density (mass divided by total volume, including the air inside) becomes less than that of water. The "Plimsoll line" marked on the hull of ships indicates the safe loading limit, ensuring the ship displaces enough water to stay afloat in different water densities (e.g., fresh water vs. salt water).
2. Hot Air Balloons: Upthrust works in gases just as it does in liquids. A hot air balloon floats because the air inside the balloon is heated, making it less dense than the cooler air outside. The weight of the cold air displaced by the balloon is greater than the total weight of the balloon (envelope, basket, burners, and the hot air inside). This creates a net upward force, causing the balloon to rise.
3. Hydrometers: This is a simple instrument used to measure the density of a liquid. It is a sealed glass tube with a weighted bottom. It floats upright in the liquid. The denser the liquid, the greater the upthrust for the same volume displaced, so the hydrometer floats higher. The density is read from a scale on the stem. It is commonly used to test battery fluid or the alcohol content in spirits.
4. Swimming and Submarines: Fish control their buoyancy using an organ called a swim bladder, filling it with gas to become less dense and rise, or releasing gas to become denser and sink. Submarines use ballast tanks. To dive, they fill these tanks with water, increasing the submarine's overall density. To surface, they pump the water out and replace it with air, decreasing the density.
Common Mistakes and Important Questions
Q: Is upthrust only dependent on the volume of the object?
No, this is a common misconception. Upthrust depends on the volume of the object that is submerged (which equals the volume of fluid displaced), the density of the fluid, and gravity. It does not depend on the depth of the object (once fully submerged), the object's mass, or its density. For a fully submerged object in a uniform fluid, the upthrust remains constant regardless of how deep it goes because the volume displaced is constant.
Q: Why do I feel lighter when I'm in a swimming pool?
Your body is submerged in water and experiences an upthrust. This upward force opposes the downward pull of gravity (your weight). The net force acting on you is less than your actual weight, so you feel lighter. This is sometimes called your "apparent weight". Apparent weight = Actual weight – Upthrust.
Q: If a coin sinks in water, does it still experience an upthrust?
Yes, absolutely. Every submerged object experiences an upthrust. The coin sinks not because there is no upthrust, but because the upthrust acting on it is less than its weight. If you could tie the coin to a very light, large, hollow object that displaces a lot of water, the combined density might become less than water's, and the "coin-boat" would float.
Footnote
1 Buoyant Force: Another term for upthrust; the upward force exerted by a fluid on a submerged or partially submerged object.
2 Archimedes' Principle: A law of physics stating that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces.
3 Density ($ \rho $): A measure of mass per unit volume, typically expressed in kilograms per cubic meter (kg/m³). It describes how much matter is packed into a given space.
4 Displaced Fluid: The volume of fluid that is pushed out of the way when an object is placed in it. This volume is exactly equal to the volume of the part of the object that is submerged.
5 Plimsoll Line: A reference mark located on a ship's hull that indicates the maximum depth to which the vessel may be safely immersed when loaded with cargo in different water conditions.