Upthrust

Definition of Upthrust

Upthrust is the upward force that a fluid (liquid or gas) exerts on an object placed in it. This force acts opposite to the weight of the object and can make the object feel lighter or even cause it to float. Upthrust arises because the pressure in a fluid increases with depth, so the pressure pushing up on the bottom of the object is greater than the pressure pushing down on the top, creating a net upward force.

Cause of Upthrust

Fluids exert pressure on objects submerged in them. This pressure increases with depth due to the weight of the fluid above. Therefore, the pressure at the bottom of an object submerged in a fluid is higher than the pressure at the top. This difference in pressure results in a net upward force called upthrust.

For example, if a cube is submerged in water, the water pressure on its bottom surface is greater than on its top surface, pushing the cube upwards.

The greater the depth, the larger the pressure difference, and so the greater the upthrust.

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 principle explains why some objects float while others sink:

• If the upthrust equals the object's weight, the object floats.
• If the upthrust is less than the object's weight, the object sinks.

This principle is fundamental in understanding buoyancy and is widely used in ship design and other applications involving fluids.

For instance, a boat floats because it displaces a volume of water whose weight is equal to the weight of the boat.

Factors Affecting Upthrust

The size of the upthrust force depends on several factors:

• Volume of fluid displaced: The larger the volume of fluid displaced by the object, the greater the upthrust. This is because more fluid weight is being pushed aside.
• Density of the fluid: Denser fluids exert a greater upthrust for the same volume displaced. For example, upthrust in seawater is greater than in freshwater because seawater is denser.
• Shape and immersion of the object: The shape affects how much of the object is submerged and therefore how much fluid is displaced. An object fully submerged displaces more fluid than one partially submerged, affecting the upthrust.

Learning Example

A solid cube of volume 0.02 m³ is fully submerged in freshwater (density $1000 \text{ kg/m}^3$). Calculate the upthrust acting on the cube. (Take $g = 9.8 \text{ m/s}^2$)

Using Archimedes' principle, Upthrust = volume of fluid displaced × density of fluid × gravitational field strength (g).

Weight of displaced fluid = mass × gravity

Mass of displaced fluid = volume × density = $0.02 \times 1000 = 20 \text{ kg}$

Therefore, upthrust = $20 \times 9.8 = 196 \text{ N}$

So, the cube experiences an upward force of 196 N from the water.