Archimedes' principle and upthrust

Introduction to Upthrust

Have you ever noticed that when you try to push a plastic bowl inside a bucket of water, the water pushes it back up? Or when you are lifting a bucket of water from a well, it feels very light as long as it is still inside the water, but becomes heavy once it comes out? That 'push' you feel from the water is what we call Upthrust.

In simple terms, upthrust is just the force that makes things feel lighter when they are inside water or any liquid.

The Discovery by Archimedes

Many years ago, a scientist named Archimedes discovered exactly how to calculate this upward force. He found out that the weight an object 'loses' when you put it in water is exactly the same as the weight of the water that the object pushed out of its way.

Basically, if a stone pushes away 2kg of water, the water will push that stone up with a force equal to the weight of that 2kg of water.

Apparent Weight and Real Weight

When an object is in the air, we measure its Real Weight. When it is inside water, it has an Apparent Weight. The difference between these two is the upthrust.

Upthrust = Real Weight in air - Apparent Weight in liquid.

Factors affecting Upthrust:

The volume of the object immersed (The bigger the part inside, the higher the upthrust).

The density of the liquid (Saltwater like the Bar Beach pushes up more than fresh tap water).

The acceleration due to gravity (g).

Worked Example

A piece of metal weighs 50N in air and 42N when completely immersed in water. Calculate the upthrust acting on the metal.

1. Identify the Real Weight in air = 50N.

2. Identify the Apparent Weight in water = 42N.

3. Use the formula: Upthrust = Real Weight - Apparent Weight.

4. Upthrust = 50N - 42N = 8N.

The upthrust acting on the metal is 8N.