# 1.24 Upthrust

## Upthrust

#### Archimedes' Principle

• Archimedes’ principle states:

An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object

• The object sinks until the weight of the fluid displaced is equal to its own weight
• Therefore the object floats when the magnitude of the upthrust equals the weight of the object

• The magnitude of upthrust can be calculated in steps by:
• Find the volume of the submerged object, which is also the volume of the displaced fluid
• Find the weight of the displaced fluid
• Since m = ρV (density × volume), upthrust is equal to F = mg which is the weight of the fluid displaced by the object

• Archimedes’ Principle explains how ships float: Boats float because they displace an amount of water that is equal to their weight

#### Worked example

Atmospheric pressure at sea level has a value of 100 kPa. The density of sea water is 1020 kg m-3.

At what depth in the sea would the total pressure be 250 kPa?

A. 20 m               B. 9.5 m               C. 18 m          D. 15 m #### Worked example

Icebergs typically float with a large volume of ice beneath the water. Ice has a density of 917 kg m-3 and a volume of Vi.

The density of seawater is 1020 kg m-3.What fraction of the iceberg is above the water?

A. 0.10 Vi          B. 0.90 Vi          C. 0.97 Vi          D. 0.20 Vi  #### Exam Tip

Don't get confused by the two step process to find upthrust.

• Step 1: You need the volume of the submerged object, but only because you want to know how much fluid was displaced
• Step 2: What you really want to know is the weight of the displaced fluid.

A couple of familiar equations will help;

• m = ρV to get mass (and that's the V from step 1 out of the way),

then

• W = mg to get weight

If you are feeling particularly mathematical, you can combine your equations, so that W = ρVg ### Get unlimited access

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