Physics - Archimedes' Principle

What is Archimedes’ principle?

The upthrust on an object in a fluid is equal to the weight of fluid displaced.

What is the force of upthrust on a boat?

The weight of water that the boat displaces.

In , why is there a resultant force upwards?

Pressure increases with depth. There is more pressure on the bottom of the object.

In , why is there pressure on the sides?

Pressure is just particles bumping into the side, so particles bump into the side too.

In , what is the resultant motion?

The object accelerates upwards.

In , what does $d$ represent?

The depth of the object.

In , what does $h$ represent?

The height of the object.

What is the formula for the force of pressure $P$ over an area $A$?

\[A \times P\]

What is the formula for the force of pressure at a height $h$ over an area $A$?

\[\rho h g A\]

In , what is the distance to the bottom of the object?

\[d + h\]

In , what is the pressure at the top of the object if it has a surface area $A$?

\[\rho d g A\]

In , what is the pressure at the bottom of the object if it has a surface area $A$?

\[\rho (d + h) g A\]

What do you get if you expand $\rho (d + h) g A$?

\[\rho d g A + \rho h g a\]

In , if $\rho d g A + \rho h g a$ is the force at the bottom of the object and $\rho d g A$ is the force at the top, what is the resultant force?

\[\rho h g A\]

In , the resultant force on the object is $\rho h g A$. How could you simplify this?

\[\rho g V\]

How can you think about the equation $\text{upthrust} = \rho g V$?

What is the quation for upthrust?

\[U = \rho g V\]