# Physics - Archimedes' Principle

> Source: https://ollybritton.com/notes/a-level/physics/topics/archimedes-principle/ · Updated: 2020-11-11 · Tags: physics, pressure, year-1, school

##### 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 ![PHOTO](object-in-fluid.png), why is there a resultant force upwards??
Pressure increases with depth. There is more pressure on the bottom of the object.

##### In ![PHOTO](object-in-fluid.png), why is there pressure on the sides??
Pressure is just particles bumping into the side, so particles bump into the side too.

##### In ![PHOTO](object-in-fluid.png), what is the resultant motion??
The object accelerates upwards.

##### In ![PHOTO](object-in-fluid-depth.png), what does $d$ represent??
The depth of the object.

##### In ![PHOTO](object-in-fluid-depth.png), 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 ![PHOTO](object-in-fluid-depth.png), what is the distance to the bottom of the object??
$$
d + h
$$

##### In ![PHOTO](object-in-fluid-depth.png), what is the pressure at the top of the object if it has a surface area $A$??
$$
\rho d g A
$$

##### In ![PHOTO](object-in-fluid-depth.png), 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 ![PHOTO](object-in-fluid-depth.png), 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 ![PHOTO](object-in-fluid-depth.png), 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 $\text{upthrust} = \rho g V$??
* $\rho V$ is the mass of the water displaced
* $\rho g V$ is the weight of the water displaced

##### What is the quation for upthrust??
$$
U = \rho g V
$$

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