How Archimedes Solved the Buoyant Force Puzzle 2000 Years Ago

Why does an iceberg float on the ocean instead of sinking, and how much is lurking under the surface? The answer is all about the buoyant force. Get the notes for free here: courses.physicswithelliot.com...
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[@sirwinston2368]

New subscriber - Yeah, there's always a guy like me who makes a comment like this - I don't believe you described HOW Archimedes solved the buoyant force problem. It wasn't about dropping a crown in the bathtub. In any event - I love your videos Elliot. I am a 63-year old engineer (BSChE) who is going to retire in about a year and go back to my alma mater (Michigan Tech) and get a degree in physics. I've been boning up for the past year or so with MIT OCW, you, ViaScience, and others [plus texts by Pauling/Bright, Griffiths, Feynman, Jackson, and Dirac (4th ed. 1958, and it's way over my head, just like the Jackson book)]. Great stuff! My goal is to understand Dirac! The more I understand, the more I realize just how ignorant I am, so I keep pressing ahead. Thanks again Elliot. I appreciate the time and effort you put into your videos.

[@TIO540S1]

When discussion come up regarding the GOAT mathematician, Archimedes is at or near the top of my list. Oh, and by the way, as usual, an excellent video!

[@PhysicswithElliot]

Thanks Rob!

[@davidbrisbane7206]

1. NEWTON.
2. GAUSS.
3. ARCHIMEDES.

[@cursive1805]

​@@davidbrisbane7206*Euler

[@KiWi13th]

So I have a solution to the ice cube on water problem:
---Spoiler----
.
.
.
.
We only care for the difference of water level after we have added the ice cubes.
So, when we look at the volume of water that is displaced by the ice cube, it is equal to the volume of the ice cube multiplied with the ratio of densities (density of ice cube over density of water). I like to then separate the ice cube and water in my thought. The ice cube has a mass that is conserved, so volume times density stays the same even after melting (even though it hasn't got the shape of a cube anymore): The new volume of the "melted" ice cube will be the original volume of the ice cube times the ice density divided by the liquid density. This is exactly equal to the volume that was initially displaced by the ice cube, and thus, the volume stays the same and the water level doesn't rise.
I like to think that the ice cube, which becomes more dense when melting, then just perfectly "fits" into the volume it once displaced. So when we said, only 10 % of the ice cube were above the surface, those 10 % now additionally fit perfectly in the displaced volume, because it's no longer displaced by ice, but displaced by the denser water.

[@PhysicswithElliot]

You might like my follow up video about the melting ice cube puzzle!

[@KiWi13th]

@@PhysicswithElliot Cheers, I hadn't seen that one. This reminds me of my fluid dynamic lectures, where we started with puzzles like that. Another great puzzle was: Imagine you stand in a boat, which floats on a lake, and carry a rock. Now you throw the rock into the water. Does the water level rise, fall, or stay the same?

[@krasimirronkov17]

Didnt understand how do you know that the buoyant force is equal to the weight of the water that was displaced by the duck. And also can you make a video on what is pressure is fluid mechanics

[@sabouedcleek611]

From what I can recall, you can start by thinking of a body of water. Since the water stays stationary, it means that the forces acting on any enclosed volume of water must be zero.
The forces on any body of water includes: the water above pushing it down, the water below pushing it up, and the weight of the volume of water.
It you replace the enclosed volume with an object with the same shape, then the force upwards(buoyancy?) will be exactly equal to the weight of the original volume of water(because it used to counteract it and was equal in magnitude).
(Just realized that this was introduced in the video, oh well, a different interpretation does no harm)

[@LarrySchneider]

I was waiting to find out how the water’s salinity impacts the water!s density and therefore result. I hope you delve into this in a future video and possibly describe what effects the atoms of salt have on the atoms of water in various situations and why.

[@PhysicswithElliot]

Saltwater is a couple percent denser, which increases the buoyant force slightly. But you’ll have to subscribe to a chemistry channel to learn more about that!

[@davidbrisbane7206]

Hello Elliot.

[@robertcantwell9569]

👏👏👏

[@krishpandey9725]

I signed in for notes with two different IDs No mails so far

[@PhysicswithElliot]

Maybe it went in your spam folder? If you can't find it send me an email ([e-mail])

[@krishpandey9725]

@@PhysicswithElliot no it's not in spam I checked already I have sent you a mail.