We all know the story of Archimedes jumping out a bathtub naked shouting Eureka !! 
Not sure if the story is true (Did Archimedes coin the term Eureka?), but all of us learn about it in school along with the famous Archimedes’ Principle.
I will come back to what the principle is, after I talk about how we learned this thru an interesting experiment in this week’s Stable Bow session.
I started by posing this puzzle of the two identical bottles.
One has marbles in it (total weight 250gms) and the other has coins (total weight 500gms). The two bottles are identical in shape and watertight. See the picture below.
Now, here is the question I posed to all the children.
If I dip both of these bottles into water, which bottle will feel more force due to water, and hence greater reduction in weight. See the picture below.
What would your answer be? Any WHY? Don’t look for the answer below. Think for a minute.
Most children answered that the heavier bottle will feel more force upwards, hence Y > X. A few said that the lighter bottle will feel more force, as they see it floating up faster, so X > Y.
This is what our intuition tells us.
Well the right answer is that X = Y. We tested it and found in both cases the weight
reduced by 200gms.
The loss in weight of the bottle (or any object) depends on the submerged volume and not the weight of the bottle (as well as the what the liquid is).
This is very counter intuitive. That is why Archimedes was a genius to recognise this.
With a simple weighting scale, two bottles bought at a local grocery store, some marbles and coins – we discovered the Archimedes’ principle at work for ourselves !!
There are two important things I want to point out in this learning process.
We had to try and guess the answer before we learn the theory or a new concept. Secondly, we had to experience it to see how counter intuitive it is. Just regurgitating the principle from a text book doesn’t register and stay with you.
Try it at home or in the classroom.
Going back to my promise.
This the principle in technical terms:
Archimedes’ principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Archimedes’ principle is a law of physics fundamental to fluid mechanics. (Source Wikipedia)
Any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. (Source On Floating Bodies by Archimedes of Syraccuse)
p.s. It is NOT ‘volume of the liquid displaced is equal to the volume of the object submerged’. That is true, but is a common misunderstanding about what the Archimedes’ Principle states.
