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Monday, April 1, 2013

1+1 sometimes is not 2

This is one of the greatest math problems, side by side with the one that states that 0 is different than 0. But this demonstration is not about math, is about Archimedes' Principle.

Archimedes' Principle states:
" a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid"

In other words, when we place a body in a fluid, like water, the volume of the object equals the volume of displaced water.

The simplest example is a bath. If we fill the tub with water up to the top and we lay down inside it, the water will exit, and your bathroom will be a very wet place similar to a lake. The amount of water that came out equals your body volume. You can, with some time and work, calibrate the tub to find out your body volume, 1L=1dm3.
In this example 1+1=2, but sometimes 1+1= "not sure" 

What we need :
  • glass container,
  • tape, one you can write on
  • pen,
  • sugar,
  • glass container with a scale,
  • paper towel,
  • straw,
  • spoon,
  • hot water.
How to:
  1. Clean the container;
  2. Apply a vertical strip of tape in the container;
  3. Fill the scaled container with hot water (container A);
  4. Pour the water in the other container (container B); 
  5. Use the pen on the tape to mark the water level in container B;
  6. Fill the container A again and add the water to the container B
  7. Use the pen again and mark the water level in container B;
  8. Reject the water;
  9. With the paper towel clean and dry container B;
  10. Repeat step 3, 4 and 5;
  11. Now fill up the container A with sugar;
  12. Add the sugar to container B;
  13. Use the spoon to mix the solution;
  14. Use the pen to mark the level;
What happens?
1 volume of hot water + 1 volume of sugar it's different from 2 volumes of hot water.

Water molecules are organized like a net. This net is stable and cohesive due to hydrogen bridges. When this net is formed some hydrogen atoms link to neighbor water molecules by a "false" bond with the oxygen, those are called hydrogen bridges. When this happens some "blank spaces" are left between the molecules- in the net. This spaces are as big as the molecules are excited, thats why we used hot water- more empty space makes dissolution more efficient.

When we add the sugar the sugar molecules occupy the empty spaces between water molecules, thats why:

1 sugar unit+ 1 water unit doesn't equal 2 water units

This is a demonstration, but you can make it an experiment:

Go further:
Try with 1 unit of water+ 1 unit of sugar. Does that equals 2 units of sugar?
Try with cold and ice water, what happens?

Et Voilá!
Now you can teach some stuff to your math teacher


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