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The cartesian diver

The cartesian diver
Materials and mounting
instructions:
  a half litre plastic bottle and the cap of a ball-point pen (preferably transparent). Fix to the cap two clips to make it heavy, fill the bottle of water and immerge vertically the cap: if the dimension of the cap and the weight of the clips are correct, the cap will float.
How to play:   close the bottle; if you squeeze the bottle as shown in the picture, the “diver” sinks, if you release the pressure, it comes up and floats.
Physics:  
  • when the cap is immerged vertically into the water, a blob of air is trapped inside the cap (if the cap is transparent, the blob of air is clearly visible) and the cap floats (Archimedes lift),
  • by squeezing, the pressure applied by the hand propagates in all directions inside the water (Pascal’s principle) and to the air trapped in the cap,
  • the increase of pressure reduces the volume of the trapped air (Boyle’s law - if the cap is transparent, the shinkage of the blob of air is clearly visible),
  • the reduction of the volume of the air trapped inside the cap causes a reduction of Archimedes lift and the cap sinks,
  • by releasing the pressure applied by the hand, the blob of air trapped inside the cap expands and the cap rises until it floats.
Educational aspects:  
  • feel the force needed to apply a pressure to the tapped bottle (Pa),
  • discover the propagation of pressure in the water (Pb),
  • discover the variations of volume in the air (Sc),
  • analyse the relation between pressure and volume in the air (Pb),
  • inquire about the conditions for sinking or floating (Pc),
  • compare with your expectations.
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Last modified: Thu Nov 16 11:09:00 CET 2000