CALCULATIONS | walking-on-water-tpe

Calculations

Because we met lots of difficulties to determine the volume of polystyrene which is necessary to allow a person of 75 kilos to walk on water with experiments, we decided to determinate it with calculations.

So we have considered that our piece of polystyrene will be a rectangular-parallelepiped and the fluid will be water.

Two strengths are applied on this object: gravity (called ) and the Archimedes’ principle (called ).

We decided to use four pieces of polystyrene to allow a person of 75 kilos to walk on water, so each piece of polystyrene should be able to support 25 kg (supposing that during the walking, the person will always have at least 3 resting points.)

And finally, we decided to neglect the mass of the polystyrene compared to the mass of the subject (here 75 kilos).

We can express the two strengths which are applied on the polystyrene :

Gravity:

The Archimedes’ Principle:

In this formula, we decided to keep S as a constant : S = 0,41 x 0,58 = 0,24 m².

We determined the size of our pieces of polystyrene according to the dimensions of the plates of polystyrene which are sold (125 x 60 x 4 cm). Furthermore, we took into account the fact that we had to remove 1cm on the edges because of the notches.

Then, so that the polystyrene floats, it is necessary that = .

So we need to cut 4 pieces of polystyrene of 41 centimeters wide by 58 centimeters long and 10 centimeter thick.

After building our pieces of polystyrene, we weighed one of them (with the fixations) and founded 850g.

We now have to verify our hypothesis that m(poly) << m(personne) :

0,850

= 3,4 %

Finally, the mass of the polystyrene is negligible compared to the human mass (indeed it represents only 3,4%).