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According to the Archimedes principle, the behavior of a solid immersed in a liquid depends on two elements: its weight, which acts from top to bottom, and the hydrostatic thrust, equal to the weight of the liquid moved by the body, which acts from bottom to top.
Therefore, so that a body float, it is sufficient that, immersed, move a quantity of water with a weight equal to or greater than its own.
The principle demonstrated by Archimedes is exactly what happens with ships. These large structures, thanks to their shape, move enormous quantities of water and receive a sufficient boost to allow them to float. It is clear, however, that being afloat also depends on certain factors such as the density of the material, that is the ratio between its weight and volume. The ship is made of dense materials, such as iron, but inside it contains hollow areas, full of air, which allow the density to stay below that of the water and allow it to float.

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-Pascal principle: any change in the pressure applied to a completely enclosed fluid is trasmitted undiminished to all parts of the fluid and the enclosing walls.
When the syringe is filled with water, pushing the plunger water comes out from all nozzles with equal speed perpendicularly to the surface of the conteiner.
-A Pascal's principle application: The Hydraulic Press
https://youtu.be/XuLO_TuvB80
Experiment's explanation:
Pressure is equal to the force divided by the area on which it acts. According to Pascal’s principle, in a hydraulic system a pressure exerted on a piston produces an equal increase in pressure on another piston in the system. If the second piston has an area 10 times that of the first, the force on the second piston is 10 times greater, though the pressure is the same as that on the first piston.
P1= F1/A1
P2= F2/A2
F2= P2 A2= 10 x F1

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In this experiment we can see that we can broke a barrell only with water.
This barrell must be full of water and if we add some water from small hole the pressure of the water added will be the same in every point of the water in the barrell, so the barrell will break

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The pressure at a point in a liquid in static equilibrium depends only on the depth at that point, so if we have two point, the deeper point have more pressure than the higher

P= Po + g · d · H

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Hydrostatics is the branch of fluid mechanics that studies fluids.
A fluid is a substance that can flow. Liquid and aeriform substances (gasses and vapours) are fluids.
Fluids conform to the boundaries of the container in which they are placed.
-DENSITY: at a given temperature, each substance has its own density which is the ratio of a given mass of the substance and its volume.
density: mass/volume = m/v
SI unit of measurement: Kg/m³
Normally, the higher is the temperature of a substance, the smaller is its density because its volume increases with temperature.
-PRESSURE: is the magnitude F of a force acting perpendicular to a surface divided by the area S of the surface over which the force acts.
P= F⊥/S
SI unit of measurament: N/m = Pa (Pascal).
Pressure is not a vector quality but a scalar quantity!
1) For a given pressure , Force and Area are directly proportional;
2) For a given force, Pressure and Area are inversely proportional;
3) For a given area, Pressure and Force are directly proportional;

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EXPERIMENTS AT HOME
1)BALLOONS AND PINS
Inflate two balloons. Then place a pin on the table. If we support the balloon,it breaks out. But if we place many pins on the table and we support the balloon,it doesn't burst,because it all depends on the pressure exerted on the balloon. The pressure exerted in a single point is greater than that exerted in several points,so the balloon burst.

2)MILK CARTON AND FLOUR
Place two piles of flour on the table,then take the empty milk carton placed vertically and press it on the first pile of flour to create a furrow. Repeat the same action with the same intensity,but this time put the milk carton horizontally. We notice that a deeper furrow is created in the pile of flour made with vertical carton,because the pressure is greater than the one exerted with the carton milk placed horizontally(if the area is smaller the pressure is bigger

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1) Why snowshoes are much more effective for walking in snow?
2) Why does a sharp knife cut better than a dull knife?
3) Why a karate chop is much more effective than an open-handed slap?

1)Snowshoes are much more effective for walking in snow because the pressure exerted is lower than the one exerted by normal shoes, since the largestis the surface the lower is the pressure.
2/3) The sharp knife and the karate chop are muhc more effective becouse we have a smaller surface so we need a lower force to get an high pressure.

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-Materials:
2 platicine balls of the same   weight and size;
a basinful of water;
-Procedure:
Immerse the first plasticine ball in   water. It sink. Then model the     second plasticine ball at will and   immerse it. It floats.

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-Materials:
2 syringes;
a plastic tube;
-Procedure:
Connect two syringes with a   plastic tube. Then if you push the   first syringe, the second one rise   up.

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-Materials:
a glass with coloured water;
2 syrings;
a plastic tube;
Procedure:
First of all, connect the two syringes with the plastic tube. Then fill the syringes with the same level of coloured water. Finally, if you move the syringes, you see that the water level remains the same.

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-Materials:
a bottle with water;
a plastic fish (or another object);
-Procedure:
By exerting a slight pressure on the surface of the bottle, it can be noticed that the object inside it, which is initially in a floating state, tends to descend downwards, and then ascend again when the pressure ceases to be exerted.

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-Materials:
a plastic bottle;
a needle to make holes in the bottle;
a scotch to plug holes;
-Procedure:
first of all, take the plastic bottle, then use the needle to make two vertical holes. After this, take the tape and close the holes. Finally, fill the bottle and remove the tape.
From this experiment, we observe that the water comes out in different ways depending on the position of the holes; from the hole at the top, the water jet is less powerful, while in the lower one the jet is more powerful.

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-Material:
a plastic bottle;
needle;
scotch;
-Procedure:
first of all, take the bottle and make a hole in the bottle. Then close the hole with the tape, fill the bottle and close the bottle with the cap.
Finally, remove the scotch from the holes and you will notice that the water does not come out, while removing the cap, the liquid will come out.

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-Materials:
a syringe;
scotch;
-Procedure:
First of all, place the scotch around the tip of the syringe. Then fill the syringe with water, remove the scotch and press the syringe plunger. The water comes out in different directions.

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A ship is not only made of iron but is hollow inside it and is therefore full of air, which makes it very light. It is important that even when the ship is loaded, it does not exceed the weight of the moving water and that there is no leak in the hull and no water embarkation.
Titanic, therefore, as soon as it was filled with water, added to the weight of the hardware, became denser than the water itself and sank.

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1)If the buoyancy is lower tan the weight (B<W),the body completely immersed in a fluid sinks.
2)If the B is equal to the W (B=W)the body immersed in a fluid stays in the same position.
3)If the B is higher than the W (B>W)the body immersed in a fluid goes up,it will raise because the forces of the body are the same.
Formula: d • V • g= B=W =d • V • g

An object FLOATS if its density is lower than the density of the fluid.
Example: The density of a boat is bigger than the density of the water, but it floats because we have to consider also the air inside the boat.

IS BETTER COOK PASTA NEAR THE SEA OR IN MOUNTAIN?
In mountain water boils more quickly than at the sea level. Near the sea,the atmospheric pressure is higher than in mountain,so it takes more time to boil water,because a liquid boils when its pressure becomes the same of the atmosphere. So it's better cook pasta in mountain because we can cook it more quickly than here.