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THE BOTTLE OF WATER WITH A SACHET OF MAYONNAISE A disciplinary project based on the principles of hydrostatics and their applications, starting out with an unusual experiment Francesco Serafini, Physics teacher from Liceo “Raffaello”, Urbino, Italy

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Didactic and Cultural Objectives: Didactic objectives: - to introduce the students to the concept of pressure, Pascal’s Principle and the Archimedes’ Law. - to make the students consider realistic cases from everyday life, resolving them through the use of various concepts of Physics. - to get the students to apply theoretical concepts in practical situations. Cultural objectives: - to demonstrate to the students that Physics is a part of daily life and that it can be a way of understanding “non ordinary” phenomenon. - to make the students consider real-life situations that aren’t easily solved, therefore stimulating confrontation, curiosity and problem-solving of situations in an age-group such as adolescents, which is a time of growth and of confrontation. - to give Physics a fun, thought-provoking and stimulating image, preferring an understanding-based knowledge to a memory- based knowledge.

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Methodology: - TO MAKE experimental Physics with easily-obtainable objects which are available to everyone, and which don’t hide electronic mechanisms that often mask the phenomenon of Physics. - to discuss, to compare ideas, take risks, and try out new approaches to solutions in order to interpret phenomena that is difficult to resolve. - to review ideas that have already been looked at, at a later moment, after the introduction of a selection of concepts of Physics. - to have fun whilst investigating unusual or strange phenomena.

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Didactic Outline First step: the bottle of water with the sachet of mayonnaise is shown to the students. - How does it work? When the plastic bottle filled with water is squeezed whilst in a vertical position, the sachet which was originally floating now sinks, and when the grip on the bottle is released the sachet once again floats. - Why does this happen? - What happens if you put the bottle in a horizontal position and then squeeze it? - And if I turn the bottle upside down?

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First step (continued) The students usually cite the word ‘pressure’. The concept of pressure is introduced. Pressure = Force/surface and the units of measurement [N/m2]=[Pa] Let’s construct the 'infernal' equipment Take a sachet of mayonnaise, and at one end of the sachet attach as many paper-clips as are necessary to make the sachet float in a vertical position with the top-most side remaining marginally above the surface of the water. Put the sachet of mayonnaise complete with paperclips attached inside a plastic bottle and fill the bottle to the very top with water and then fasten the lid tightly on the bottle.

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Second step: Show the students what happens to pressure when under water. In a very simple manner they are shown the equation of hydrostatic pressure and are made to take note of how this changes with variations in height in a theoretical way. A second piece of equipment is presented : a pressure measurer made with a small rubber tube. When one end of the tube is immersed in a container of water we can see that the coloured water within the tube rises and moves towards the opposite end of the tube. What pressure is a person subject to when below 10m of water? P H = d H2O gh = 1000*9.81*10 = Pa A large value! But is it a lot or a little? If the surface area of our body were one square metre we would have a weight of N of water above us.

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Third step: So why aren't we squashed down towards the bottom when we go underwater? This is the moment to illustrate Pascal's Principle. Using the measure we can show how the pressure is substantially the same, by changing the shape of the tube underwater. This doesn't solve the problems of our scuba diver, on the contrary worse still he is now shoved in all directions, left, right, head first, all over. But is the pressure that the scuba diver is subjected to under ten metres of water really so great? Normally what pressure are we subjected to when in a normal room? We now introduce Torricelli's Experiment. The value of atmospheric pressure is quite high 1.01 *105Pa. So our scuba diver doesn't really suffer so much.

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Fourth step: Is atmospheric pressure always the same? It changes with altitude (effect: my ears block up when going down a big hill) and it changes with meteorological conditions. To demonstrate this fact in an experimental way a baroscope is left in the classroom on top of a cupboard. Also some “magic tricks” caused by atmospheric pressure can be shown, such as the possibility of not spilling a vase of water that is closed with a small sheet of plastic.

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Fifth step: Is the sachet of mayonnaise still floating in the bottle of water? We need to understand why things float. So, wood floats, iron doesn't, light things float and heavy things don't. And why does an aircraft carrier float even though it is heavy and made of iron? Let's do another experiment: let's take a ball of plasticine. Does it float? No, but if we turn it into the shape of a dish or a boat then it does float. Has the weight changed? No, the plasticine is still just the same; has the material changed? No, the plasticine is still plasticine. What has changed? The shape. This is the departure point in illustrating the Archimedes' Principle. This explains why a heavy iron boat floats, because inside it is empty and the volume that it displaces creates an Archimedes' Force that is equal to the weight of the boat.

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Fifth step: continued A classic experiment Let's measure the Archimedes' Force with a dynamometer, weighing an object in the air and then immersing it in water. It can be interesting to reflect on some experimental situations: What happens to the Archimedes' Force if we immerse the object below 4cm of water? What happens to the Archimedes' Force if we immerse the object below 4cm of water? What happens to the Archimedes' Force if the body is half-immersed? What happens to the Archimedes' Force if the body is half-immersed? What happens if we use a cylinder of aluminium instead of a cylinder of iron? What happens if we use a cylinder of aluminium instead of a cylinder of iron? Last but not least, the classic of classics, we can use an empty cylinder of the same volume identical to the cylinder immersed. The Archimedes' Force is compensated for by filling the empty cylinder with water. And if we were to fill it with small stones?

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Fifth step: continued Another experiment Here we use a type of scale with a glass full of water suspended on one side of it. If I put a piece of iron in the water within the glass, without letting go of the iron, what happens to the scale, which side will it weigh down on? What happens if instead of suspending the glass we suspend the cylinder of iron and then immerse it in the glass of water?

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Sixth step: What happens to the mayonnaise inside the bottle? We now have all the instruments necessary to understand this: At first the sachet floats, so the weight of the sachet is the same as the Archimedes' Force. When we put pressure on the bottle the sachet sinks and so either the weight has increased (impossible) or the Archimedes' Force has diminished. But what has changed the Archimedes' Force? The density of the water? In no significant degree. The acceleration of gravity? I'd say not, if we are still on planet earth. It is the volume that is moved by the sachet of mayonnaise, which diminishes due to the increase in pressure within the water (Pascal's Principle), therefore making the Archimedes' Force decrease. When the grip on the bottle is released the pressure within it returns to normal, the sachet regains its volume, its Archimedes' Force and its initial position.

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The Cartesian Devil Historically this type of experiment was called “The Cartesian Devil”. In historical manuals (e.g. Ganot 1858) it is proposed as a game of observation. The historic model was made up of a tube of glass filled with water with a piston at the top. A small glass or ceramic doll (sometimes shaped precisely in the form of a devil) was placed within the water and with the increase in pressure it was capable of taking in water through a small hole, it therefore became heavier and so sank to the bottom.

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Other Cartesian Devils Two other teaching models of Cartesian Devils are proposed, which sink with the change in pressure by taking in water and therefore changing weight. The second model amazes the students because if you squeeze the front and back of the bottle one pipette sinks to the bottom whereas if you squeeze the bottle at its sides the second pipette rises.

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Conclusion: The type of study path presented here gives value to Physics in its theoretical and experimental studies, even in the eyes of students who are sometimes unmotivated and bored. The series of small experiments carried out with simple and commonly used material brings Physics into everyday life and brings the study of Sciences to a level that is open to discussion. I sometimes found myself asking the students why and how a certain phenomenon occurred, and they replied: “there will be a mechanism that does this, another mechanism that does that, the job of understanding it and resolving it will be done by a technical instrument, by a black box, by a computer or by an electronic system”. Destroying the students' largely utilitarian vision of the Sciences (and in particular of Physics) is of fundamental importance in re- motivating and empassioning the students, in stirring their curiosity, to see the world as something to discover and to understand by reasoning with ever-better theoretical, practical and experimental means.

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