a) What is the measure of all interactions? b) What are the characteristics of a vector quantity? c) What are the characteristics of a scalar quantity? d) What are the examples of vector quantities and scalar quantities? e) What is the densitydensitydensity? f) What determines the density of the body? g) What do the prefixes kilo-, hekto-, mega- mean?
a) The measure of all interactions is the force acting on the body associated with the specific interaction. b) Vector quantity is characterized by specifying direction (direction and return or sense), magnitude and point of application (not always taken into account). c) The scalar quantity is uniquely described by a number accompanied by a unit, defining its magnitude. It is an isotropic quantity, which means that its magnitude is not dependent on the direction considered in the description of the phenomenon associated with this quantity. d) The vector quantities are force, displacement and velocity. The scalar quantities are mass, temperature, volume. e) DensitydensityDensity is the amount of matter per unit of volume, i.e. the quantity defined as the ratio of the mass of the substance to the volume occupied by it. f) Density of a body depends on its physical state. The density of solids is similar to the density of liquids. The density of gases is many orders of magnitude smaller. g) Frequently used prefixes in the SI system are kilo- 10Indeks górny 33, hecto- 10Indeks górny 22 and mega- 10Indeks górny 66.
Zdjęcie przedstawia trzy pary butów: Od lewej: buty damskie na wysokim obcasie - Photo 1 High-heels, buty turystyczne za kostkę - Photo 2 Hiking shoes, tenisówki - Photo 3 Sneakres.
Shoes
Source: GroMar, licencja: CC BY 3.0.
In which shoes would you go:
a) to the cinema, b) to the mountains, c) to the ball?
a) To the cinema in sneakers, because they are comfortable and have large contact area with the floor surfacesurfacesurface. Rubber sole prevents slipping. b) In the mountains in hiking shoes, because of the large area of the sole, which gives a good grip, the rigid material of the sole is resistant to abrasion. c) To the ball in high heels because they are elegant, although not very comfortable, and the contact area with the floor is small.
1. Smooth the surface of the flour in the box. 2. Place a cuboid with the side of medium area on the flour. 3. Lift it so that the imprint remains on the surface of the flour. 4. Repeat the same for the other sides of cuboid.
In each of the three examined cases, the force (cuboid weight) and its direction (vertically down) were the same. Only the area of the surface on which this force acted was changed. The larger the area, the smaller the hollow in the flour.
The effect of the contact interaction of the force distributed over the surface depends on the contact surface area of the interacting bodies.
The smaller the area of the interaction, the greater the effect of the interaction.
View the GeoGebra applet „Effect of varying force on the same surface area” depicting a cylinder placed on the sand. Different forces F from 0 N to 10 N act on the cylinder. With increasing force, the cylinder is getting deeper into the sand.
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Geogebra aplet - skutek działania różnej siły na tą samą powierzchnię. Galeria z opisami alternatywnymi poniżej.
Geogebra aplet - skutek działania różnej siły na tą samą powierzchnię. Galeria z opisami alternatywnymi poniżej.
Ilustracja przedstawia schematycznie doświadczenie prezentujące wpływ zmiennej siły na tę samą powierzchnię. Po lewej stronie poziomą linię opisaną od lewej 0, 5, 10 N, poniżej applied force równa się. Na linię w miejscu opisanym 0 wskazuje strzałka pionowa skierowana w dół, symbolizująca, że na cylinder nie działa żadna siła. Po prawej stronie ilustracji prostopadłościan, symbolizujący piasek, opisany penetration równa się 0 mm. Na nim pionowo narysowany walec opisany applied force równa się 0 N.
Effect of varying force on the same surface area - 1
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Ilustracja przedstawia schematycznie doświadczenie prezentujące wpływ zmiennej siły na tę samą powierzchnię. Po lewej stronie poziomą linię opisaną od lewej 0, 5, 10 obok N, poniżej applied force równa się. Na linię w miejscu opisanym 5 wskazuje strzałka pionowa skierowana w dół, symbolizująca, że na cylinder działa siła o wartości pięciu niutonów. Po prawej stronie ilustracji prostopadłościan, symbolizujący piasek, opisany penetration równa się 4,0 mm, wskazujące zagłębienie cylindra. Pionowo narysowany walec częściowo wciśnięty w prostopadłościan opisany applied force równa się 5 N. Nad walcem strzałka skierowana pionowo w dół dotykająca górnej podstawy walca, symbolizująca siłę przyłożoną do cylindra.
Effect of varying force on the same surface area - 2
The effects of the force depend on its magnitude and the area of the surfacesurfacesurface on which this force acts.
A force that is not applied at a point but acts perpendicular to the surface that an object contacts, is called the normal forcenormal forcenormal force.
The physical quantity, which is the force applied perpendicular to the surface of the object per unit of surface on which this force operates, is called pressurepressurepressure.
The pressure is indicated by a lowercase letter p. In order to calculate the pressure, the normal force F should be divided by the surface area S, over which this force is distributed.
The formula for pressure
then:
The unit of pressure in the SI system is pascal (Pa).
Is there a relationship between the hydrostatic pressurehydrostatic pressurehydrostatic pressure exerted by the liquid and the height of the liquid columnheight of the liquid columnheight of the liquid column?
a) Make a few holes (four or five) in the bottle one above the other. Keep even gaps between them. b) Put the bottle in a bowl on the support. c) Fill the bottle with water.
Summary
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Zdjęcie przedstawia plastikową przezroczystą butelkę z wodą. Wzdłuż butelki zrobione są małe dziurki, przez które wylatuje woda.
The range of the water jet flowing out through the hole closest to the bottom of the bottle is the largest, and the range of the jet flowing out through the highest hole - the smallest.
The hydrostatic pressure depends on the height of the liquid columnheight of the liquid columnheight of the liquid column. The higher it is, the larger the pressure exerted by the liquid.
The influence of the liquid density on the pressure it exerts
a) three identical, small plastic drinks bottles, b) three balloons, c) three rubber bands, d) scissors, e) three laboratory retort stands, f) water, g) denatured alcohol, h) oil.
a) Cut the bottoms of the bottles with scissors. b) Cut out three membranes from the balloons. c) Put a membrane on each bottle (instead of the cap). d) Seal each membrane on the edge of the bottle with a rubber band. e) Attach the bottles to retort stands. f) Put the same volume of different liquids into each of them: the first one - water, the second - denatured alcohol, and the third - oil.
Summary
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Ilustracja przedstawia trzy przezroczyste butelki plastikowe, które mają odcięte dna i trzymane są do góry nogami. Na każdą z butelek zamiast zakrętki założony jest balonik i uszczelniony gumką recepturką. W każdej z nich znajduje się taka sama objętość różnych cieczy, od lewej – woda, denaturat, olej. Widać różnicę w wielkości baloników; ostatni trzeci napełniony olejem jest najmniejszy.
After deformation of the membranes, it can be assumed that the highest pressure is exerted by the liquid with the largest density (in our experiment it is water), and the smallest - by the liquid with the lowest density (i.e. denatured alcohol).
All membranes had the same surfacesurfacesurface area. So if we use the definition of pressure, we come to the conclusion that the highest pressure was exerted by the liquid with the largest density - water, the medium pressure exerted oil, and the lowest pressure – denatured alcohol, because its density is the smallest. Experiment showed that the pressure of the liquid depends not only on the height of the column, but also on the type of liquid, and more specifically on its density.
The hydrostatic pressure depends on the height of the liquid column and the density of the liquid.
The force is equal to the weight of the liquid above the surface S. The formula for weight (not only liquids) is:
and for density:
After transformation:
It follows that:
And since the volume is equal to the product of the base surface area and the height:
hence, after substituting the above expression to the formula for weight, we get:
And then, we substitute the expression for the weight to the formula for the pressure and we get:
after simplification, we got the formula for hydrostatic pressurehydrostatic pressurehydrostatic pressure:
where: p [] - pressure exerted by the liquid, d [] - densitydensitydensity of the liquid, g [] - standard gravity, h [] - the height of the liquid columnheight of the liquid columnheight of the liquid column.
View photos 1,2,3,4 showing different barometers and answer the questions.
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Zdjęcia od lewej: barometr domowej stacji pogody - Photo 1 Barometer of the home weather station, barometr ozdobny stojący w parku - Photo 2 Decorative barometer, analogowy zegarowy barometr - Photo 3 analogue barometer i tablicowy cyfrowy barometr - Photo 4 Digital barometer.
a) What physical quantity can be measured using the instruments in pictures 1‑4? b) What determines the atmospheric pressureatmospheric pressureatmospheric pressure? c) Is the atmospheric pressure on the Earth the same everywhere? d) Where is the higher atmospheric pressure in the mountains or by the sea?
a) The barometers shown in the pictures are used to measure atmospheric pressurepressurepressure. b) Atmospheric pressure depends among others on the water content in the atmosphere. c) Atmospheric pressure is different at different places on the Earth's surface. d) The atmospheric pressure in the lowlands and by the sea is higher than the atmospheric pressureatmospheric pressureatmospheric pressure in the mountains.
The pressurepressurepressure is the physical quantity that informs us how large is the force exerted on a surface area unit.
The pressure is indicated by a lowercase letter p.
To calculate the pressure, the normal force F acting perpendicular to the surface should be divided by the surface area S, on which this force acts.
The basic pressure unit in the SI system is pascalpascalpascal (1 Pa).
1 pascalpascalpascal is the pressure exerted by a force of 1 newton acting on a surface of 1 mIndeks górny 22. Practically often used pressure units are also hektopascal (1 hPa = 100 Pa), kilopascal (1 kPa = 1000 Pa) and megapascal (1 MPa = 1000000 Pa).
The pressure due to the weight of the liquid at rest is called hydrostatic pressurehydrostatic pressurehydrostatic pressure. The hydrostatic pressure depends both on the height of the liquid columnheight of the liquid columnheight of the liquid column and its densitydensitydensity.
Atmospheric pressureatmospheric pressureAtmospheric pressure is the pressure exerted by the atmosphere on the bodies in its area or on the surfacesurfacesurface of the Earth. Atmospheric pressure - like hydrostatic pressure - is related to the weight of the air above the level at which we measure the pressure. The closer to the Earth's surface, the higher the atmospheric pressure, and conversely - it is lower on mountain peaks than in the valleys. With the height increase by one meter, counting from the sea level, the atmospheric pressure decreases by approximately 11,3 Pa. Atmospheric pressure is changing. Its value at sea level is approximately 1013,25 hPa. We name it normal pressure.
Exercises
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Exercise 5
Wersja alternatywna ćwiczenia: Choose the correct sentence. Możliwe odpowiedzi: 1. The surface area of the snow on which our weight acts doesn’t matter whether or not we fall into it., 2. The smaller the surface area of the snow on which our snow loads, the deeper we fall into it., 3. The smaller the surface area of the snow on which our weight loads, the deeper we fall into it., 4. Our weight does not affect the depth at which we fall in the snow.
Wersja alternatywna ćwiczenia: Choose the correct sentence. Możliwe odpowiedzi: 1. The surface area of the snow on which our weight acts doesn’t matter whether or not we fall into it., 2. The smaller the surface area of the snow on which our snow loads, the deeper we fall into it., 3. The smaller the surface area of the snow on which our weight loads, the deeper we fall into it., 4. Our weight does not affect the depth at which we fall in the snow.
Choose the correct sentence.
The surface area of the snow on which our weight acts doesn’t matter whether or not we fall into it.
The smaller the surface area of the snow on which our snow loads, the deeper we fall into it.
The smaller the surface area of the snow on which our weight loads, the deeper we fall into it.
Our weight does not affect the depth at which we fall in the snow.
Exercise 6
Calculate the pressure that petrol exerts on the bottom of a canister with a height of 50 cm, if the canister is filled up to of the height. What would be the pressure if the same canister was filled with water? Density of petrol d = 700 , density of water d = 1000 .
Use the formula for pressure of liquid column:
where: p [] - liquid pressure, d [] - liquid density, g [] - gravitational acceleration, h [] - the height of the liquid column.
Exercise 7
Write in English why you can drink through a straw?
There is a pressure difference between atmospheric pressure and air pressure in our lungs. When the air is drawn into the lungs, the pressure on the upper surface of the liquid in the straw decreases. This pressure is lower than atmospheric pressure, which is exerted on the liquid from the bottom side of the straw. The difference in gas pressures between the top surface of the liquid in the straw and the bottom surface of the liquid in the straw causes the liquid to be forced into the straw, which allows us to drink.
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Exercise 8
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. ciśnienie - pressure, 2. ciśnienie hydrostatyczne - hydrostatic pressure, 3. ciśnienie atmosferyczne - atmospheric pressure, 4. parcie - normal force, 5. gęstość - surface, 6. powierzchnia - density
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. ciśnienie - pressure, 2. ciśnienie hydrostatyczne - hydrostatic pressure, 3. ciśnienie atmosferyczne - atmospheric pressure, 4. parcie - normal force, 5. gęstość - surface, 6. powierzchnia - density
Indicate which pairs of expressions or words are translated correctly.
ciśnienie - pressure
ciśnienie hydrostatyczne - hydrostatic pressure
ciśnienie atmosferyczne - atmospheric pressure
parcie - normal force
gęstość - surface
powierzchnia - density
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Match Polish terms with their English equivalents.
ciśnienie hydrostatyczne
atmospheric pressure
normal force
ciśnienie
pressure
parcie
surface
ciśnienie atmosferyczne
powierzchnia
hydrostatic pressure
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.
