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Archimedes’ principle

Source: licencja: CC 0.

Prawo Archimedesa

Siła wyporu

Od czego zależy siła wyporu

You will learn
  • about Archimedes’ principle and learn to use it using English vocabulary.

Introduction
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nagranie abstraktu

We already know that the hydrostatic pressure depends on the height of the liquid column, the density of the liquid and the standard gravity.

We measure body density as a ratio of body mass to its volume.

We measure the weightweightweight of a body using a dynamometer or a suitable weight.

Experiment 1
Experiment 1
Research problem
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nagranie abstraktu

Does water affect the weightweightweight of the body immersed in it.

Hypothesis
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nagranie abstraktu

The real weight of the body does not change, but the apparent weight of the body immersed in water is smaller than the weight of the same body in the air.

You will need
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nagranie abstraktu

a) dynamometer,
b) tripod,
c) cuboids of the same dimensions, made of various metals, e.g. copper, aluminium and iron,
d) beaker with water.

Instruction
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nagranie abstraktu

1. Using the dynamometer, determine the weightweightweight of this cuboid.
2. Record the result in the table.
3. Immerse the suspended cuboid completely in a beaker of water; do not immerse the hook of the dynamometer itself.
4. Read the result again and record the dynamometer readings.
5. Make the same measurements for the other cuboids.

Save the results of the experiment in the table.

Copper cuboid

Iron cuboid

Aluminium cuboid

Body weight, dynamometer readings in the air F [N]

Dynamometer readings when the body is immersed in FIndeks dolny water [N]

Difference between the above readings FIndeks dolny w = F - FIndeks dolny water

Summary
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nagranie abstraktu

Experiment has shown that the dynamometer reading during the measurement when the body was immersed in water is smaller than during the measurement when it was in the air.

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Apparently the weight of the body immersed in water is smaller then the weight of the body immersed in the air
Source: GroMar, licencja: CC BY 3.0.
Conclusions
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nagranie abstraktu
  • The difference between measurements does not depend on the material from which the rectangles are made, and is always constant, provided that their volumes are the same.

  • The observed regularity applies to all liquids.

  • An additional force acts on the body immersed in any liquid, which has the opposite direction with respect to the force of gravityforce of gravityforce of gravity.

  • This force is called the buoyancy force, and its value does not depend on the type of substance from which the immersed body is made.

Task 1
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nagranie abstraktu

Give the names of the forces shown in the figure.

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Ilustracja interaktywna przedstawia prostokąt z zaokrąglonymi rogami ucięty od góry, zakolorowany od dołu na niebiesko symbolizujący naczynie z wodą. Wewnątrz kółko, które nie dotyka żadnego boku. Z środka kółka narysowana jest strzałka skierowana pionowo do góry oznaczona numerem 1 oraz strzałka skierowana pionowo do dołu oznaczona numerem 2. Na ilustracji widoczne są numery, a na nich podpisy. 1. buoyant force {audio}, 2. force of gravity {audio}.
Apparently the weight of the body immersed in water is smaller then the weight of the body immersed in the air
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Perform the experiment according to the given scheme.

Experiment 2
Experiment 2
Research problem
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nagranie abstraktu

What determines the buoyant force?

Summary
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nagranie abstraktu

The buoyant forcebuoyant forcebuoyant force depends on the type of liquid in which the body is completely immersed.

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The buoyant force depends on the type of liquid in which the body is completely immersed
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

The buoyant force depends on the volume of the immersed body.

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The buoyant force depends on the volume of the immersed body
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Perform the experiment according to the given scheme.

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nagranie abstraktu

Perform the experiment under the supervision of an adult.

Experiment 3
Experiment 3
Research problem
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nagranie abstraktu

What does the buoyant force depend on?

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nagranie abstraktu
Hypothesis

The buoyant force does not depend on the body shape, liquid volume, immersion depth, body weightweightweight.

You will need
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nagranie abstraktu

a) beakers of various volumes,
b) water,
c) dynamometer.
d) plasticine ball,
e) cord.

Instruction
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nagranie abstraktu

1. Hang the ball on a cord.
2. Determine the weightweightweight of the ball with a dynamometer.
3. Immerse the ball completely in beakers of various volumes of water.
4. Read the dynamometer readings.
5. Immerse the ball in water - read the dynamometer readings.
6. Change the shape of the ball and repeat step 5.
7. Immerse the ball in a measuring cylinder filled with water and read the value of the buoyant force at the different depth of the ball's immersion.

Summary
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nagranie abstraktu

The buoyant force does not depend on the shape of the body (point 6 of the instructions).

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The buoyant force acting on the body completely immersed in the liquid does not depend on the shape of this body
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

The buoyant forcebuoyant forcebuoyant force does not depend on the volume of liquid in which it is immersed (point 3 of the instructions).

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The buoyant force acting on the body completely immersed in the liquid does not depend on the volume of the liquid in which it is immersed
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

The buoyant force does not depend on the immersion depth of the body (point 7 of the instructions).

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The buoyant force does not depend on the depth of immersion in the liquid
Source: GroMar, licencja: CC BY 3.0.
Conclusions
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nagranie abstraktu
  • The buoyant force acting on the body immersed in the liquid depends on the density of the liquid and the volume of the immersed body. The buoyant force does not depend on the shape of the body, body weightweightweight, liquid volume, immersion depth.

  • Based on the above‑mentioned experiments, we can formulate the content of Archimedes' principle.

  • For every body immersed in a liquid there is a buoyant force which is directed upward and equal in magnitude to the weight of the displaced liquiddisplaced liquiddisplaced liquid.

  • The magnitude of buoyant force FIndeks dolny w is calculated according to the formula:

    Fw=d·V·g

    where:
    d - density of displaced liquid,
    V - volume of displaced liquid,
    g - standard gravity.

Exercise 1
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nagranie abstraktu

Answer the question.

Is Archimedes' principle valid for bodies immersed in gas?

Suggest a way to confirm the validity of the principle for gases.

Summary
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nagranie abstraktu
  1. The buoyant forcebuoyant forcebuoyant force affects the body immersed in liquid or gas.

  2. The buoyant force is always directed upward.

  3. The buoyant force depends on the density of the liquid or gas and the volume of the body immersed in the liquid or gas.

  4. Archimedes' principle:
    For each body immersed in a liquid (or gas), there is a buoyant force that is directed upward and equal in magnitude to the weightweightweight of the displaced liquiddisplaced liquiddisplaced liquid (or displaced gas).

  5. The buoyant force can be calculated using the formula:

    Fw=d·V·g

    where:
    d - density of displaced liquid,
    V - volume of displaced liquid,
    g - standard gravity.

Exercises

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Exercise 2
Exercise 3

A figurine of volume of 50 cmIndeks górny 3 and a weight of 250 g was immersed in water. What is the net force acting on this figurine? What is the magnitude of the buoyant force? (the density of water is d = 1 gcm3).

Exercise 4

Write in English what value the dynamometer would indicate after immersing a bag filled with water in water and why?

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Exercise 5
Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. siła wyporu - buoyant force, 2. ciężar - weight, 3. wyparta ciecz - displaced volume, 4. wyparta objętość - displaced liquid, 5. głębokość zanurzenia - depth of immersion, 6. siła ciężkości - force of grawity
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.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

Archimedes’ principle
Archimedes’ principle

prawo Archimedesa

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wymowa w języku angielskim: Archimedes’ principle
buoyant force
buoyant force

siła wyporu

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wymowa w języku angielskim: buoyant force
depth of immersion
depth of immersion

głębokość zanurzenia

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wymowa w języku angielskim: depth of immersion
displaced liquid
displaced liquid

wyparta ciecz

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wymowa w języku angielskim: displaced liquid
displaced volume
displaced volume

wyparta objętość

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wymowa w języku angielskim: displaced volume
force of gravity
force of gravity

siła ciężkości

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wymowa w języku angielskim: force of gravity
weight
weight

ciężar

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wymowa w języku angielskim: weight

Keywords

Archimedes’ principleArchimedes’ principleArchimedes’ principle

buoyant forcebuoyant forcebuoyant force

displaced volumedisplaced volumedisplaced volume