Topicm6a5c9b6acf8adadf_1528449000663_0Topic

Conditions of equilibrium for floating bodies

Levelm6a5c9b6acf8adadf_1528449084556_0Level

Second

Core curriculumm6a5c9b6acf8adadf_1528449076687_0Core curriculum

V. Matter's properties. The student:
9c) demonstrates Archimedes' principle and, on this basis, analyses floating of a body; determines the densitydensitydensity of liquids or solids.

Timingm6a5c9b6acf8adadf_1528449068082_0Timing

45 minutes

General learning objectivesm6a5c9b6acf8adadf_1528449523725_0General learning objectives

Determining conditions of equilibrium for floating bodies.

Key competencesm6a5c9b6acf8adadf_1528449552113_0Key competences

1. Identifies the types of forces acting on a floating body.

2. Determines the conditions of body swimming.

3. Defines the buoyancy force.

4. Determines the relationship between body and liquid density on the behavior of a body immersed in a liquid.

Operational (detailed) goalsm6a5c9b6acf8adadf_1528450430307_0Operational (detailed) goals

The student:

- defines buoyancy,

- defines the conditions for swimming,

- determines the relation between body and liquid density on the behavior of a body immersed in a liquid.

Methodsm6a5c9b6acf8adadf_1528449534267_0Methods

1. Learning by observation.

2. Problem lecture.

Forms of workm6a5c9b6acf8adadf_1528449514617_0Forms of work

1. Individual work - using the acquired knowledge in practice.

2. Work with the whole class during solving tasks.

Lesson stages

Introductionm6a5c9b6acf8adadf_1528450127855_0Introduction

Task 1

Answer the questions:

1. When does the buoyant force act on the body?
2. What does and what does not the buoyancy force depend on?
3. What is the content of Archimedes' principle?
4. What direction does the buoyant force have?

Answer:

1. The buoyant force acts on the body immersed in liquids and gases.
2. The buoyant force depends on the density of the liquid and the volumevolumevolume of the immersed part of the body. This force does not depend on the shape of the body, its mass, liquid volume.
3. For each body immersed in a liquid (or gas), there is a buoyant force that is directed upwards and equal in magnitude to the weightweightweight of the displaced liquiddisplaced liquiddisplaced liquid (or displaced gas).
4. The buoyant force has a vertical upward direction.

Procedurem6a5c9b6acf8adadf_1528446435040_0Procedure

Task 2

Look at the pictures and answer the questions under the pictures:

[Interactive graphics]

1. What forces act on the immersed block that comes up to the surface of the liquid?

2. What is the relationship between these forces:

a) when the block is immersed,
b) when the block floats partially immersed.

3. What is the relationship between the body and liquid densitydensitydensity values of the case when the body flows to the surface?

Answer:

1. The gravitational force ($\overrightarrow{Q}$) and the buoyant forcebuoyant forcebuoyant force ($\overrightarrow{F_B}$) act on the emerging block.

2. There are various relationships between the buoyant force and the gravitational force:

a) when the block emerges, the magnitude of the buoyant force is greater than the magnitude of the gravitational force,
b) when the block is emerging (floats partially immersed), the gravitational force is balanced by the buoyant force - the magnitudes of these forces are equal.

3. The weight of the liquid displaced by the body ($\overrightarrow{F_B}$) is larger than the weight of the immersed body ($\overrightarrow{Q}$). Since the volume of the displaced liquid and the volumevolumevolume of the immersed body are the same, it can be concluded that the density of the liquid is larger than the density of the body.

Task 3

[Illustration 1]

1. What forces act on the immersed block that floats completely immersed in the liquid?
2. What is the relationship between these forces?
3. What is the relationship between the density of the body and the liquid?

Answer:

1. The gravitational force ($\overrightarrow{Q}$) and buoyant force ($\overrightarrow{F_B}$) act on the floating block completely immersed in the liquid.
2. The magnitudes of the gravitational force ($\overrightarrow{Q}$) and buoyant force ($\overrightarrow{F_B}$) are equal.
3. The weight of the liquid displaced by the body ($\overrightarrow{F_B}$) is equal to the weight of the immersed body ($\overrightarrow{Q}$). Since the volume of displaced liquiddisplaced liquiddisplaced liquid and the volume of the immersed body are the same, it can be concluded that the density of the liquid is equal to the density of the body.

Task 4

[Illustration 2]

1. What forces act on the immersed block that sinks?
2. What is the relationship between these forces?
3. What is the relationship between the density of the body and the liquid?

Answer:

1. The gravitational force ($\overrightarrow{Q}$) and buoyant force ($\overrightarrow{F_B}$) act on the block sinking in the liquid.
2. The magnitude of the gravitational force ($\overrightarrow{Q}$) is greater than the magnitude of the buoyant force ($\overrightarrow{F_B}$).
3. The weight of the liquid displaced by the body ($\overrightarrow{F_B}$) is smaller than the weight of the immersed body ($\overrightarrow{Q}$). Since the volume of the displaced liquid and the volume of the immersed body are the same, it can be concluded that the density of the liquid is smaller than the density of the body.

Task 5

View the photo gallery „Examples of buoyant force in liquids and gases” and answer the questions:

[Illustration 3]

1. Does the buoyant force act on every body shown in the photos?
2. In which photo is the buoyant force smaller than the gravitational force?
3. In which photo is the buoyant force larger than the gravitational force?
4. In which photo may the buoyant force be equal to the gravitational force?
5. What should you do to make the submarine emerge?

Answers:

1. Yes. There is a buoyant force acting on each of the bodies depicted in the photos.
2. Smaller buoyant force acts on the submarine (photo 2).
3. In photos 3 and 5 the buoyant force is larger than the gravitational force.
4. The buoyant force may be equal to the gravitational force in photos 1 and 4.
5. In order for the submarine to emerge, it would be necessary to empty the ballast tanks, i.e. pump out the water from these tanks replacing it with gas.m6a5c9b6acf8adadf_1527752263647_01. Yes. There is a buoyant force acting on each of the bodies depicted in the photos.
2. Smaller buoyant force acts on the submarine (photo 2).
3. In photos 3 and 5 the buoyant force is larger than the gravitational force.
4. The buoyant force may be equal to the gravitational force in photos 1 and 4.
5. In order for the submarine to emerge, it would be necessary to empty the ballast tanks, i.e. pump out the water from these tanks replacing it with gas.

Task 6

Determine whether the sentences below are true or false:

a) If the body does not change the depth of its immersionimmersionimmersion in water, the weightweightweight of this body is equal to the buoyant forcebuoyant forcebuoyant force.
b) If the body settles to the bottom of the ocean, the buoyant force acting on this body is 0.
c) If a ship floats on the surface of the sea, the weight of the water displaced by the ship is equal to the weight of the ship.

Answer:

a) True.
b) False.
c) True.

Lesson summarym6a5c9b6acf8adadf_1528450119332_0Lesson summary

The body sinks in liquid or gas, i.e. settles to the bottom when:

- the buoyant force is smaller than the gravitational force of the body,
- the densitydensitydensity of the body is larger than the density of liquid or gas.

The body floats at any depth in liquid or gas:

- the buoyant force is equal to the gravitational force of the body,
- the density of the body is equal to the density of the liquid or gas.

The body floats on the surface of the liquid (partially immersed):

- the buoyant force is equal to the gravitational force of the body, if the body submerged deeper, the buoyant force would be greater than the gravitational force of the body,
- the density of the body is smaller than the density of the liquid on the surface of which the body floats.

The body rises up being immersed in gas or water:

- the buoyant force is larger than the gravitational force of the body,
- the density of the body is smaller than the density of the gas or liquid in which the body rises.

Selected words and expressions used in the lesson plan

Archimedes’ principleArchimedes’ principleArchimedes’ principle

buoyant forcebuoyant forcebuoyant force

densitydensitydensity

displaced liquiddisplaced liquiddisplaced liquid

floating of bodiesfloating of bodiesfloating of bodies

immersionimmersionimmersion

immersion depthimmersion depthimmersion depth

sinkingsinkingsinking

volumevolumevolume

weightweightweight