Conditions for floating bodies physics. Statics

When preparing a salt solution of a certain density, housewives immerse a raw egg in it: if the density of the solution is insufficient, the egg sinks, if it is sufficient, it floats. The density of sugar syrup during canning is determined in the same way. from the material in this paragraph you will learn when a body floats in a liquid or gas, when it floats and when it sinks.

We substantiate the floating conditions of bodies

You can probably give many examples of bodies floating. Ships and boats, wooden toys and balloons float, fish, dolphins and other creatures swim. What determines the body's ability to swim?

Let's conduct an experiment. Let's take a small vessel with water and several balls made of different materials. We will alternately immerse the bodies in water, and then release them without an initial speed. Further, depending on the density of the body, different options are possible (see table).

Option 1. Dive. The body begins to sink and eventually sinks to the bottom of the vessel. Let's find out why this happens. Two forces act on the body:

The body sinks, which means that the downward force is greater:

a body sinks in a liquid or gas if the density of the body is greater than the density of the liquid or gas.

Option 2. Floating inside the liquid. The body does not sink or float, but remains floating inside the liquid.

Try to prove that in this case the density of the body is equal to the density of the liquid:

a body floats inside a liquid or gas if the density of the body is equal to the density of the liquid or gas.

Option 3. Ascent. The body begins to float and eventually stops on the surface of the liquid, partially immersed in the liquid.

While the body floats up, the Archimedean force is greater than the force of gravity:

Stopping a body on the surface of a liquid means that the Archimedean force and the force of gravity are balanced: ^ strand = F arch.

a body floats in a liquid or gas or floats on the surface of a liquid if the density of the body is less than the density of the liquid or gas.

We observe the floating of bodies in wildlife

The bodies of the inhabitants of seas and rivers contain a lot of water, so their average density is close to the density of water. To move freely in a liquid, they must “control” the average density of their body. Let's give examples.

In fish with a swim bladder, such control occurs due to changes in the volume of the bladder (Fig. 28.1).

The nautilus mollusk (Fig. 28.2), which lives in tropical seas, can quickly float up and sink to the bottom again due to the fact that it can change the volume of internal cavities in the body (the mollusk lives in a spiral-twisted shell).

The water spider, widespread in Europe (Fig. 28.3), carries with it into the depths an air shell on its abdomen - it is this that gives it a reserve of buoyancy and helps it return to the surface.

Learning to solve problems

Task. A copper ball weighing 445 g has a cavity inside with a volume of 450 cm 3. Will this ball float in water?

Analysis of a physical problem. To answer the question of how a ball will behave in water, you need to compare the density of the ball (sphere) with the density

in °dy (water).

To calculate the density of a ball, you need to determine its volume and mass. The mass of air in the ball is insignificant compared to the mass of copper, so t of the ball = t of copper. The volume of the ball is the volume of the copper shell. Copper and the volume of the cavity V - . The volume of the copper shell can be determined by knowing

mass and density of copper.

We learn about the densities of copper and water from density tables (p. 249).

It is advisable to solve the problem in the presented units.

2. Knowing the volume and mass of the ball, we determine its density:

Analysis of the result: the density of the ball is less than the density of water, so the ball will float on the surface of the water.

Answer: yes, the ball will float on the surface of the water.

Let's sum it up

A body sinks in a liquid or gas if the density of the body is greater than the density of the liquid or gas (p t >p g) · A body floats inside a liquid or gas if the density of the body is equal to the density of the liquid or gas (t = p g). A body floats in a liquid or gas or floats on the surface of a liquid if the density of the body is less than the density of the liquid or gas

Control questions

1. Under what condition will a body sink in a liquid or gas? Give examples. 2. What condition must be met for a body to float inside a liquid or gas? Give examples. 3. Formulate the condition under which a body in a liquid or gas floats up. Give examples. 4. Under what condition will a body float on the surface of a liquid? 5. Why and how do the inhabitants of seas and rivers change their density?

Exercise No. 28

1. Will a uniform lead block float in mercury? in water? in sunflower oil?

2. Place the balls shown in Fig. 1, in order of increasing density.

3. Will a block with a mass of 120 g and a volume of 150 cm 3 float in water?

4. According to Fig. 2 Explain how a submarine dives and surfaces.

5. The body floats in kerosene, completely immersed in it. Determine the mass of the body if its volume is 250 cm3.

6. Three liquids that do not mix were poured into the vessel - mercury, water, kerosene (Fig. 3). Then three balls were lowered into the vessel: steel, foam and oak.

How are the layers of liquids arranged in the vessel? Determine which ball is which. Explain your answers.

7. Determine the volume of the part of the amphibious vehicle submerged in water if an Archimedean force of 140 kN acts on the vehicle. What is the mass of the amphibious vehicle?

8. Compose a problem inverse to the problem discussed in § 28 and solve it.

9. Establish a correspondence between the density of a body floating in water and the part of this body located above the surface of the water.

Ar t = 400 kg/m 3 1 0

B r t = 600 kg/m 3 2 °D

Vrt = 900 kg/m 3 3 0, 4

G r t = 1000 kg/m 3 4 0, 6

10. A device for measuring the density of liquids is called a hydrometer. Using additional sources of information, learn about the structure of a hydrometer and the principle of its operation. Write instructions on how to use a hydrometer.

11. Fill out the table. Consider that in each case the body is completely immersed in the liquid.

Experimental task

"Cartesian Diver". Make a physical toy inspired by the French scientist Rene Descartes. Pour water into a plastic jar with a tight-fitting lid and place a small beaker (or small medicine bottle) partially filled with water, hole down, in it (see picture). There should be enough water in the beaker so that the beaker protrudes slightly above the surface of the water in the jar. Close the jar tightly and squeeze the sides together. Observe the behavior of the beaker. Explain the operation of this device.

LABORATORY WORK No. 10

Subject. Determination of the floating conditions of bodies.

Purpose: to experimentally determine under what conditions: a body floats on the surface of a liquid; the body floats inside the liquid; the body sinks in the liquid.

Equipment: test tube (or small medicine bottle) with a stopper; thread (or wire) 20-25 cm long; container with dry sand; a measuring cylinder half filled with water; scales with weights; paper napkins.

instructions for work

Preparing for the experiment

1. Before you begin, make sure you know the answers to the following questions.

1) What forces act on a body immersed in a liquid?

2) What formula is used to find the force of gravity?

3) What formula is used to find the Archimedean force?

4) What formula is used to find the average density of a body?

2. Determine the scale division value of the measuring cylinder.

3. Secure the test tube to the thread so that, holding the thread, you can immerse the test tube into the measuring cylinder and then remove it.

4. Remember the rules for working with scales and prepare the scales for use. Experiment

Strictly follow the safety instructions (see flyleaf). Immediately enter the measurement results into the table.

Experiment 1. Determination of the condition under which a body sinks in a liquid.

1) Measure the volume of water V 1 in the measuring cylinder.

2) Fill the test tube with sand. Close the plug.

3) Lower the test tube into the measuring cylinder. As a result, the test tube should be at the bottom of the cylinder.

4) Measure the volume V 2 of water and test tubes; determine the volume of the test tube:

5) Take out the test tube and wipe it with a napkin.

6) Place the test tube on the scales and measure its mass to the nearest 0.5 g. Experiment 2. Determining the condition under which a body floats inside a liquid.

1) By pouring sand out of the test tube, make sure that the test tube floats freely inside the liquid.

Experiment 3. Determination of the condition under which a body rises and floats on the surface of a liquid.

1) Pour some more sand out of the test tube. Make sure that after being completely immersed in the liquid, the test tube floats to the surface of the liquid.

2) Repeat the steps described in points 5-6 of experiment 1.

Processing of experiment results

1. For each experience:

1) make a schematic drawing in which you depict the forces acting on the test tube;

2) calculate the average density of the test tube with sand.

2. Enter the calculation results into the table; complete filling it out.

Analysis of the experiment and its results

After analyzing the results, draw a conclusion indicating under what condition: 1) the body sinks in the liquid; 2) the body floats inside the liquid; 3) the body floats on the surface of the liquid.

Creative task

Suggest two ways to determine the average density of an egg. Write down a plan for each experiment.

This is textbook material

We know that any body in a liquid is acted upon by two forces directed in opposite directions: gravity and Archimedean force. The force of gravity is equal to the weight of the body and is directed downward, while the Archimedean force depends on the density of the liquid and is directed upward. How physics explains the floating of bodies, and what are the conditions for floating bodies on the surface and in the water column?

Condition of floating bodies

According to Archimedes' law, the condition for the floating of bodies is as follows: if the force of gravity is equal to the Archimedean force, then the body can be in equilibrium anywhere in the liquid, that is, float in its thickness. If the force of gravity is less than the Archimedean force, then the body will rise from the liquid, that is, float. In the case when the weight of the body is greater than the Archimedean force pushing it out, the body will sink to the bottom, that is, sink. The buoyancy force depends on the density of the liquid. But whether a body floats or sinks depends on the density of the body, since its density will increase its weight. If the density of the body is higher than the density of water, the body will drown. What to do in this case?

The density of dry wood due to cavities filled with air is less than the density of water and the tree can float on the surface. But iron and many other substances are much denser than water. How is it possible to build ships from metal and transport various cargoes by water in this case? And for this the man came up with a little trick. The hull of a ship that is immersed in water is made voluminous, and inside this ship has large cavities filled with air, which greatly reduce the overall density of the ship. The volume of water displaced by the ship is thus greatly increased, increasing its buoyant force, and the total density of the ship is made less than the density of water, so that the ship can float on the surface. Therefore, each ship has a certain limit on the mass of cargo that it can carry. This is called the ship's displacement.

Distinguish empty displacement is the mass of the ship itself, and total displacement- this is the empty displacement plus the total mass of the crew, all equipment, supplies, fuel and cargo that a given vessel can normally carry without the risk of drowning in relatively calm weather.

The body density of organisms inhabiting the aquatic environment is close to the density of water. Thanks to this, they can stay in the water column and swim thanks to the devices given to them by nature - flippers, fins, etc. A special organ, the swim bladder, plays an important role in the movement of fish. The fish can change the volume of this bubble and the amount of air in it, due to which its total density can change, and the fish can swim at different depths without experiencing inconvenience.

The density of the human body is slightly greater than the density of water. However, a person, when he has a certain amount of air in his lungs, can also calmly float on the surface of the water. If, for the sake of experiment, while in the water, you exhale all the air from your lungs, you will slowly begin to sink to the bottom. Therefore, always remember that swimming is not scary, it is dangerous to swallow water and let it into your lungs, which is the most common cause of tragedies on the water.

Floating bodies- the state of equilibrium of a solid body, partially or completely immersed in liquid(or gas).

The main task of the theory of floating bodies is to determine the equilibrium of a body immersed in a liquid and to clarify the conditions for the stability of equilibrium. Indicates the simplest conditions for the floating of bodies Archimedes' law. Let's consider these conditions.

As is known, all bodies immersed in a liquid are acted upon by the Archimedes force F A(pushing force) directed vertically upward, but not all of them float up. To understand why some bodies float and others sink, it is necessary to take into account another force acting on all bodies - gravity Ft which is directed vertically downwards, i.e. opposite F A. If a body is left inside a liquid at rest, it will begin to move in the direction in which the largest force is directed. The following cases are possible:

1. if Archimedean force is less than gravity ( F A< F т ), then the body will sink to the bottom, i.e., drown (Fig. A);
2. if Archimedean force is greater than gravity ( F A > F t), then the body will float up (Fig. b);

If this force turns out to be greater than the force of gravity acting on the body, then the body will fly up. Aeronautics is based on this.

Aircraft used in aeronautics are called balloons(from Greek aer- air, status- standing). Uncontrolled free-flight balloons with a shell shaped like a ball are called balloons. Not so long ago, huge balloons were used to study the upper layers of the atmosphere (stratosphere). stratospheric balloons. Controlled balloons (having an engine and propellers) are called airships.

The balloon not only rises up on its own, but can also lift some cargo: the cabin, people, instruments. In order to determine what kind of load an air container can lift, you need to know its lifting force. The lifting force of a balloon is equal to the difference between the Archimedean force and the force of gravity acting on the balloon:

F = F A - F t.

The lower the density of the gas filling a balloon of a given volume, the less the force of gravity acting on it and the greater the resulting lifting force. Balloons can be filled with helium, hydrogen or heated air. Although hydrogen has a lower density than helium, helium is still more often used for safety reasons ( hydrogen- flammable gas).

It is much easier to lift and lower a balloon filled with hot air. To do this, place a burner under the hole located in the lower part of the ball. It allows you to regulate the air temperature, and therefore its density and lifting force.

You can choose this temperature ball, at which the weight of the ball and the cabin will be equal to the buoyancy force. Then the ball will hang in the air, and it will be easy to make observations from it.

Lesson developments (lesson notes)

Line UMK A.V. Peryshkin. Physics (7-9)

Attention! The site administration is not responsible for the content of methodological developments, as well as for the compliance of the development with the Federal State Educational Standard.

Lesson topic: Sailing conditions tel.

Lesson objectives:

• Educational: teach to analyze, highlight (main, essential),
• bring you closer to solving problem situations on your own.
• Developmental: develop interest in specific activities in the lesson,
• develop the ability to compare, classify, generalize facts and concepts.
• Educational: create an atmosphere of collective search, emotional elation, joy of learning, joy of overcoming difficulties.

Place of the lesson in the section:"Pressure of solids, liquids and gases", after studying the topic "Pressure of liquids and gases on a body immersed in them. Archimedean force."

Lesson type: Lesson on reviewing subject knowledge.

Basic terms and concepts: mass, volume, density of matter, body weight, gravity, Archimedean force.

Interdisciplinary connections: mathematics

Visibility: demonstration of the behavior of different bodies immersed in water; body floating conditions depending on density.

Equipment:

a) for demonstration

• a plastic jar with water, three objects on a string: an aluminum cylinder, a plastic ball, a hermetically sealed bottle of water (prepared in advance by the teacher), which can be in equilibrium anywhere in the liquid;
• a bath of water, a plate of aluminum foil, pliers.

b) for frontal work

• Scales with weights, measuring cylinder (beaker), float capsule with lid (3 each), dry sand, threads, filter paper, electrical tape, instructions for completing frontal experiment tasks, notebooks for laboratory work.

Forms of work in the lesson: frontal in pairs, individual.

Lesson Plan

1. Organizing time;
2. Initial check of understanding of previously studied material;
3. Practical work to verify the findings;
4. Reflection;
5. Homework.

Progress of the lesson

I. Organizational moment

Today in the lesson we will continue to study the behavior of bodies immersed in water. Let's look at a few experiments; you will carry out some of the experiments yourself and perform some calculations.

II. Initial check of understanding of previously studied material

Experience 1

We lower an aluminum cylinder, a ball and a bottle of water into the water in succession. We observe the behavior of bodies.

Result: the cylinder sinks, the ball floats up, the bubble floats, completely immersed in water.

Problem situation: Why? – (Ratio of forces acting on the body).

– All bodies in water are acted upon by two forces: the force of gravity, directed downward, and the buoyant force (Archimedes’ force), directed upward.

– From the rule of addition of forces acting on a body along one straight line, it follows: sinks if F t ˃ F A; floats up if F t ˂ F A; floats if F t = F A.

III. Practical work to verify the findings

Let's do an experiment and check the relationship between gravity and buoyant force. (The laboratory work “Elucidation of the conditions for floating bodies in a liquid” is taken as a basis - page 211 of the textbook).

Exercise 1.

1. Fill the capsule 1/4 full with sand, determine its mass in grams on the scale. Convert the mass value into kg and write it in the table.
2. Place the capsule in water and determine the volume of displaced water in cm3. To do this, mark the water levels in the beaker before and after immersing the capsule in water. Record the volume value in m3 in the table.

P = F heavy = mg And F A = ρ f gV t

Task 2.

1. Fill the capsule completely with sand and determine its mass in grams on the scale. Convert the mass value into kg and write it in the table.
2. Place the capsule in water and determine the volume of displaced water in cm3. To do this, mark the water levels in the beaker before and after immersing the capsule in water. Write the volume value in m 3 in the table.
3. Calculate gravity and Archimedean force using the formulas:

P = F heavy = mg And F A = ρ f gV

Compare Archimedean force with gravity. Enter the calculation results in the table and note: the capsule sinks or floats.

	Body mass, m, kg	Gravity, F heavy, N	Volume of displaced water, V, m 3	Archimedes' power F A, N	Comparison F cord and F A	Behavior of the capsule in water
						pops up

Task 3.

1. Determine at what ratio of gravity and Archimedean force the capsule will float anywhere in the liquid, completely immersed in it? What value will the volume of water displaced by the capsule have?
2. Determine the mass for the floating body (without calculation).
3. Fill the capsule with sand to the required mass, then lower it into the water and verify from experience that your reasoning is correct.
4. Draw a conclusion about the condition for a body to float in a liquid.

Experience 2

Let's check the floating conditions depending on the density of the substance from which the bodies are made and the density of the liquid. For this we have a bath of water, a plate of aluminum foil, and pliers.

1. By bending the corners, we will make a box from the plate. Let's lower it to the surface of the water. We observe the box floating on the surface of the water.
2. Let's take the box out of the water and return the plate to its flat appearance. fold the plate in half, in four, etc. Using pliers, squeeze the foil and lower it into the water.

Result: the box-shaped plate floats, but when compressed it sinks.

Problem situation: Why? – (Ratio of body and water densities).

• density boxes made of aluminum foil is less dense than water, and the density of a compressed lump of foil is greater than the density of water.
• Conditions for floating bodies: sinks if ρ t ˃ ρ water; floats up if ρ t ˂ ρ water; floats if ρ t = ρ water. (ρ aluminum = 2700 kg/m3; ρ water = 1000 kg/m3).

IV. Reflection

Experience 3. Look and explain the operation of the device made by the student according to the assignment for §52 (p. 55 of the textbook). "Cartesian Diver". Instead of a clear bottle, the student used a regular pipette.

The device allows you to demonstrate the laws of floating of bodies.

V. Homework

§52; exr 27(3,5,6).

Self-analysis of the lesson

The topic of the physics lesson in grade 7 is “Conditions for floating bodies.” There are 20 students in the class. The majority of them have good mathematical training. The guys are inquisitive and active. They work well in a team. Participate in preparing equipment for the lesson.

The purpose of the lesson: to interest students, to bring them closer to independently solving problem situations. During the lesson, children learn to independently plan ways to achieve goals, including alternative ones, and consciously choose the most effective ways to solve a problem.

The type of lesson - a lesson on repeating subject knowledge - allows you to test the knowledge acquired in the previous lesson and prepare for solving problems on the topic in the next lesson.

The selected stages of the lesson are logically connected with each other, there is a smooth transition from one to another. During the lesson, the teacher only guides and corrects the actions of the students, who work independently for almost the entire lesson. To save time when completing the practical part, during additional classes, students prepared two capsules with sand, fully and partially filled (tasks 1 and 2), the third remained empty. During the lesson, the children learned to draw conclusions from the experiment and actively discussed solutions to problem situations. At the final stage, the children’s attention was once again focused on the topic of the lesson. The teacher commented on the homework and gave grades for oral answers; after the lesson, the notebooks for laboratory work were checked.

I believe that the goals of the lesson were achieved: the children learned to analyze, highlight (the main, essential), compare, classify, generalize facts and concepts, and find solutions to problem situations. The lesson created an atmosphere of collective search, emotional elation, the joy of learning, and the joy of overcoming difficulties.