Bodies floating conditions

The purpose of the lesson: clarification of the conditions for the floating of bodies, depending on the density of matter and liquid.

Tutorials:

familiarization by students with the concepts: the condition of swimming bodies

formation of a holistic perception of the scientific picture of the world

Developing:

development of the operational style of thinking of students;

development of students' synthetic thinking;

development of the ability and skill of conducting an experiment;

continuation of work on the development of intellectual skills and abilities: highlighting the main thing, analysis, the ability to draw conclusions, concretization;

Educators:

formation of students' interest in the study of physics;

education of accuracy, ability and skill of rational use of one's time, planning one's activities.

Equipment for the lesson:

Test tube with stopper, potato ball, plasticine, water, saturated salt solution, vessel, dynamometer, scales with weights

1. Introduction. Knowledge update.

A student in your class will start the lesson today. So listen carefully

In a blue whale, the tongue weighs 3 tons, the liver - 1 ton, the heart - 600-700 kg, its blood - 10 tons, the diameter of the dorsal artery - 40 cm, in the stomach - 1-2 tons of food; whale's mouth - a room of 24 m2. AT thrown ashore, almost instantly dies.

An interesting plant lives in the Pacific Ocean - this is macrocystis. Its length reaches 57 meters, and its weight is 100 kilograms. This algae is called bladderwort. Near each leaf plate is a bubble the size of a large apple. The shell is thick, do not pierce! It is inflated tightly, tightly with some kind of gas that the algae itself produces. This plant is very useful.

L swans and ducks, heavy and clumsy on the shore, but so light and graceful in the water.

G an air of iron sinks, but a ship made of iron floats

2. Formulate the topic of the lesson???

Bodies floating conditions

Lesson objectives:

Learn to derive formulas for the conditions for floating bodies.

Learn to work with devices, observe, analyze and compare the results of experiments, draw conclusions.

Find out the condition under which a body sinks in a liquid, and the condition for the floating of bodies completely immersed in a liquid.

3.Experience:

- I have in my hands several bars and balls of the same volume. Will the buoyant forces of these bodies be the same when they are immersed in water? (same)

Let's try to put them in the water. What do we see? Some bodies drowned, others float. Why? What else did we not take into account when we talked about the immersion of bodies in a liquid?

Conclusion from experience:

This means that whether a body sinks or not depends not only on the force of Archimedes, but also on the force of gravity.

4. Let's repeat the material of the last lesson

What force is called Archimedean?

On what quantities does it depend?

What formula is used to calculate it?

How else can you determine the buoyant force

In what units is it measured?

How is the Archimedean force directed?

How to determine gravity

How is gravity directed?

What is the resultant force?

What is the resultant of two forces acting in the same straight line in the same direction? In different directions?

How will a body behave under the action of two equal but oppositely directed forces?

5. Presentation of new material. Primary fastening.

Let's look at different situations

(Ft >FA) (Ft =FA) (Ft< FА)

Make assumptions (hypothesis)

if the force of gravity is greater than the force of Archimedes (Ft > FA) - the body sinks

if the force of gravity is equal to the force of Archimedes (Fт = FA) - The body floats,

if the force of gravity is less than the force of Archimedes (Fт< FА) ---Тело всплывает

The assumption must be tested experimentally.

Before you are various bodies and devices.

What materials should be used to prove our assumptions

(dynamometer, fluid, body)

What measurements to make. (Determine the force of Archimedes and the force of gravity and compare them with each other) or calculate using formulas.

Fill in the table

A= ρ andV g =

F t = mg =

conclusion (the ratio of gravity and Archimedean force determines the ability of the body: to swim, sink or float)

The ratio of gravity and Archimedean force determines the body's ability to float, sink or float.

Demonstrations: 1. A test tube body floats in water. 2. A ball of potatoes sinks in water. 3. The same potato ball floats in salt water. 4. A plasticine ball sinks in water 5. A plasticine boat floats in water

In order for a body to float, it is necessary that the force of gravity acting on it is balanced by the Archimedean (buoyant) force.

F t \u003d F a (1)

Archimedean force: F a = ρ x V x g (2)

Gravity: F t = mg = ρVg (3)

Let us substitute expressions (2) and (3) into equality (1): ρVg = ρ x V x g

Dividing both parts of this equality by g, we obtain the condition for the bodies to float in a new form:

ρV = ρ f V f

In order for the body to float, partially protruding above the surface of the liquid, the density of the body must be less than the density of the liquid. When the density of the body is greater than the density of the liquid, the body sinks, because gravity is greater than the Archimedean force.

Analysis of the exercise:

- What substances (ice, stearin, wax, rubber, brick) will float in water, milk, mercury?

- Using the table, determine which metals sink in mercury? (osmium, iridium, platinum, gold)

What substances will float in kerosene? (cork, pine, oak)

4. Application of conditions for floating bodies

A) sailing ships

“And now we must explain why a steel nail sinks, but a steel ship floats?”

- Let's take plasticine. If you put it in water, it will sink. How to make it so that it does not sink?

B) Swimming fish and whales

How can fish and whales change their diving depth? (fish due to a change in the volume of the swim bladder, whales due to a change in the volume of the lungs, which means due to the force of Archimedes)

The density of living organisms inhabiting the aquatic environment differs very little from the density of water, so their weight is almost completely balanced by the Archimedean force. The fish can change the volume of its body by compressing the swim bladder with the efforts of the pectoral and abdominal muscles, thereby changing the average density of its body, thanks to which it can regulate the depth of its dive.

The swim bladder of a fish easily changes its volume. When the fish, with the help of muscles, descends to a great depth and the water pressure on it increases, the bubble contracts, the volume of the fish's body decreases, and it swims in depth. When rising, the swim bladder and the volume of the fish increases and it emerges. So the fish regulates the depth of its dive. The swim bladder of a fish

Whales regulate their diving depth by increasing and decreasing their lung capacity. It is interesting

The average density of living organisms inhabiting the aquatic environment differs little from the density of water, so their weight is almost completely balanced by the Archimedean force. Thanks to this, aquatic animals do not need strong and massive skeletons. For the same reason, the trunks of aquatic plants are elastic.

Birds have a thick layer of feathers and down that does not let water through, which contains a significant amount of air, due to which the average density of their body is very low, so ducks do not immerse themselves in water when swimming.

B) sailing submarines

- Due to what submarines can rise and fall to different depths? (due to a change in its mass, and hence the force of gravity)

D) Human swimming in fresh water and salt water

The average density of the human body is 1030 kg/m. Will a man swim or drown in a river and in a salt lake?

Swimming bodies

203. A swimmer lying motionless on his back takes a deep breath and exhale. How does the position of the swimmer's body change in relation to the surface of the water? Why?

204. Are the buoyant forces acting on the same wooden block floating first in water and then in kerosene the same?

205. Why does a plate, placed flat on the surface of the water, float, and sinking edge-on into the water?

206. Can a lifeline hold any number of people grabbing onto it?

207. Heavy lead plates are placed on the diver's chest and back, and lead soles are attached to the shoes. Why do they do it?

208. A piece of wood is lowered into a vessel with water. Will this change the pressure on the bottom of the vessel if the water does not pour out of the vessel?

209. A glass is filled to the brim with water. A piece of wood is placed in it so that it floats freely. Will the weight of the glass change if the water still fills it to the brim?

Answers: 203. When inhaling, the swimmer emerges, while exhaling, he sinks deeper into the water, since when breathing, the volume of the chest changes and the Archimedean force changes accordingly.

(When inhaling, the swimmer emerges, while exhaling, he sinks deeper into the water, since the volume of the chest changes during breathing, and the body weight remains almost constant. Therefore, the total volume of the body increases during inhalation, decreases during exhalation, and the volume of the part of the body immersed in water, does not change.)

204. Are the same. The block floats in both liquids, which means that the buoyant force in each of them is equal to the force of gravity acting on it.

206. No, since the lifting force (the difference between the maximum Archimedean force and the force of gravity) of the circle has a limited value.

207. To increase the force of gravity and make it more than the Archimedean force, otherwise the diver will not dive to the required depth.

208. The pressure will increase, as the level of water in the vessel will rise.

209. Will not change, since the weight of a piece of wood is equal to the weight of the water displaced by it (and poured out of the glass).

6. Experimental task.

Determine body weight:m=

DetermineF t according to the formula and using a dynamometer, fill in the table.

Define FBUTaccording to the formula and using a dynamometer, fill in the table.

Formulate a conclusion (the ratio of gravity and Archimedean force determines the ability of the body: to swim, sink or float)

Fill in the table

A= ρ andV g =

F t = mg =

conclusion(based on experiment)

output (actually)

F t =

7. Homework:

8. Conclusion: with Now our lesson time is coming to an end. And even though we have not solved all the problems, our journey along the roads of physics does not end!

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

Bodies floating condition

According to the law of Archimedes, 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 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 buoyant force depends on the density of the liquid. But whether the body will float or sink 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, then the body will sink. How to be in such a case?

The density of a dry tree 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 of metal and transport various cargoes by water in this case? And for this man came up with a little trick. The hull of a ship that is submerged 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 pushing 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 take away. 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, stores, fuel and cargo, which this vessel can normally take away without the risk of drowning in relatively calm weather.

The density of the body in organisms inhabiting the aquatic environment is close to the density of water. Thanks to this, they can be 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.

A body immersed in a liquid, in addition to gravity, is affected by a buoyant force - the Archimedes force. The fluid presses on all faces of the body, but the pressure is not the same. After all, the lower face of the body is immersed in the liquid more than the upper, and the pressure increases with depth. That is, the force acting on the lower face of the body will be greater than the force acting on the upper face. Therefore, a force arises that tries to push the body out of the liquid.

The value of the Archimedean force depends on the density of the liquid and the volume of that part of the body that is directly in the liquid. The Archimedes force acts not only in liquids, but also in gases.

Law of Archimedes: a body immersed in a liquid or gas is subjected to a buoyant force equal to the weight of the liquid or gas in the volume of the body. In order to calculate the Archimedes force, it is necessary to multiply the density of the liquid, the volume of the part of the body immersed in the liquid, and the constant value g.

Two forces act on a body that is inside a liquid: the force of gravity and the force of Archimedes. Under the influence of these forces, the body can move. There are three conditions for floating bodies:

If gravity is greater than the Archimedean force, the body will sink, sink to the bottom.

If gravity is equal to the Archimedes force, then the body can be in equilibrium at any point in the fluid, the body floats inside the fluid.

If the force of gravity is less than the Archimedean force, the body will float, rise up.

Floating bodies on the surface of a liquid

In the surface position, two forces act on the floating body along the OZ axis (Fig. 1.1). This is the force of gravity of the body G and buoyant Archimedean force P z .

swimming, i.e. submerged . The main concepts of the theory of navigation include the following:

- sailing plane(I-I) - the plane of the free surface of the liquid intersecting the body;

- waterline - the line of intersection of the body surface and the swimming plane;

- draft (y)- the depth of immersion of the lowest point of the body. The greatest allowable draft of the vessel is marked on it with a red waterline;

- displacement - the weight of water displaced by the ship. The ship's displacement at full load is its main technical characteristic;

The center of displacement (point D, Fig. 1.1) is the center of gravity of the displacement through which the line of action of the buoyant Archimedean force passes;

Axis of navigation (О О ") - a line passing through the center of gravity C and the center of displacement D when the body is in balance.

To maintain balance, the melting axis must be vertical. If an external force acts on a floating ship in the transverse direction, for example, the force of wind pressure, then the ship will roll, the navigation axis will turn relative to point C and a torque M k will appear, rotating the ship about the longitudinal axis counterclockwise (Fig. 1.2)

The stability of a floating body depends on the relative position of points C and D. If the center of gravity C is below the center of displacement D, then during surface navigation the body is always stable, since the torque M k that occurs during a roll is always directed in the direction opposite to the roll.

If point C is above point D (Fig. 1.3), then the floating body can be stable and unstable. Let's consider these cases in more detail.

With a roll, the center of displacement D shifts horizontally towards the roll, since one side of the ship displaces a larger volume of water than the other.

Then the line of action of the buoyant Archimedean force P z will pass through the new center of displacement D "and intersect with the navigation axis OO" at the point M, called metacenter. To formulate the stability condition, we denote the segment

M D 1 = b,aCD 1 =∆ , where b - metacentric radius; ∆- eccentricity.

Stability condition: the body is stable if its metacentric radius is greater than the eccentricity, i.e. b > ∆.

Graphical interpretation of the stability condition is shown in fig. 1.3, which shows that in case a) b > ∆ and the resulting torque is directed in the direction opposite to the roll, and in case b) we have: b< ∆ and moment M to rotates the body in the direction of roll, i.e. the body is unstable.

Displacement ship (vessel) - the amount of water displaced by the underwater part of the ship (vessel) hull. The weight of this amount of liquid is equal to the weight of the entire ship, regardless of its size, material and shape.

Distinguish volumetric and massive standard, normal, complete, greatest, empty displacement.

Displacement Waterline(dutch. waterline) - the line of contact of a calm water surface with the hull of a floating vessel. Also - in the theory of the ship, an element of the theoretical drawing: a section of the hull by a horizontal plane.

Mass displacement

Standard displacement

Normal displacement

Full displacement

Maximum displacement

Light displacement

Underwater displacement

surface displacement

Stability of floating bodies

Stability floating bodies is called their ability to return to their original position after they were removed from this position due to the influence of any external forces.

To give a floating body stability, it is necessary that when it deviates from the equilibrium position, a pair of forces is created, which will return the body to its original position. Such a pair of forces can only be created by forces G and P n. There are three different options for the mutual arrangement of these forces (Fig. 5.3).

Rice. 5.3. Stability of semi-submerged bodies with mutual arrangement of the center of gravity and the center of displacement a and b- stable balance

The center of mass is located below the center of displacement.When heeling, the center of displacement moves both due to a change in the position of the body, and due to a change in the shape of the displaced volume. In this case, a couple of forces arise, striving to return the body to its original position. Therefore, the body has positive stability.

The center of mass coincides with the center of displacement- the body will also have positive stability due to the displacement of the center of displacement due to a change in the shape of the displaced volume.

The center of mass is above the center of displacement.Here there are two main options (Fig. 5.4):

1) the point of intersection of the lifting force with the axis of navigation M (metacenter) lies below the center of mass - the balance will be unstable (Fig. 5.4, a);

2) the metacenter lies above the center of mass - the balance will be stable (Fig. 5.4, b). The distance from the metacenter to the center of mass is called metacentric height. Metacenter - the point of intersection of the lift force with the axis of navigation. If point M lies above the point FROM, then the metacentric height is considered positive if it lies below the point FROM- then it is considered negative.

Thus, the following conclusions can be drawn:

the stability of a body in a semi-submerged state depends on the relative position of the points M and FROM(from metacentric height);

the body will be stable if the metacentric height is positive, i.e. the metacenter is located above the center of gravity. Almost all military floating vehicles are built with a metacentric height of 0.3-1.5m.

Rice. 5.4. Stability of semi-submerged bodies with the relative position of the center of gravity and the metacenter:

a- unstable balance; b- stable balance

Displacement ship (vessel) - the amount of water displaced by the underwater part of the ship (vessel) hull. The mass of this amount of liquid is equal to the mass of the entire ship, regardless of its size, material and shape.

Distinguish volumetric and massive displacement. According to the state of the load of the ship, they distinguish standard, normal, complete, greatest, empty displacement.

For submarines, there are underwater displacement and surface displacement.

Displacement

displacement equal to the volume of the underwater part of the ship (vessel) to the waterline.

Mass displacement

displacement equal to the mass of the ship (vessel).

Standard displacement

displacement of a fully equipped ship (vessel) with a crew, but without fuel, lubricants and drinking water in tanks.

Normal displacement

a displacement equal to the standard displacement plus half the fuel, lubricants and potable water in the tanks.

Full displacement

displacement equal to the standard displacement plus full reserves of fuel, lubricants, drinking water in tanks, cargo.

Maximum displacement

a displacement equal to the standard displacement plus the maximum reserves of fuel, lubricants, drinking water in tanks, cargo.

Light displacement)

displacement of an empty ship (vessel), that is, a ship (vessel) without a crew, fuel, supplies, etc.

Underwater displacement

displacement of a submarine (batyscaphe) and other underwater vessels in a submerged position. Exceeds the surface displacement by the mass of water taken when immersed in the main ballast tanks.

surface displacement

displacement of a submarine (bathyscaphe) and other underwater vessels in a position on the water surface before immersion or after surfacing.

Swimming is the ability of a body to stay on the surface of a liquid or at a certain level within a liquid.

We know that any body in a fluid is subject to two forces directed in opposite directions: the force of gravity and the Archimedean force.

The force of gravity is equal to the weight of the body and is directed downwards, while the Archimedean force depends on the density of the liquid and is directed upwards. How does physics explain the floating of bodies, and what are the conditions for floating bodies on the surface and in the water column?

Archimedean force is expressed by the formula:

Fvyt \u003d g * m well \u003d g * ρ well * V well \u003d P well,

where m w is the mass of the liquid,

and P W is the weight of the fluid displaced by the body.

And since our mass is equal to: m W = ρ W * V W, then from the formula of the Archimedean force we see that it does not depend on the density of the immersed body, but only on the volume and density of the fluid displaced by the body.

Archimedean force is a vector quantity. The reason for the existence of the buoyancy force is the difference in pressure on the upper and lower parts of the body. The pressure shown in the figure is P 2 > P 1 due to greater depth. For the emergence of the Archimedes force, it is enough that the body is immersed in a liquid, at least partially.

So, if a body floats on the surface of a liquid, then the buoyant force acting on the part of this body immersed in the liquid is equal to the gravity of the entire body. (Fa = P)

If gravity is less than the Archimedean force (Fa > P), 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 (Fa

From the ratio obtained, important conclusions can be drawn:

The buoyant force depends on the density of the liquid. Whether a body will sink or float in a liquid depends on the density of the body.

A body floats completely immersed in a liquid if the density of the body is equal to the density of the liquid

The body floats, partially protruding above the surface of the liquid, if the density of the body is less than the density of the liquid

- if the density of the body is greater than the density of the liquid, swimming is impossible.

Fishermen's boats are made of dry wood, the density of which is less than that of water.

Why do ships float?

The hull of a ship that is submerged 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 pushing 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 take away. This is called the ship's displacement.