Balance conditions of bodies presentation. Presentation for the lesson "Conditions of equilibrium of a rigid body. Types of balance" presentation for a lesson in physics (grade 10) on the topic. center of gravity rises

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Presentation on physics on the topic: "Equilibrium of bodies, conditions of equilibrium of bodies." Pupils of the 10th grade GBOU Secondary School No. 1465 Kazakova Alena. Physics teacher L.Yu. Kruglov. The branch of mechanics that studies the conditions for the balance of forces is called statics.

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Physics presentation on the topic: "Equilibrium of bodies, conditions of equilibrium of bodies"

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"Equilibrium of bodies, conditions of equilibrium of bodies" Pupils of the 10th grade of the State Budgetary Educational Institution of Secondary School No. 1465 Kazakova Alena. Physics teacher L.Yu. Kruglova

The balance of forces is called statics. The point through which the resultant of gravity passes at any position of the body is called the center of gravity.

The interaction of bodies in dynamics is the occurrence of accelerations. However, it is often necessary to know under what conditions a body, which is acted upon by several different forces, does not move with acceleration. Let's hang the ball on the thread. The ball is acted upon by gravity, but does not cause accelerated motion towards the Earth. This is prevented by the action of an elastic force of equal modulus and directed in the opposite direction. The force of gravity and the force of elasticity balance each other, their resultant is equal to zero, therefore the acceleration of the ball is also equal to zero.

Uniform rectilinear translational motion of a body or its rest is possible only when the geometric sum of all forces applied to the body is equal to zero. A non-rotating body is in equilibrium if the geometric sum of forces applied to the body is equal to zero. \u003d + +… + \u003d 0

Rotation. In everyday life and technology, there are often bodies that cannot translate, but can rotate around an axis. Examples of such bodies are doors and windows, car wheels, swings, etc. If the force vector lies on a straight line intersecting the axis of rotation, then this force is balanced by the elastic force from the axis of rotation.

The force vector does not intersect the axis of rotation, then this force cannot be balanced by the elastic force from the side of the axis of rotation, and the body rotates around the axis.

The action of one force can be stopped by the action of the second force. Experience shows that if two forces and separately cause the body to rotate in opposite directions, then with their simultaneous action the body is in equilibrium if the condition is met: F1 d1 \u003d F2 d2 where d1 and d2 are the shortest distances from the straight lines on which the force vectors lie F1 and F2. The distance d is called the arm of the force, and the product of the modulus of the force F by the arm d is called the moment of force M: M \u003d Fd

Combining the two conclusions, we can formulate the general condition of equilibrium of bodies: The body is in equilibrium if the geometric sum of the vectors of all forces applied to it and the algebraic sum of the moments of these forces about the axis of rotation are equal to zero. (RULE OF MOMENTS) When the general condition of equilibrium is satisfied, the body is not necessarily in rest. According to Newton's First Law, when the resultant of all forces is equal to zero, the acceleration of the body is zero, and the body can be both at rest and move uniformly and rectilinearly.

Types of balance. In practice, an important role is played not only by the fulfillment of the equilibrium condition for bodies, but also by a qualitative characteristic of equilibrium, called stability. There are three types of body balance: stable, unstable and indifferent.

Located on a horizontal surface. Equilibrium is called unstable if, with a small displacement of the body from the equilibrium position, the resultant of the forces applied to it is nonzero and directed from the equilibrium position.

Conducted through the center of gravity C, does not cross the support area, then the body overturns. Body balance on a support. If a vertical line drawn through the center of gravity C of the body intersects the support area, then the body is in equilibrium.

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Slide captions:

Equilibrium conditions for bodies. Types of balance.

2 The section of mechanics in which the equilibrium of absolutely rigid bodies is studied is called statics. Body balance is a state of rest, or even and straight body movement. An absolutely rigid body is a body in which deformations arising under the action of forces applied to it are negligible.

The first condition for the equilibrium of a rigid body: a rigid body is in equilibrium if the geometric sum of external forces applied to it is equal to zero.

The second condition for equilibrium of a rigid body: a rigid body is in equilibrium if the algebraic sum of the moments of external forces acting on it with respect to any axis is zero. M 1 + M 2 + M 3 + ... \u003d 0

The center of gravity of a body is the point of application of the resultant force of gravity. Find the center of gravity of the given shapes.

6 Types of balance Stable Indifferent Unstable

7 Conditions for the stability of equilibrium 1. Bodies are in a state of stable equilibrium if at the slightest deviation from the equilibrium position a force or moment of force arises that returns the body to the equilibrium position.

2. Bodies are in a state of unstable equilibrium if, at the slightest deviation from the equilibrium position, a force or moment of force arises that removes the body from the equilibrium position.

3. Bodies are in a state of indifferent equilibrium if, at the slightest deviation from the equilibrium position, neither a force nor a moment of force appears that changes the position of the body.

10 O stable N d Types of equilibrium unstable indifferent F t F t N O O F t F t N d F t

The support area is understood as the area of \u200b\u200bcontact of the body with the support or the area limited by possible axes relative to which the body can overturn (turn) under the action of external forces.

12 Equilibrium of bodies on supports A body having an area of \u200b\u200bsupport will be in equilibrium as long as the line of action of the force of gravity passes through the area of \u200b\u200bsupport. F t F t F t F t ℓ ℓ

F t F t If the deflection of a body with an area of \u200b\u200bsupport increases the center of gravity, then the balance will be stable. In stable equilibrium, the vertical line passing through the center of gravity will always pass through the support area.

F t F t F t F t F t Two bodies that have the same weight and support area, but different heights, have a different limiting angle of inclination. If this angle is exceeded, the bodies overturn. A \u003d F t h

F t F t F t F t F t A \u003d F t h With a lower position of the center of gravity, it is necessary to spend more work to overturn the body. Consequently, tipping work can serve as a measure of its stability.

16 Balance of bodies on supports

17 Sustainability of transport

The section of mechanics in which it is studied
balance of absolutely rigid bodies,
called statics.
Body balance is a state of rest
or uniform and straight
body movements.
An absolutely solid body is a body, u
which deformations occurring
under the influence of the attached
forces are negligible.
2

The first equilibrium condition
solid: solid
is in balance,
if the geometric sum
external forces applied
to it, is zero.

Second equilibrium condition
solid: solid
is in equilibrium if
algebraic sum of moments
external forces acting on
him relative to any axis,
is zero.
M1 + M2 + M3 + ... \u003d 0

The body's center of gravity is a point
annexes
resultant force
gravity.

Balance types

Sustainable
Unstable
Indifferent
6

Equilibrium stability conditions

1. Bodies are in a state
stable equilibrium if
at the slightest deviation from
equilibrium positions
a force or moment arises
forces returning the body to
equilibrium position.
7

2.Bodies are in a state
unstable equilibrium if
at the slightest deviation from
equilibrium positions
a force or moment arises
the forces that remove the body from
equilibrium position.

3. The bodies are in
state of indifference
equilibrium if at
the slightest deviation from
equilibrium position not
neither force nor
moment of force changing
body position.

Balance types
d
Fт
N
ABOUT
Fт
N
ABOUT
Fт
Fт
Fт
N d
ABOUT
sustainable
unstable
indifferent
10

The support area is understood as the area of \u200b\u200bcontact of the body with
support or an area limited by possible axes,
over which overturning can occur (
turn) of the body under the influence of external forces.

Balance of bodies on supports

ℓ
ℓ
Fт
Fт
Fт
Fт
A body with a support area will
be in equilibrium until
the line of action of gravity will be

12

Fт
Fт
If, when deflecting a body with an area of \u200b\u200bsupport,
there is an increase in the center of gravity, then the balance will
sustainable. With stable equilibrium, the vertical
a straight line passing through the center of gravity will always be
pass through the support area.

A \u003d FFт т h
Fт
Fт
Fт
Fт
Two bodies that have the same weight and support area, but
different heights, have different limiting angle of inclination. If
exceed this angle, then the bodies overturn.

A \u003d Fт Fтh
Fт
Fт
Fт
Fт
With a lower center of gravity,
spend a lot of work to overturn the body.
Therefore tipping work can serve as a measure
its stability.

Class: 10

Lesson presentation

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Lesson objectives:Study the state of balance of bodies, get acquainted with different types of balance; find out the conditions under which the body is in equilibrium.

Lesson Objectives:

• Educational:Study two conditions of equilibrium, types of equilibrium (stable, unstable, indifferent). Find out under what conditions the bodies are more stable.
• Developing:Promote the development of a cognitive interest in physics. Development of skills to compare, generalize, highlight the main thing, draw conclusions.
• Educational:To educate attention, the ability to express one's point of view and defend it, to develop the communication skills of students.

Lesson type:a lesson in learning new material with computer support.

Equipment:

1. Disc "Work and Power" from "Electronic Lessons and Tests.
2. Equilibrium conditions table.
3. Tilting prism with a plumb line.
4. Geometric bodies: cylinder, cube, cone, etc.
5. Computer, multimedia projector, interactive whiteboard or screen.
6. Presentation.

During the classes

Today in the lesson we will learn why the crane does not fall, why the toy "Vanka-Vstanka" always returns to its original state, why the Leaning Tower of Pisa does not fall?

I. Repetition and actualization of knowledge.

1. Formulate Newton's first law. What state does the law say?
2. What question does Newton's second law answer? Formula and wording.
3. What question does Newton's third law answer? Formula and wording.
4. What is called the resultant force? How is it located?
5. From the disc "Movement and interaction of bodies" complete task number 9 "Resultant forces with different directions" (the rule of adding vectors (2, 3 exercises)).

II. Learning new material.

1. What is called balance?

Equilibrium is a state of rest.

2. Equilibrium conditions.(slide 2)

a) When is the body at rest? What law does this follow?

First equilibrium condition:The body is in equilibrium if the geometric sum of the external forces applied to the body is equal to zero. ∑F \u003d 0

b) Let two equal forces act on the board, as shown in the figure.

Will she be in balance? (No, she will turn)

Only the central point is at rest, and the rest are moving. This means that for the body to be in equilibrium, it is necessary that the sum of all the forces acting on each element be equal to 0.

Second equilibrium condition: The sum of the moments of forces acting clockwise must equal the sum of the moments of forces acting counterclockwise.

∑ M clockwise \u003d ∑ M counterclockwise

Moment of force: M \u003d F L

L - force shoulder - the shortest distance from the fulcrum to the line of force action.

3. The center of gravity of the body and its location.(slide 4)

Body center of gravity - this is the point through which the resultant of all parallel gravity forces acting on individual elements of the body passes (for any position of the body in space).

Find the center of gravity of the following shapes:

4. Types of balance.

a) (slides 5-8)

Conclusion: Equilibrium is stable if, with a small deviation from the equilibrium position, there is a force tending to return it to this position.

Stable is the position in which its potential energy is minimal. (slide 9)

b) Stability of bodies located on the fulcrum or on the line of support. (slides 10-17)

Conclusion:For the stability of a body located on one point or line of support, it is necessary that the center of gravity be below the point (line) of support.

c) Stability of bodies on a flat surface.

(slide 18)

1) Support surface - it is not always a surface that is in contact with the body (but one that is bounded by the lines connecting the legs of the table, tripods)

2) Analysis of the slide from "Electronic lessons and tests", disc "Work and power", lesson "Types of balance".

Picture 1.

1. How are stools different? (Support area)
2. Which one is more stable? (With a larger area)
3. How are stools different? (The location of the center of gravity)
4. Which one is the most stable? (With lower center of gravity)
5. Why? (Because it can be tilted to a larger angle without tipping over)

3) Experiment with a deflecting prism

1. We put a prism with a plumb line on the board and begin to gradually raise it by one edge. What do we see?
2. As long as the plumb line crosses the surface bounded by the support, balance is maintained. But as soon as the vertical, passing through the center of gravity, begins to go beyond the boundaries of the support surface, the stack overturns.

Parsing slides 19-22.

Conclusions:

1. The body with a larger support area is stable.
2. Of two bodies of the same area, the one with the lower center of gravity is stable. it can be tilted without tipping over a large angle.

Parsing slides 23-25.

Which ships are the most stable? Why? (For which the cargo is located in the holds, not on the deck)

Which cars are the most stable? Why? (To increase the stability of cars on bends, the road bed is tilted towards the bend.)

Conclusions:Equilibrium can be stable, unstable, indifferent. The greater the support area and the lower the center of gravity, the greater the stability of the bodies.

III. Application of knowledge about the stability of bodies.

1. What specialties are most needed to know about the balance of bodies?
2. Designers and constructors of various structures (high-rise buildings, bridges, television towers, etc.)
3. Circus artists.
4. Drivers and other professionals.

(slides 28-30)

1. Why does Vanka-Vstanka return to the balance position at any inclination of the toy?
2. Why is the Leaning Tower of Pisa tilted and not falling?
3. How do cyclists and motorcyclists keep their balance?

Conclusions from the lesson:

1. There are three types of balance: stable, unstable, indifferent.
2. The position of the body is stable, in which its potential energy is minimal.
3. The stability of bodies on a flat surface is the greater, the larger the support area and the lower the center of gravity.

Homework: § 54 – 56 (G.Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky)

Used sources and literature:

1. G. Ya. Myakishev, B.B. Bukhovtsev, N.N. Sotsky. Physics. Grade 10.
2. Filmstrip "Stability" 1976 (scanned by me on a film scanner).
3. Disc "Motion and interaction of bodies" from "Electronic lessons and tests".
4. Disk "Work and Power" from "Electronic Lessons and Tests".

Equilibrium, in which the body brought out of the equilibrium position returns to it again is stable.

axis of rotation

the center of gravity

A body with a fixed axis of rotation.

An equilibrium in which a body unbalanced does not return to its initial position is unstable.

the center of gravity

axis of rotation

A body with a fixed axis of rotation.

Equilibrium is indifferent: if, when the body is deflected or moved, it remains in equilibrium.

axis of rotation

the center of gravity

A body that has a fulcrum.

The ball is in steady balance.

The ball is in unstable balance.

Ball in indifferent equilibrium.

The ball is taken out of balance:

center of gravity rises

- stable balance;

center of gravity goes down

- the balance is unstable;

the center of gravity is at the same level - the equilibrium is indifferent.

The world famous Leaning Tower of Pisa:

it seems that it is about to fall.

Tower in white marble.

Its height is 56.7 m,

weight 14 454 tons.

It was once believed that the tilt of the tower was part of the project.

In 1178 a third floor was built and the tower gradually began to tilt.

A body that has an area of \u200b\u200bsupport.

the center of gravity

support area

The center of gravity is only 2 meters from the middle of its support. Will "fall" if the deviation is about 14 meters!

The overall center of gravity of the crane, load and counterweight does not extend beyond the support area.

counterweight

How to determine body stability?

α - the angle of rotation to transfer the body to unstable balance.

The larger the angle α,

the more stable the initial position of the body.

How to increase body stability?

The center of gravity of the body is lowered:

- make the lower body more massive;

- part of the body is buried in the Earth (create a foundation);

- increase the area of \u200b\u200bsupport of the body.

In a tumbler doll, the secret lies in the downward center of gravity of the body.

Alexandrian column

on the Palace Square of St. Petersburg:

downward center of gravity of the column.

The height of the structure is 47.5 m.

The column shaft height is 25.6 m.

The lower column diameter is 3.5 m, the upper one - 3.15 m.

The mass of the structure is 704 tons.

The mass of the stone shaft of the column is about 600 tons.

The sculptor Falcone brought the sculpture into balance

" Bronze Horseman" :

- increased support area

(placed the snake under the horse's hind hooves);

Center of gravity above the support area (the front part of the rider is lightened, and the horse's croup, its hind legs and tail are massive);

- the overall center of gravity of the entire monument is lowered (a pedestal is installed).

A person does not fall down until:

To make the support area larger, the legs are set wider.

Less support area:

balance is difficult.

It is difficult for circus performers to keep balance on a narrow rope.

Why is it difficult to stand on one leg?

reduced support area

Why do people wave their arms when they walk?

center of gravity shifts

Why does a person carrying a load on their back lean forward?

the position of the center of gravity changes

Descending from the mountain, the skier crouches slightly. Why?

center of gravity goes down

In what position is a person more stable: when he sits or when he stands?

the person is sitting: the center of gravity is lower than when he is standing

Why does an athlete always take a step forward when lifting the bar?

to increase the support area

Why do ducks and geese walk waddling from foot to foot?

Geese and ducks have legs wide apart. So that the vertical line passing through the center of gravity passes through the fulcrum (paw).

When a tree has a higher center of gravity: in summer or autumn, when the leaves have fallen?

higher in summer when there are many leaves on the trees

Interesting fact!

In a dense forest, you can always find trees felled by the wind, and in an open field, where the wind is much stronger, trees are rarely felled by the wind.

In the shade of the forest, the lower branches of the trees die off. The center of gravity is at the top.

Sit someone on a chair so that he keeps his torso straight, touching the back of the chair, and does not move his legs under the seat of the chair.

Now ask him to stand up without changing the position of his legs or bending the body forward.

Offer to stand with your right foot and right shoulder against the wall and lift your left leg.

Can a person not lose balance at the same time?

Secret Box:

When the balance is disturbed, the center of gravity rises: balance will be restored because gravity will pull the body down.

Virtuosos