branch of mechanics that studies
equilibrium of perfectly rigid bodies,
called static.
Body balance is a state of rest
or uniform and straight
body movements.
A perfectly rigid body is a body
which deformations arising
under the influence of the
forces are negligible.
2

Types of balance

Conditions for stability of equilibrium

Balance of bodies on supports

Like share 452 Views

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

Download Presentation

Presentation in physics on the topic: "Equilibrium of bodies, conditions for the equilibrium of bodies"

E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

"Balance of bodies, conditions of balance of bodies" Pupils of the 10th grade of GBOU secondary school No. 1465 Alena Kazakova. Physics teacher L.Yu. Kruglova

The conditions for the balance of forces are called statics. The point through which the resultant of gravity passes at any location 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. Hang the ball on a string. The force of gravity acts on the ball, but does not cause accelerated motion towards the Earth. This is prevented by the action of an elastic force equal in absolute value and directed in the opposite direction. The force of gravity and the force of elasticity balance each other, their resultant is zero, therefore, the acceleration of the ball is also zero.

Uniform rectilinear translational motion of a body or its rest is possible only if 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 zero. = + + … + = 0

Rotations. AT Everyday life and technology, there are often bodies that cannot move forward, 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 that intersects the axis of rotation, then this force is balanced by the elastic force from the side of the axis of rotation.

The force vector does not cross 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 a second force. Experience shows that if two forces and individually cause the rotation of the body in opposite directions, then with their simultaneous action the body is in equilibrium if the condition is met: F1 d1=F2 d2 where d1 and d2 are the shortest distances from the 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 force F and the arm d is called the moment of force M: M = Fd

Combining the two conclusions, we can formulate the general condition for the equilibrium of bodies: A 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) general condition equilibrium, the body is not necessarily at rest. According to Newton's First Law, when the resultant of all forces is equal to zero, the acceleration of the body is equal to zero, and the body can be both at rest and move uniformly and rectilinearly.

Types of balance. In practice big role plays not only the fulfillment of the condition of equilibrium of bodies, but also a qualitative characteristic of equilibrium, called stability. There are three types of balance of bodies: stable, unstable and indifferent.

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

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

To use the preview of presentations, create an account for yourself ( account) Google and sign in: https://accounts.google.com

Slides captions:

Conditions for the equilibrium of bodies. Types of balance.

2 The section of mechanics that studies the equilibrium of absolutely rigid bodies is called statics. Body balance is a state of rest or uniform and rectilinear motion of the body. An absolutely rigid body is a body in which the deformations that occur 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 the external forces applied to it is zero.

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

The center of gravity of a body is the point of application of the resultant force of gravity. Find the centroid of these figures.

6 Types of equilibrium 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 arises that changes the position of the body.

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

Under the support area is understood the area of ​​contact of the body with the support or the area limited by the possible axes, relative to which the body can overturn (rotate) under the action of external forces.

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

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

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

F t F t F t F t F t A = F t h With a lower center of gravity, more work must be expended to overturn the body. Therefore, the work of overturning can serve as a measure of its stability.

16 Balance of bodies on supports

17 Transport sustainability

Equilibrium, in which the body removed from the equilibrium position returns to it again - stable.

axis of rotation

center of gravity

A body with a fixed axis of rotation.

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

center of gravity

axis of rotation

A body with a fixed axis of rotation.

Equilibrium is indifferent: if, when a body is deflected or moved, it remains in balance.

axis of rotation

center of gravity

A body with a fulcrum.

The ball is in stable equilibrium.

The ball is in unstable equilibrium.

The ball is in indifferent equilibrium.

The ball is taken out of equilibrium:

center of gravity rises

- stable balance;

center of gravity is lowered

- the balance is unstable;

center of gravity at the same level - indifferent balance.

The world-famous Leaning Tower of Pisa:

looks like it's about to fall off.

White marble tower.

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, the third floor was erected and the tower gradually began to lean.

A body with an area of ​​support.

center of gravity

footprint

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

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

counterweight

How to determine the stability of the body?

α - the angle of rotation to bring the body into unstable equilibrium.

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;

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

- increase the area of ​​​​support of the body.

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

Alexandrian column

on Palace Square in St. Petersburg:

shifted down the center of gravity of the column.

The height of the structure is 47.5 m.

The height of the column shaft is 25.6 m.

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

The mass of the structure is 704 tons.

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

Sculptor Falcone ensured the balance of the sculpture

" Bronze Horseman" :

- increased footprint

(placed the snake under the hind hooves of the horse);

The center of gravity is above the area of ​​​​support (the front of the rider is lightened, and the horse's croup, his hind legs and tail are massive);

- the general center of gravity of the entire monument was lowered (a pedestal was installed).

A person does not fall until:

To increase the area of ​​\u200b\u200bthe support, the legs are placed wider.

The area of ​​support is less:

it is difficult to keep balance.

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

Why is it difficult to stand on one leg?

reduced footprint

Why do people swing their arms when they walk?

center of gravity shifts

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

center of gravity changes

Going down the mountain, the skier crouches slightly. Why?

center of gravity is lowered

In what position is a person more stable: when he is sitting or when he is standing?

a 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 barbell?

to increase the footprint

Why do ducks and geese walk from foot to foot?

Geese and ducks have widely spaced paws. So that the vertical line passing through the center of gravity passes through the fulcrum (paw).

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

higher in summer when the trees have a lot of leaves

Interesting fact!

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

In the shade of the forest, the lower branches of the trees die off. Center of gravity at the top.

Sit someone who wants to sit 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 the legs and without bending the body forward.

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

Can a person not lose his balance?

Secret box:

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

Virtuosi