The action of bodies on each other is described with the help of forces. Strength is the measure of the action of one body on another.

For example, by kicking a ball, you apply force to it (Figure 14.1). At the same time, you feel that the ball is "pushing" your leg with some force.

Rice. 14.1. When hitting the ball, the player applied force to the ball. As a result, the speed of the ball has changed.

What are the characteristics of forces? You can hit the ball harder or weaker - which means that the strength is characterized by a numerical value. In addition, you can hit in different directions - which means that the force also has a certain direction.

Quantities that are characterized by a numerical value and direction are called vector quantities. Thus, force is a vector quantity.

The numerical value of a vector quantity is called the modulus of this quantity. For example, the numerical value of the force is called the modulus of force.

Forces are indicated in the drawings by arrows (directed segments). The beginning of the arrow coincides with the point of application of the force, the direction of the arrow shows the direction of the force, and the length of the arrow is proportional to the modulus of the force. For example, in Fig. 14.2 depicts the force acting on the ball from the side of the leg.

Rice. 14.2. Force designation in the figure

Unit of strength. In SI, the force is taken as a unit of force, under the action of which a body at rest with a mass of 1 kg acquires a speed of 1 m / s in 1 s.

In honor of the English scientist Isaac Newton, this unit of force was named Newton (N).

Please note: the names of units of physical quantities named after scientists are written with a lowercase letter, and the designations of such units - with an uppercase.

Rice. 14.3. The apple presses on the palm with a force of approximately 1 N

Is the force 1 N great? To feel this power, place a small apple (weighing about 100 g) on ​​your palm (Fig. 14.3). Any of you can apply tens and even hundreds of Newtons. When you stand on the floor, you press on it with a force of several hundred Newtons.

If the body is accelerating, then something acts on it. How to find this "something"? For example, what are the forces acting on a body near the surface of the earth? This is the force of gravity directed vertically downward, proportional to the mass of the body and for heights much less than the radius of the earth $ (\ large R) $, almost independent of the height; it is equal

$ (\ large F = \ dfrac (G \ cdot m \ cdot M) (R ^ 2) = m \ cdot g) $

$ (\ large g = \ dfrac (G \ cdot M) (R ^ 2)) $

so called acceleration of gravity... In the horizontal direction, the body will move at a constant speed, but the movement in the vertical direction according to Newton's second law:

$ (\ large m \ cdot g = m \ cdot \ left (\ dfrac (d ^ 2 \ cdot x) (d \ cdot t ^ 2) \ right)) $

after reducing $ (\ large m) $, we get that the acceleration in the direction of $ (\ large x) $ is constant and equal to $ (\ large g) $. This is the well-known motion of a freely falling body, which is described by the equations

$ (\ large v_x = v_0 + g \ cdot t) $

$ (\ large x = x_0 + x_0 \ cdot t + \ dfrac (1) (2) \ cdot g \ cdot t ^ 2) $

How is strength measured?

In all textbooks and smart books, it is customary to express force in Newtons, but except in the models with which physicists operate, Newtons are not used anywhere. This is extremely inconvenient.

Newton newton (N) is a derived SI unit of force.
Based on Newton's second law, the newton unit is defined as a force that changes in one second the speed of a body weighing one kilogram by 1 meter per second in the direction of the force.

Thus, 1 N = 1 kg · m / s².

A kilogram-force (kgf or kg) is a gravitational metric unit of force equal to the force that acts on a body weighing one kilogram in the earth's gravitational field. Therefore, by definition, the kilogram-force is 9.80665 N. The kilogram-force is convenient in that its value is equal to the weight of a body weighing 1 kg.
1 kgf = 9.80665 Newtons (approximately ≈ 10 N)
1 N ≈ 0.10197162 kgf ≈ 0.1 kgf

1 N = 1 kg x 1m / s2.

Law of gravitation

Every object in the Universe is attracted to any other object with a force proportional to their masses and inversely proportional to the square of the distance between them.

$ (\ large F = G \ cdot \ dfrac (m \ cdot M) (R ^ 2)) $

It can be added that any body reacts to a force applied to it by acceleration in the direction of this force, which is inversely proportional to the body mass in magnitude.

$ (\ large G) $ - gravitational constant

$ (\ large M) $ - land mass

$ (\ large R) $ - earth radius

$ (\ large G = 6.67 \ cdot (10 ^ (- 11)) \ left (\ dfrac (m ^ 3) (kg \ cdot (sec) ^ 2) \ right)) $

$ (\ large M = 5.97 \ cdot (10 ^ (24)) \ left (kg \ right)) $

$ (\ large R = 6.37 \ cdot (10 ^ (6)) \ left (m \ right)) $

Within the framework of classical mechanics, gravitational interaction is described by Newton's law of universal gravitation, according to which the force of gravitational attraction between two bodies of mass $ (\ large m_1) $ and $ (\ large m_2) $, separated by the distance $ (\ large R) $ is

$ (\ large F = -G \ cdot \ dfrac (m_1 \ cdot m_2) (R ^ 2)) $

Here $ (\ large G) $ is a gravitational constant equal to $ (\ large 6.673 \ cdot (10 ^ (- 11)) m ^ 3 / \ left (kg \ cdot (sec) ^ 2 \ right)) $. The minus sign means that the force acting on the test body is always directed along the radius vector from the test body to the source of the gravitational field, i.e. gravitational interaction always leads to the attraction of bodies.
The gravity field is potential. This means that the potential energy of the gravitational attraction of a pair of bodies can be introduced, and this energy will not change after the bodies move along a closed loop. The potential of the gravity field entails the conservation law of the sum of kinetic and potential energy, which, when studying the motion of bodies in a gravity field, often greatly simplifies the solution.
Within the framework of Newtonian mechanics, gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential and force depend only on the position of the body at a given moment in time.

Harder - Lighter

The weight of the body $ (\ large P) $ is expressed by the product of its mass $ (\ large m) $ by the acceleration of gravity $ (\ large g) $.

$ (\ large P = m \ cdot g) $

When on the ground the body becomes lighter (weaker pressure on the scales), this comes from a decrease masses. Everything is not so on the moon, the decrease in weight is caused by a change in another factor - $ (\ large g) $, since the acceleration of gravity on the surface of the moon is six times less than on earth.

land mass = $ (\ large 5.9736 \ cdot (10 ^ (24)) \ kg) $

mass of the moon = $ (\ large 7,3477 \ cdot (10 ^ (22)) \ kg) $

acceleration of gravity on Earth = $ (\ large 9.81 \ m / c ^ 2) $

acceleration of gravity on the Moon = $ (\ large 1,62 \ m / c ^ 2) $

As a result, the product $ (\ large m \ cdot g) $, and hence the weight, is reduced by 6 times.

But it is impossible to designate both of these phenomena with the same expression "make it easier." On the moon, the bodies do not become lighter, but only they fall less rapidly "less falling"))).

Vector and scalar quantities

A vector quantity (for example, a force applied to a body), in addition to a value (modulus), is also characterized by a direction. A scalar quantity (for example, length) is characterized only by a value. All classical laws of mechanics are formulated for vector quantities.

Picture 1.

In fig. 1 shows various options for the location of the vector $ (\ large \ overrightarrow (F)) $ and its projection $ (\ large F_x) $ and $ (\ large F_y) $ on the axis $ (\ large X) $ and $ (\ large Y ) $ respectively:

• A. the quantities $ (\ large F_x) $ and $ (\ large F_y) $ are nonzero and positive
• B. the values ​​$ (\ large F_x) $ and $ (\ large F_y) $ are nonzero, while $ (\ large F_y) $ is a positive value, and $ (\ large F_x) $ is negative, because the vector $ (\ large \ overrightarrow (F)) $ is directed in the direction opposite to the direction of the axis $ (\ large X) $
• C.$ (\ large F_y) $ is a positive non-zero value, $ (\ large F_x) $ is equal to zero, because the vector $ (\ large \ overrightarrow (F)) $ is directed perpendicular to the $ (\ large X) $ axis

Moment of power

A moment of power is called the vector product of the radius vector drawn from the axis of rotation to the point of application of the force by the vector of this force. Those. according to the classical definition, the moment of force is a vector quantity. Within the framework of our problem, this definition can be simplified to the following: the moment of force $ (\ large \ overrightarrow (F)) $, applied to the point with the coordinate $ (\ large x_F) $, relative to the axis located at the point $ (\ large x_0 ) $ is a scalar value equal to the product of the modulus of force $ (\ large \ overrightarrow (F)) $ by the shoulder of force - $ (\ large \ left | x_F - x_0 \ right |) $. And the sign of this scalar quantity depends on the direction of the force: if it rotates the object clockwise, then the sign is plus, if against, then minus.

It is important to understand that we can choose the axis in an arbitrary way - if the body does not rotate, then the sum of the moments of forces relative to any axis is equal to zero. The second important note is that if a force is applied to the point through which the axis passes, then the moment of this force relative to this axis is zero (since the shoulder of the force will be equal to zero).

Let us illustrate the above with an example, in Fig. 2. Suppose that the system shown in Fig. 2 is in equilibrium. Consider the support on which the loads are standing. It is affected by 3 forces: $ (\ large \ overrightarrow (N_1), \ \ overrightarrow (N_2), \ \ overrightarrow (N),) $ points of application of these forces A, V and WITH respectively. The figure also contains the forces $ (\ large \ overrightarrow (N_ (1) ^ (gr)), \ \ overrightarrow (N_2 ^ (gr))) $. These forces are applied to the weights, and according to Newton's 3rd law

$ (\ large \ overrightarrow (N_ (1)) = - \ overrightarrow (N_ (1) ^ (gr))) $

$ (\ large \ overrightarrow (N_ (2)) = - \ overrightarrow (N_ (2) ^ (gr))) $

Now consider the condition of equality of the moments of forces acting on the support, relative to the axis passing through the point A(and, as we agreed earlier, perpendicular to the plane of the figure):

$ (\ large N \ cdot l_1 - N_2 \ cdot \ left (l_1 + l_2 \ right) = 0) $

Note that the equation does not include the moment of force $ (\ large \ overrightarrow (N_1)) $, since the shoulder of this force relative to the axis in question is $ (\ large 0) $. If, for some reason, we want to choose an axis passing through the point WITH, then the condition of equality of the moments of forces will look like this:

$ (\ large N_1 \ cdot l_1 - N_2 \ cdot l_2 = 0) $

It can be shown that from a mathematical point of view, the last two equations are equivalent.

The center of gravity

Center of gravity of a mechanical system is called a point relative to which the total moment of the forces of gravity acting on the system is zero.

Center of mass

The point of the center of mass is remarkable in that if a great many forces act on the particles that form the body (it does not matter whether it is solid or liquid, a cluster of stars or something else) (meaning only external forces, since all internal forces compensate each other), then the resulting the force leads to such an acceleration of this point, as if it contains the entire mass of the body $ (\ large m) $.

The position of the center of mass is determined by the equation:

$ (\ large R_ (c.m.) = \ frac (\ sum m_i \, r_i) (\ sum m_i)) $

This is a vector equation, i.e. actually three equations - one for each of the three directions. But consider only the $ (\ large x) $ direction. What does the following equality mean?

$ (\ large X_ (c.m.) = \ frac (\ sum m_i \, x_i) (\ sum m_i)) $

Suppose the body is divided into small pieces with the same mass $ (\ large m) $, and the total mass of the body will be equal to the number of such pieces $ (\ large N) $ multiplied by the mass of one piece, for example, 1 gram. Then this equation means that you need to take the coordinates $ (\ large x) $ of all the pieces, add them and divide the result by the number of pieces. In other words, if the masses of the pieces are equal, then $ (\ large X_ (c.m.)) $ Will be just the arithmetic mean of the $ (\ large x) $ coordinates of all pieces.

Mass and density

Mass is a fundamental physical quantity. Mass characterizes several properties of the body at once and itself has a number of important properties.

• Mass serves as a measure of the substance contained in the body.
• Mass is a measure of the body's inertia. Inertia is the property of a body to maintain its speed unchanged (in an inertial frame of reference) when external influences are absent or compensate each other. In the presence of external influences, the inertness of the body is manifested in the fact that its speed does not change instantly, but gradually, and the slower, the greater the inertness (i.e. mass) of the body. For example, if a billiard ball and a bus are moving at the same speed and braking with the same force, then it takes much less time to stop the ball than to stop the bus.
• The masses of bodies are the cause of their gravitational attraction to each other (see the section "The force of gravity").
• The mass of a body is equal to the sum of the masses of its parts. This is the so-called mass additivity. Additivity makes it possible to use a standard of 1 kg for mass measurement.
• The mass of an isolated system of bodies does not change with time (the law of conservation of mass).
• Body weight does not depend on the speed of its movement. Mass does not change when moving from one frame of reference to another.
• Density a homogeneous body is the ratio of body weight to its volume:

$ (\ large p = \ dfrac (m) (V)) $

Density does not depend on the geometric properties of the body (shape, volume) and is a characteristic of the body's substance. The densities of various substances are presented in the look-up tables. It is advisable to remember the density of water: 1000 kg / m3.

Newton's second and third laws

The interaction of bodies can be described using the concept of force. Force is a vector quantity that is a measure of the impact of one body on another.
As a vector, force is characterized by modulus (absolute value) and direction in space. In addition, the point of application of the force is important: the same in magnitude and direction, the force applied at different points of the body can have a different effect. So, if you grab the rim of a bicycle wheel and pull tangentially to the rim, the wheel will begin to rotate. If you drag along the radius, there will be no rotation.

Newton's second law

The product of the body mass by the acceleration vector is the resultant of all forces applied to the body:

$ (\ large m \ cdot \ overrightarrow (a) = \ overrightarrow (F)) $

Newton's second law connects the vectors of acceleration and force. This means that the following statements are true.

1. $ (\ large m \ cdot a = F) $, where $ (\ large a) $ is the acceleration modulus, $ (\ large F) $ is the modulus of the resultant force.
2. The acceleration vector has the same direction as the resultant force vector, since the body mass is positive.

Newton's third law

Two bodies act on each other with forces equal in magnitude and opposite in direction. These forces have the same physical nature and are directed along the straight line connecting their points of application.

Superposition principle

Experience shows that if several other bodies act on a given body, then the corresponding forces add up as vectors. More precisely, the principle of superposition is true.
The principle of superposition of forces. Let the forces act on the body$ (\ large \ overrightarrow (F_1), \ overrightarrow (F_2), \ \ ldots \ overrightarrow (F_n)) $ If you replace them with one force$ (\ large \ overrightarrow (F) = \ overrightarrow (F_1) + \ overrightarrow (F_2) \ ldots + \ overrightarrow (F_n)) $ , then the result of the impact will not change.
The force $ (\ large \ overrightarrow (F)) $ is called resultant forces $ (\ large \ overrightarrow (F_1), \ overrightarrow (F_2), \ \ ldots \ overrightarrow (F_n)) $ or the resulting by force.

Forwarder or carrier? Three secrets and international cargo transportation

Freight Forwarder or Carrier: Which one to Prefer? If the carrier is good and the forwarder is bad, then the first. If the carrier is bad and the forwarder is good, then the second. The choice is simple. But how to decide when both applicants are good? How to choose from two seemingly equivalent options? The point is that these options are not equivalent.

Scary stories of international traffic

BETWEEN HAMMER AND ANVILS.

It is not easy to live between the customer of the transportation and the very cunning and economical owner of the cargo. Once we received an order. Freight for three kopecks, additional conditions for two sheets, the collection is called .... Loading on Wednesday. The car is already in place on Tuesday, and by lunchtime the next day, the warehouse begins to slowly throw into the trailer everything that your forwarder has collected for his customers-recipients.

ENCHANTED PLACE - PTO KOZLOVICHI.

According to legends and experience, everyone who transported goods from Europe by road knows what a terrible place the PTO Kozlovichi, Brest customs, is. What chaos the Belarusian customs officers are doing, finding fault in every possible way and tearing at exorbitant prices. And it is true. But not all ...

HOW WE HAVE BEEN CARRYING IN DRY MILK FOR THE NEW YEAR.

Loading with groupage cargo at a consolidation warehouse in Germany. One of the cargoes is milk powder from Italy, the delivery of which was ordered by the Freight Forwarder .... A classic example of the work of a “transmitter” forwarder (he does not delve into anything, he only transmits along the chain).

Documents for international transport

International road transport of goods is very organized and bureaucratic, the consequence is that for the implementation of international road transport of goods, a bunch of unified documents are used. It does not matter whether it is a customs carrier or an ordinary one - he will not go without documents. Although not very exciting, we have tried to simplify the purpose of these documents and the meaning that they have. They gave an example of filling in TIR, CMR, T1, EX1, Invoice, Packing List ...

Calculation of axle load for road freight

The goal is to study the possibility of redistributing loads on the axles of the tractor and semitrailer when changing the location of the load in the semitrailer. And the application of this knowledge in practice.

In the system we are considering, there are 3 objects: a tractor $ (T) $, a semi-trailer $ (\ large ((p.p.))) $ And a load $ (\ large (gr)) $. All variables associated with each of these objects will be superscripted $ T $, $ (\ large (p.p.)) $ And $ (\ large (gr)) $ respectively. For example, the unladen weight of a tractor unit will be denoted as $ m ^ (T) $.

Why don't you eat fly agarics? Customs exhaled sadness.

What is happening in the international road transport market? The Federal Customs Service of the Russian Federation has banned the issuance of TIR Carnets without additional guarantees for several federal districts. And she notified that from December 1 of this year she would completely break the contract with the IRU as inappropriate to the requirements of the Customs Union and put forward non-childish financial claims.
The IRU replied: “The explanations of the Russian FCS regarding the allegedly owed debt of 20 billion rubles to ASMAP are sheer fiction, since all the old TIR claims were completely settled ..... What do we, ordinary carriers, think?

Stowage Factor Weight and volume of cargo when calculating the cost of transportation

The calculation of the cost of transportation depends on the weight and volume of the cargo. For sea transport, volume is most often decisive, for air - weight. For road transport of goods, a complex indicator plays a role. Which parameter for calculations will be selected in one case or another depends on specific weight of the cargo (Stowage factor) .

You need to know the point of application and direction of each force. It is important to be able to determine which forces are acting on the body and in which direction. Force is denoted as, measured in Newtons. In order to distinguish between forces, they are designated as follows

Below are the main forces at work in nature. It is impossible to invent non-existent forces when solving problems!

There are many forces in nature. Here are considered the forces that are considered in the school physics course in the study of dynamics. Other forces are also mentioned, which will be discussed in other sections.

Gravity

Every body on the planet is affected by the gravity of the Earth. The force with which the Earth attracts each body is determined by the formula

The point of application is at the center of gravity of the body. Gravity always points straight down.

Friction force

Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises from the fact that the surfaces, when viewed under a microscope, are not as smooth as they appear. The friction force is determined by the formula:

The force is applied at the point of contact between the two surfaces. Directed in the opposite direction to the movement.

Support reaction force

Imagine a very heavy object lying on a table. The table flexes under the weight of the object. But according to Newton's third law, a table acts on an object with exactly the same force as an object on a table. The force is opposite to the force with which the object pushes against the table. That is, up. This force is called the support reaction. The name of the force "speaks" support reacts... This force always arises when there is an impact on the support. The nature of its occurrence at the molecular level. The object, as it were, deformed the usual position and bonds of molecules (inside the table), they, in turn, tend to return to their original state, "resist".

Absolutely any body, even a very light one (for example, a pencil lying on the table), deforms the support at the micro level. Therefore, a support reaction occurs.

There is no special formula for finding this force. It is designated by a letter, but this force is just a separate type of elastic force, therefore it can be designated as

The force is applied at the point of contact of the object with the support. Directed perpendicular to the support.

Since the body is represented as a material point, the force can be depicted from the center

Elastic force

This force arises as a result of deformation (change in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.

Hooke's law

The elastic force is directed opposite to the deformation.

Since the body is represented as a material point, the force can be depicted from the center

When connecting springs in series, for example, the stiffness is calculated by the formula

Parallel connection stiffness

The rigidity of the sample. Young's modulus.

Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material, its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. Young's modulus is tabular.

Learn more about properties of solids.

Body weight

Body weight is the force with which an object acts on a support. You say, it's gravity! The confusion is as follows: indeed, often the weight of the body is equal to the force of gravity, but these forces are completely different. Gravity is a force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!

There is no formula for determining weight. This force is designated by a letter.

The reaction force of the support or the elastic force arises in response to the action of the object on the suspension or support, therefore the weight of the body is always numerically the same as the elastic force, but has the opposite direction.

The reaction force of the support and the weight are forces of the same nature, according to Newton's 3 law they are equal and oppositely directed. Weight is a force that acts on the support, not on the body. The force of gravity acts on the body.

Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state is called weightlessness... Weightlessness is a state when an object does not interact with a support, for example, a state of flight: there is gravity, and the weight is zero!

It is possible to determine the direction of acceleration if we determine where the resultant force is directed

Note, weight is force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not the weight, but our own mass! In this example, our weight is equal to gravity, which is approximately 500N!

Overload- the ratio of weight to gravity

Archimedes' strength

Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upward (pushes). Determined by the formula:

We neglect the power of Archimedes in the air.

If the force of Archimedes is equal to the force of gravity, the body floats. If the force of Archimedes is greater, then it rises to the surface of the liquid, if less, it sinks.

Electrical forces

There are forces of electrical origin. Occur when there is an electrical charge. These forces, such as the Coulomb force, the Ampere force, the Lorentz force, are discussed in detail in the Electricity section.

Schematic designation of forces acting on a body

The body is often modeled with a material point. Therefore, in the diagrams, various points of application are transferred to one point - to the center, and the body is depicted schematically as a circle or rectangle.

In order to correctly designate the forces, it is necessary to list all the bodies with which the investigated body interacts. Determine what happens as a result of interaction with each: friction, deformation, attraction, or perhaps repulsion. Determine the type of force, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.

The main thing to remember

1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces

Distinguish between external (dry) and internal (viscous) friction. External friction occurs between touching solid surfaces, internal - between layers of liquid or gas during their relative motion. There are three types of external friction: static friction, sliding friction, and rolling friction.

Rolling friction is determined by the formula

The resistance force arises when a body moves in a liquid or gas. The magnitude of the resistance force depends on the size and shape of the body, the speed of its movement and the properties of the liquid or gas. At low speeds of movement, the resistance force is proportional to the speed of the body

At high speeds, it is proportional to the square of the speed

Consider the mutual attraction of an object and the Earth. Between them, according to the law of gravity, there is a force

Now let's compare the law of gravity and the force of gravity

The magnitude of the acceleration due to gravity depends on the mass of the Earth and its radius! Thus, you can calculate with what acceleration objects will fall on the Moon or on any other planet, using the mass and radius of that planet.

The distance from the center of the Earth to the poles is less than to the equator. Therefore, the acceleration of gravity at the equator is slightly less than at the poles. At the same time, it should be noted that the main reason for the dependence of the acceleration of gravity on the latitude of the area is the fact of the Earth's rotation around its axis.

With distance from the surface of the Earth, the force of gravity and the acceleration of gravity change in inverse proportion to the square of the distance to the center of the Earth.

1. Newton's laws of dynamics

laws or axioms of motion (in the formulation of Newton himself from the book "Mathematical Principles of Natural Philosophy" in 1687): "I. Every body continues to be held in its state of rest or uniform and rectilinear motion, as long as and insofar as it is compelled by the applied forces to change this state. II. The change in the momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts. III. Action is always equal and opposite reaction, otherwise the interactions of two bodies against each other are equal and directed in opposite directions. "

2. What is strength?

Strength is characterized by magnitude and direction. Force characterizes the action of other bodies on a given body. The result of the action of the force on the body depends not only on its magnitude and direction, but also on the point of application of the force. The resultant force is one force, the result of which will be the same as the result of the action of all real forces. If the forces are co-directed, the resultant is equal to their sum and is directed in the same direction. If the forces are directed in opposite directions, then the resultant is equal to their difference and is directed towards the greater force.

Gravity and body weight

Gravity is the force with which a body is attracted to the Earth due to gravity. All bodies in the Universe are attracted to each other, and the greater their mass and the closer they are located, the stronger the attraction.

To calculate the force of gravity, the body weight should be multiplied by a factor denoted by the letter g, which is approximately equal to 9.8N / kg. Thus, the force of gravity is calculated by the formula

Body weight is the force with which the body presses against the support or stretches the suspension due to its attraction to the Earth. If the body has no support or suspension, then the body has no weight either - it is in a state of weightlessness.

Elastic force

The elastic force is the force that arises inside the body as a result of deformation and prevents the change in shape. Depending on how the shape of the body changes, several types of deformation are distinguished, in particular, tension and compression, bending, shear and shear, and torsion.

The more the shape of the body is changed, the greater the elastic force arising in it.

Dynamometer - a device for measuring force: the measured force is compared with the elastic force arising in the spring of the dynamometer.

Friction force

The resting friction force is the force that prevents the body from moving.

The reason for friction is that any surfaces have irregularities that mesh with each other. If the surfaces are polished, then the cause of friction is the forces of molecular interaction. When a body moves on a horizontal surface, the friction force is directed against the motion and is directly proportional to the force of gravity:

The sliding friction force is the resistance force when one body slides over the surface of another. The rolling friction force is the resistance force when one body rolls on the surface of another; it is significantly less than the sliding friction force.

If friction is beneficial, it is intensified; if it is harmful, they reduce it.

3. CONSERVATION LAWS

CONSERVATION LAWS, physical laws, according to which some property of a closed system remains unchanged for any changes in the system. The most important are laws of conservation of matter and energy. The Law of Conservation of Matter states that matter is neither created nor destroyed; during chemical transformations, the total mass remains unchanged. The total amount of energy in the system also remains unchanged; energy only transforms from one form to another. Both of these laws are only approximately true. Mass and energy can transform one into another according to the equation E = mc 2. Only the total amount of mass and its equivalent energy remains unchanged. Another conservation law concerns electric charge: it also cannot be created and cannot be destroyed. As applied to nuclear processes, the conservation law is expressed in the fact that the total charge, spin and other QUANTUM NUMBERS of interacting particles should remain the same for particles that have arisen as a result of interaction. With strong interactions, all quantum numbers are conserved. In weak interactions, some of the requirements of this law are violated, especially with regard to PARITY.

The law of conservation of energy can be explained by the example of the fall of a ball weighing 1 kg from a height of 100 m. The initial total energy of the ball is its potential energy. When it falls, the potential energy gradually decreases and the kinetic energy increases, but the total amount of energy remains unchanged. Thus, energy conservation takes place. A - kinetic energy increases from 0 to maximum: B - potential energy decreases from maximum to zero; C - the total amount of energy, which is equal to the sum of kinetic and potency. The law of conservation of matter states that in the course of chemical reactions matter is not created and does not disappear. This phenomenon can be demonstrated using the classic experiment in which a candle is weighed under a glass cover (A). At the end of the experiment, the weight of the bell and its contents remained the same as at the beginning, although the candle, the substance of which consists mainly of carbon and hydrogen, "disappeared" because volatile reaction products (water and carbon dioxide) were released from it. Only after the late 18th century scientists recognized the principle of conservation of matter, a quantitative approach to chemistry became possible.

Mechanical work occurs when the body moves under the action of a force applied to it.

Mechanical work is directly proportional to the distance traveled and proportional to the force:

Power

The speed of performing work in technology is characterized by power.

Power is equal to the ratio of work to the time during which it was completed:

Energy it is a physical quantity that shows what kind of work the body can do. Energy is measured in joules.

When doing work, the energy of the bodies is measured. Perfect work equals a change in energy.

Potential energy is determined by the mutual position of interacting bodies or parts of the same body.

E p = F h = gmh.

Where g = 9.8 N / kg, m - body weight (kg), h - height (m).

Kinetic energy the body possesses as a result of its movement. The greater the body mass and speed, the greater its kinetic energy.

5.the basic law of the dynamics of rotational motion

Moment of power

1. The moment of force relative to the axis of rotation, (1.1) where is the projection of the force on a plane perpendicular to the axis of rotation, is the shoulder of the force (the shortest distance from the axis of rotation to the line of action of the force).

2. Moment of force relative to a fixed point O (origin). (1.2) It is determined by the vector product of the radius vector drawn from the point O to the point of application of the force by this force; - pseudovector, its direction coincides with the direction of the translational motion of the right screw when it rotates ot ("thumb rule"). Modulus of the moment of force, (1.3) where is the angle between vectors, is the shoulder of the force, the shortest distance between the line of action of the force and the point of application of the force.

Moment of impulse

1. Moment of momentum of the body rotating about the axis, (1.4) where is the moment of inertia of the body, is the angular velocity. The moment of momentum of the system from bodies is the vector sum of the moments of momentum of all bodies of the system: . (1.5)

2. Moment of momentum of a material point with momentum relative to a fixed point O (origin). (1.6) It is determined by the vector product of the radius vector drawn from point O to the material point, by the impulse vector; - pseudovector, its direction coincides with the direction of translational motion of the right screw when it rotates otk ("thumb rule"). The magnitude of the angular momentum vector, (1.7) where is the angle between the vectors, is the shoulder of the vector relative to the point O.

Moment of inertia about the axis of rotation

1. The moment of inertia of a material point, (1.8) where is the mass of the point, is its distance from the axis of rotation.

2. Moment of inertia of a discrete rigid body, (1.9) where is an element of mass of a rigid body; is the distance of this element from the axis of rotation; is the number of elements of the body.

3. Moment of inertia in the case of continuous mass distribution (solid solid). (1.10) If the body is homogeneous, i.e. its density is the same over the entire volume, then expression (1.11) is used, where is the volume of the body.

1. Force - the action of one body on another, resulting in acceleration. Those. force is a measure of the interaction of forces, as a result of which bodies are deformed or accelerated. Force is a vector quantity; it is characterized by a numerical value, a direction of action and a point of application to the body.

2. Is it possible, based on the formula F = ma, to assert that the force applied to the body depends on the body's mass and its acceleration?

2. No, you can't.

3. Is it possible, based on the expression m = F / a, to assert that the mass of a body depends on the force applied to it and on its acceleration?

3. No, you can't.

4. Is it possible, based on the equality a = F / m, to assert that the acceleration of a body depends on the force applied to it and on the mass of the body?

4. Yes. For inertial frames only.

5. How is Newton's first law formulated if we use the concept of force?

5. There are such frames of reference, relative to which a translationally moving body keeps its speed constant if the resultant of all forces applied to the body is equal to zero.

6. What is the net force?

6. The force equal to the geometric sum of all forces applied to the body (point) is called the resultant or resultant force.