Forms of mechanical energy. Work and mechanical energy

In mechanics, two types of energy are distinguished: kinetic and potential. Kinetic energy they call the mechanical energy of any freely moving body and measure it by the work that the body could perform during its deceleration to a complete stop.

Let the body V moving with speed begins to interact with another body WITH and at the same time it is inhibited. Hence the body V acts on the body WITH with some force and on an elementary section of the path ds performs work

According to Newton's third law of the body V at the same time, a force acts, the tangential component of which causes a change in the numerical value of the body's velocity. According to Newton's second law

Hence,

The work done by the body until it comes to a complete stop is equal to:

So, the kinetic energy of a translationally moving body is equal to half the product of the mass of this body by the square of its speed:

From the formula (3.7) it can be seen that the kinetic energy of the body should not be negative ().

If the system consists of n moving bodies, then to stop it, it is extremely important to slow down each of these bodies. For this reason, the total kinetic energy of a mechanical system is equal to the sum of the kinetic energies of all bodies included in it:

It is seen from formula (3.8) that E k depends only on the magnitude of the masses and the speeds of motion of the bodies included in it. In this case, it does not matter how a body with a mass m i gained speed. In other words, kinetic energy of the system is a function of the state of its motion.

The speeds essentially depend on the choice of the frame of reference. When deriving formulas (3.7) and (3.8), it was assumed that the motion is considered in the inertial frame of reference since otherwise it would be impossible to use Newton's laws. In this case, in different inertial reference frames moving relative to each other, the speed i-th body of the system, and, consequently, its kinetic energy and the entire system will not be the same. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, kinetic energy of the system depends on the choice of the reference system ᴛ.ᴇ. is the value relative.

Potential energy - ϶ᴛᴏ mechanical energy systems of bodies, determined by their mutual arrangement and the nature of the forces of interaction between them.

Numerically, the potential energy of the system in its given position is equal to the work that will be performed by the forces acting on the system when the system moves from this position to where the potential energy is conventionally assumed to be zero ( E n= 0). The concept of "potential energy" takes place only for conservative systems, ᴛ.ᴇ. systems in which the work of the acting forces depends only on the initial and final position of the system. So, for a load weighing P raised to a height h, potential energy will be equal to ( E n= 0 for h= 0); for a load attached to a spring, where is the elongation (compression) of the spring, k- its stiffness coefficient ( E n= 0 for l= 0); for two particles with masses m 1 and m 2, which are attracted by the law of all-world gravitation, where γ - gravitational constant, r Is the distance between particles ( E n= 0 for).

Consider the potential energy of the Earth - body with mass m raised to a height h above the surface of the Earth. Decrease potential energy such a system is measured by the work of the forces of gravity, performed during the free fall of the body on the Earth. If the body falls vertically, then

where E no is the potential energy of the system at h= 0 (the ʼʼ-ʼʼ sign shows that the work is done due to the loss of potential energy).

If the same body falls along an inclined plane with a length l and with an angle of inclination to the vertical (, then the work of the forces of gravity is equal to the previous value - e:

If, finally, the body moves along an arbitrary curvilinear trajectory, then one can imagine this curve consisting of n small straight sections. The work of the gravitational force on each of these sections is

On the entire curved path, the work of the gravitational forces is obviously equal to:

So, the work of the forces of gravity depends only on the difference in heights of the starting and ending points of the path.

Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, a body in a potential (conservative) field of forces has potential energy. With an infinitely small change in the configuration of the system, the work of conservative forces is equal to the increment of potential energy, taken with a minus sign, since the work is performed due to the decrease in potential energy:

In turn work dA is expressed as the scalar product of force and displacement; therefore, the last expression can be written as follows: W of the system is equal to the sum of its kinetic and potential energies:

From the definition of the potential energy of the system and the examples considered, it can be seen that this energy, like kinetic energy, is a function of the state of the system: it depends only on the configuration of the system and its position in relation to external bodies. Therefore, the total mechanical energy of the system is also a function of the state of the system, ᴛ.ᴇ. depends only on the position and velocities of all bodies in the system.

If the body can perform mechanical work, then it has mechanical energy E(J). Or, if an external force does work, acting on the body, its energy changes.

There are two types of mechanical energy: kinetic and potential.

Kinetic energy - energy of moving bodies:

where v(m / s) - speed modulus, m - body mass.

Potential energy- energy of interacting bodies.

Examples of potential energy in mechanics.

The body is lifted off the ground: E = mgh

where h is the height determined from the zero level (or from the lower point of the trajectory). The shape of the path is not important, only the start and end height matters.

Elastically deformed body. Deformation determined from the position of an undeformed body (spring, cord, etc.).

Potential energy of elastic bodies: , where k is the stiffness of the spring; x is its deformation.

Energy can be transferred from one body to another, as well as transform from one type to another.

- Full mechanical energy.

Law of energy conservation: v closed system of bodies complete energy does not change for any interactions within this system of bodies.

E k1 + E p1 = E k2 + E p2.

The sum of the kinetic and potential energy of bodies that make up a closed system and interact with each other by means of gravitational forces and elastic forces remains unchanged.

2. Transformer. Operating principle. Device. Transformation ratio. Electricity transmission.
AC conversion, in which the voltage increases or decreases several times with practically no power loss is carried out using transformers.

Transformer- a device used to increase or decrease an alternating current voltage.

The first transformers were used in 1878. Russian scientist PN Yablochkov to power the "electric candles" invented by him - a new source of light at that time.

The simplest transformer consists of two coils. Coiled on a common steel core. One coil connects to source alternating voltage. This coil is called primary winding), and from another coil (called secondary winding) remove the alternating voltage for its further transmission.

The alternating current in the primary winding creates an alternating magnetic field. Thanks to the steel core, the secondary winding, wound on the same core, penetrates almost the same variable field as the primary one.

Since all loops riddled with the same variable magnetic flux, due to the phenomenon of electromagnetic induction in every loop generated the same voltage... Therefore, the ratio of voltages 𝑈 1 and 𝑈 2 of the primary and secondary windings is equal to the ratio of the number of turns in them:

The change in voltage by a transformer characterizes the transformation ratio

Transformation ratio - a value equal to the ratio of voltages in the primary and secondary windings of the transformer:

Raising transformer - a transformer that increases the voltage (In a step-up transformer, the number of turns in the secondary winding must be greater than the number of turns in the primary winding, i.e. to<1.

Downward transformer - a transformer that reduces the voltage (In a step-down transformer, the number of turns in the secondary winding must be less than the number of turns in the primary winding, i.e. k> 1.

Broadcast electrical energy from power plants to large cities or industrial centers at distances of thousands of kilometers is a complex scientific and technical problem. To reduce the heating losses of the wires, it is necessary to reduce the current in the transmission line, and, therefore, to increase the voltage. Typically, power lines are built for a voltage of 400-500 kV, while the lines use a three-phase current with a frequency of 50 Hz.

Ticket number 12

Pascal's law. Archimedes' law. Swimming conditions tel.

Formulation of Pascal's Law

The pressure applied to the liquid or gas is transmitted to any point the same in all directions. This statement is explained by the mobility of particles of liquids and gases in all directions.

Various hydraulic devices operate on the basis of Pascal's law of hydrostatics: brake systems, presses, etc.

Archimedes' law- this is the law of statics of liquids and gases, according to which a buoyant force (Archimedes' force) acts on a body immersed in a liquid (or gas), equal to the weight of the liquid (or gas) displaced by this body.

F A = ρgV,
where ρ - density of liquid (gas),
g - acceleration of gravity,
V - the volume of a submerged body (or the volume of that part of the body that is immersed in a liquid (or gas)).

Archimedean force is directed always opposite to gravity... It is equal to zero if the body immersed in the liquid is dense, with the whole base pressed to the bottom.
It should be remembered that in a state of zero gravity, Archimedes' law does not work.

Look: a ball rolling down the path knocks down the pins, and they fly to the sides. The fan that has just been turned off continues to rotate for some time, creating an air flow. Do these bodies have energy?

Note: the ball and the fan perform mechanical work, which means they have energy. They have energy because they move. The energy of moving bodies in physics is called kinetic energy (from the Greek "kinema" - movement).

Kinetic energy depends on the mass of the body and the speed of its movement (movement in space or rotation). For example, the greater the mass of the ball, the more energy it will transfer to the pins upon impact, the further they will fly away. For example, the higher the rotation speed of the blades, the further the fan will move the air flow.

The kinetic energy of one and the same body can be different from the points of view of different observers. For example, from our point of view as the readers of this book, the kinetic energy of a tree stump on the road is zero, since the tree stump does not move. However, in relation to the cyclist, the stump has kinetic energy, since it is rapidly approaching, and in a collision it will perform a very unpleasant mechanical work - it will bend the parts of the bicycle.

The energy that bodies or parts of one body possess because they interact with other bodies (or parts of the body) is called in physics potential energy (from Latin "potential" - strength).

Let's refer to the figure. When surfacing, the ball can perform mechanical work, for example, push our palm out of the water to the surface. A weight placed at a certain height can do the job - crack a nut. The stretched bowstring of the bow can push the arrow out. Hence, the considered bodies have potential energy, since they interact with other bodies (or parts of the body). For example, a ball interacts with water - the Archimedean force pushes it to the surface. The weight interacts with the Earth - the force of gravity pulls the weight down. The bowstring interacts with other parts of the bow - it is pulled by the elastic force of the curved shaft of the bow.

The potential energy of a body depends on the force of interaction between bodies (or body parts) and the distance between them. For example, the greater the Archimedean force and the deeper the ball is immersed in water, the greater the force of gravity and the farther the weight is from the Earth, the greater the elastic force and the further the bowstring is pulled, the greater the potential energies of the bodies: the ball, the kettlebell, the bow (respectively).

The potential energy of one and the same body can be different in relation to different bodies. Take a look at the picture. When a weight falls on each of the nuts, it will be found that the fragments of the second nut will fly much further than the fragments of the first. Therefore, in relation to nut 1, the weight has less potential energy than in relation to nut 2. Important: unlike kinetic energy, potential energy does not depend on the position and movement of the observer, but depends on our choice of the "zero level" of energy.

The purpose of this article is to reveal the essence of the concept of "mechanical energy". Physics makes extensive use of this concept both practically and theoretically.

Work and energy

Mechanical work can be determined if the force acting on the body and the movement of the body are known. There is another way to calculate mechanical work. Let's consider an example:

The figure shows a body that can be in various mechanical states (I and II). The process of the body's transition from state I to state II is characterized by mechanical work, that is, during the transition from state I to state II, the body can perform work. During the implementation of work, the mechanical state of the body changes, and the mechanical state can be characterized by one physical quantity - energy.

Energy is a scalar physical quantity of all forms of motion of matter and variants of their interaction.

What is mechanical energy

Mechanical energy is a scalar physical quantity that determines the body's ability to do work.

A = ∆E

Since energy is a characteristic of the state of the system at a certain point in time, work is a characteristic of the process of changing the state of the system.

Energy and work have the same units of measure: [A] = [E] = 1 J.

Types of mechanical energy

Mechanical free energy is divided into two types: kinetic and potential.

Kinetic energy is the mechanical energy of a body, which is determined by the speed of its movement.

E k = 1 / 2mv 2

Kinetic energy is inherent in mobile bodies. When they stop, they perform mechanical work.

In different frames of reference, the velocities of the same body at an arbitrary moment of time can be different. Therefore, kinetic energy is a relative value, it is determined by the choice of the frame of reference.

If a force (or several forces simultaneously) acts on the body during movement, the kinetic energy of the body changes: the body accelerates or stops. In this case, the work of the force or the work of the resultant of all the forces that are applied to the body will be equal to the difference in kinetic energies:

A = E k1 - E k 2 = ∆Е k

This statement and formula was given a name - kinetic energy theorem.

Potential energy name the energy due to the interaction between bodies.

When falling body weight m from high h gravity does the job. Since work and energy change are related by an equation, you can write a formula for the potential energy of a body in a gravity field:

E p = mgh

Unlike kinetic energy E k potential E p can be negative when h<0 (for example, a body lying at the bottom of a well).

Another type of mechanical potential energy is deformation energy. Compressed to a distance x spring with stiffness k has potential energy (deformation energy):

E p = 1/2 kx 2

The energy of deformation has found wide application in practice (toys), in technology - automatic machines, relays and others.

E = E p + E k

Full mechanical energy bodies are called the sum of energies: kinetic and potential.

Mechanical energy conservation law

Some of the most accurate experiments carried out in the middle of the 19th century by the English physicist Joule and the German physicist Mayer showed that the amount of energy in closed systems remains unchanged. It only passes from one body to another. These studies helped discover law of energy conservation:

The total mechanical energy of an isolated system of bodies remains constant for any interactions of bodies with each other.

Unlike an impulse, which does not have an equivalent form, energy has many forms: mechanical, thermal, molecular motion energy, electrical energy with the forces of interaction of charges, and others. One form of energy can transform into another, for example, kinetic energy transforms into thermal energy during braking of a car. If there are no friction forces, and heat is not generated, then the total mechanical energy is not lost, but remains constant in the process of motion or interaction of bodies:

E = E p + E k = const

When the force of friction between the bodies acts, then there is a decrease in mechanical energy, however, in this case, too, it is not lost without a trace, but passes into heat (internal). If an external force performs work on a closed system, then there is an increase in mechanical energy by the amount of work performed by this force. If a closed system performs work on external bodies, then the mechanical energy of the system is reduced by the amount of work performed by it.
Each type of energy can be converted completely into any other type of energy.

Hence,

The work done by the body until it comes to a complete stop is equal to:

So, the kinetic energy of a translationally moving body is equal to half the product of the mass of this body by the square of its velocity:

It is seen from formula (3.7) that the kinetic energy of a body cannot be negative ().

If the system consists of n translationally moving bodies, then to stop it, it is necessary to brake each of these bodies. Therefore, the total kinetic energy of a mechanical system is equal to the sum of the kinetic energies of all bodies included in it:

It is seen from formula (3.8) that E k depends only on the magnitude of the masses and the speeds of motion of the bodies included in it. In this case, it does not matter how a body with a mass m i gained speed. In other words, the kinetic energy of the system is a function of the state of its motion.

The speeds essentially depend on the choice of the frame of reference. When deriving formulas (3.7) and (3.8), it was assumed that the motion is considered in the inertial frame of reference, since otherwise it would be impossible to use Newton's laws. However, in different inertial reference frames moving relative to each other, the speed i-th body of the system, and, consequently, its and the kinetic energy of the entire system will be unequal. Thus, the kinetic energy of the system depends on the choice of the frame of reference, i.e. is the value relative.

Potential energy- this is the mechanical energy of a system of bodies, determined by their mutual arrangement and the nature of the forces of interaction between them.

Numerically, the potential energy of the system in its given position is equal to the work that will be performed by the forces acting on the system when the system moves from this position to where the potential energy is conventionally assumed to be zero ( E n= 0). The concept of "potential energy" takes place only for conservative systems, i.e. systems in which the work of the acting forces depends only on the initial and final position of the system. So, for a load weighing P raised to a height h, potential energy will be equal to ( E n= 0 for h= 0); for a load attached to a spring, where is the elongation (compression) of the spring, k- its stiffness coefficient ( E n= 0 for l= 0); for two particles with masses m 1 and m 2 attracted by the law of universal gravitation, where γ - gravitational constant, r Is the distance between particles ( E n= 0 for).

Consider the potential energy of the Earth - body with mass m raised to a height h above the surface of the Earth. The decrease in the potential energy of such a system is measured by the work of the forces of gravity, performed during the free fall of the body on the Earth. If the body falls vertically, then

where E no is the potential energy of the system at h= 0 (the sign "-" indicates that the work is done due to the loss of potential energy).

If the same body falls along an inclined plane with a length l and with an angle of inclination to the vertical (, then the work of the gravitational forces is equal to the previous value:

On the entire curvilinear path, the work of the gravitational forces is obviously equal to:

So, the work of the forces of gravity depends only on the difference in heights of the starting and ending points of the path.

Thus, a body in a potential (conservative) field of forces has potential energy. With an infinitely small change in the configuration of the system, the work of conservative forces is equal to the increment of potential energy, taken with a minus sign, since the work is performed due to the decrease in potential energy:

In turn work dA is expressed as the dot product of force and displacement, so the last expression can be written as follows: Total mechanical energy W of the system is equal to the sum of its kinetic and potential energies:

From the definition of the potential energy of the system and the examples considered, it can be seen that this energy, like kinetic energy, is a function of the state of the system: it depends only on the configuration of the system and its position in relation to external bodies. Therefore, the total mechanical energy of the system is also a function of the state of the system, i.e. depends only on the position and velocities of all bodies in the system.