Types of fur energy. Let's remember physics: work, energy and power. Types of energy - types of energy known to mankind

In mechanics, there are two types of energy: kinetic and potential. Kinetic energy call the mechanical energy of any freely moving body and measure it by the work that the body could do when it slows down to a complete stop.
Let the body IN, moving at speed v, begins to interact with another body WITH and at the same time it slows down. Therefore the body IN affects the body WITH with some force F and on the elementary section of the path ds does work

According to Newton's third law, body B is simultaneously acted upon by a force -F, the tangent component of which -F τ causes a change in the numerical value of the body's speed. According to Newton's second law

Hence,

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

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:

(3.7)

From formula (3.7) it is clear that the kinetic energy of a body cannot be negative ( Ek ≥ 0).
If the system consists of n progressively 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:

(3.8)

From formula (3.8) it is clear that E k depends only on the magnitude of the masses and speeds of movement of the bodies included in it. In this case, it does not matter how the body mass m i gained speed ν i. In other words, the kinetic energy of a system is a function of its state of motion.
Speeds ν i depend significantly on the choice of reference system. When deriving formulas (3.7) and (3.8), it was assumed that the motion is considered in an inertial reference frame, since otherwise Newton's laws could not be used. However, in different inertial reference systems moving relative to each other, the speed ν i i th body of the system, and, consequently, its Eki and the kinetic energy of the entire system will not be the same. Thus, the kinetic energy of the system depends on the choice of the reference frame, i.e. is the quantity relative.
Potential energy- this is the mechanical energy of a system of bodies, determined by their relative position and the nature of the interaction forces between them.
Numerically, the potential energy of a system in its given position is equal to the work that will be done by the forces acting on the system when moving the system from this position to the one where the potential energy is conventionally assumed to be zero ( E n= 0). The concept of “potential energy” applies only to conservative systems, i.e. systems in which the work of the acting forces depends only on the initial and final positions of the system. So, for a load weighing P, raised to a height h, the potential energy will be equal En = Ph (E n= 0 at h= 0); for a load attached to a spring, E n = kΔl 2 / 2, Where Δl- elongation (compression) of the spring, k– its stiffness coefficient ( E n= 0 at l= 0); for two particles with masses m 1 And m 2, attracted by the law of universal gravitation, , Where γ – gravitational constant, r– distance between particles ( E n= 0 at r → ∞).
Let's consider the potential energy of the Earth system - a body of 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 gravitational forces performed during the free fall of a body to the Earth. If a body falls vertically, then

Where E no– 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 down an inclined plane of length l and with an angle of inclination α to the vertical ( lcosα = h), then the work done by the gravitational forces is equal to the previous value:

If, finally, the body moves along an arbitrary curvilinear trajectory, then we can imagine this curve consisting of n small straight sections Δl i. The work done by the gravitational force on each of these sections is equal to

Along the entire curvilinear path, the work done by the gravitational forces is obviously equal to:

So, the work of gravitational forces 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 infinitesimal change in the configuration of the system, the work of conservative forces is equal to the increase in potential energy taken with a minus sign, since the work is done due to the decrease in potential energy:

In turn, work dA expressed as the dot product of force F to move dr, so the last expression can be written as follows:

(3.9)

Therefore, if the function is known E n(r), then from expression (3.9) one can find the force F by module and direction.
For conservative forces

Or in vector form

Where

(3.10)

The vector defined by expression (3.10) is called gradient of the scalar function P; i, j, k- unit vectors of coordinate axes (orts).
Specific type of function P(in our case E n) depends on the nature of the force field (gravitational, electrostatic, etc.), as was shown above.
Total mechanical energy W system is equal to the sum of its kinetic and potential energies:

From the definition of the potential energy of a system and the examples considered, it is clear 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. Consequently, 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.

Exists two types of mechanical energy - kinetic energy of a point body and potential energy of a system of bodies. The mechanical energy of a system of bodies is equal to the sum of the kinetic energies of the bodies included in this system and the potential energies of their interaction:

Mechanical energy = Kinetic energy + Potential energy

It is important law of conservation of mechanical energy:
In an inertial reference frame, the mechanical energy of the system remains constant (does not change, is conserved) provided that the work of internal friction forces and the work of external forces on the bodies of the system is zero (or so small that they can be neglected).

Kinetic energy

As one of the types of mechanical energy, the kinetic energy of a point body is equal to the work that the body can do on other bodies by reducing its speed to zero. In this case we are talking about inertial reference systems (IRS).

The kinetic energy of a point body is calculated using the formula K = (mv 2) / 2.

The kinetic energy of a body increases when positive work is done on it. Moreover, it increases by the amount of this work. When negative work is performed on a body, its kinetic energy decreases by an amount equal to the modulus of this work. Conservation of kinetic energy (the absence of its changes) says that the work done on the body was equal to zero.

Potential energy

Potential energy is a type of mechanical energy that can only be possessed by systems of bodies or bodies considered as systems of parts, but not by a single point body. Potential energy of different systems is calculated differently.

The system of bodies often considered is the “body – Earth”, when a body is located near the surface of a planet (in this case the Earth) and is attracted to it under the influence of gravity. In this case, the potential energy is equal to the work done by gravity when the body is lowered to zero height (h = 0):

The potential energy of the body-Earth system decreases when positive work is performed by gravity. At the same time, the height (h) of the body above the Earth decreases. As the altitude increases, gravity does negative work, and the potential energy of the system increases. If the height does not change, then the potential energy is conserved.

Another example of a system with potential energy is a spring elastically deformed by another body. A spring has potential energy, since it is a system of interacting parts (particles) that strive to return the spring to its original state, i.e. the spring has an elastic force.

Elastic forces perform work when the body transitions to an undeformed state, in which the potential energy becomes equal to zero. (All systems tend to decrease their potential energy.)

The potential energy of the “spring” system is determined by the formula P = 0.5k · Δl 2, where k is the stiffness of the spring, Δl is the change in the length of the spring (as a result of compression or stretching).

A spring in an undeformed state has zero potential energy. In order for potential energy to appear in the system, external forces must do positive work against elastic forces, i.e., against internal potential forces.

Mechanical energy comes in two types: kinetic And potential. Kinetic energy (or energy of motion) is determined by the masses and velocities of the bodies in question. Potential energy (or position energy) depends on the relative position (configuration) of bodies interacting with each other.

Work is defined as the scalar product of the force and displacement vectors. The scalar product of two vectors is a scalar equal to the product of the moduli of these vectors and the cosine of the angle between them.

The concepts of energy and work are closely related to each other.

Particle kinetic energy

Taking into account that the product mV is equal to the particle momentum modulus p, expression (4) can be given the form

If the force F acting on the particle is not zero, the kinetic energy will receive an increment over time dt

where d s- movement of a particle during time dt.

Magnitude

called work, made by force F on the path ds (ds is the displacement module d s).

From (5) it follows that work characterizes the change in kinetic energy caused by the action of a force on a moving particle

If dA = Fds, a, then

Let's integrate both sides of equality (6) along the particle trajectory from point 1 to point 2:

The left side of the resulting equality represents the increment in the kinetic energy of the particle:

The right side is work A12 of force F on path 1-2:

Thus, we have arrived at the relation

from which it follows that the resultant work of all forces acting on the particle goes to increase the kinetic energy of the particle.

Conservative forces

Forces whose work does not depend on the path along which the particle moved, but depends only on the initial and final positions of the particle, are called conservative.

It is easy to show that the work done by forces on any closed path is zero. Let us divide an arbitrary closed path (Fig. 1) with points 1 and 2 (also taken arbitrarily) into two sections, designated by Roman numerals I and II. Work on a closed path consists of work performed in these sections:

Changing the direction of movement along section II to the opposite is accompanied by the replacement of all elementary displacements ds by -ds, as a result of which the sign is reversed. From this we conclude that. Making a replacement in (8), we obtain that

Due to the path independence of the work, the last expression is zero. Thus, conservative forces can be defined as forces whose work on any closed path is zero.

Potential energy

This energy is determined by the position of the body (the height to which it is raised). Therefore it is called position energy. More often it is called potential energy.

where h is measured from an arbitrary level.

Unlike kinetic energy, which is always positive, potential energy can be either positive or negative.

Let the particle move in a field of conservative forces. When moving from point 1 to point 2, work is done on it

A12 = Ep1-Ep2. (9)

In accordance with formula (7), this work is equal to the increment in the kinetic energy of the particle. Taking both expressions for work, we obtain a relation from which it follows that

The value E, equal to the sum of the kinetic and potential energies, is called the total mechanical energy of the particle. Formula (10) means that E1=E2, i.e. which is the total energy of a particle moving in a field of conservative forces. Remains constant. This statement expresses law of conservation of mechanical energy for a system consisting of one particle.

LAW OF ENERGY CONSERVATION

Let us consider a system consisting of N particles interacting with each other, under the influence of external both conservative and non-conservative forces. The interaction forces between particles are assumed to be conservative. Let us determine the work done on particles when moving a system from one place to another, accompanied by a change in the configuration of the system.

The work of external conservative forces can be represented as a decrease in the potential energy of the system in an external force field:

where is determined by formula (9).

The work done by the internal forces is equal to the decrease in the mutual potential energy of the particles:

where is the potential energy of the system in an external force field.

Let us denote the work of non-conservative forces.

According to formula (7), the total work of all forces is spent on increasing the kinetic energy of the system Ek, which is equal to the sum of the kinetic energies of the particles:

Hence,

Let us group the terms of this relationship as follows:

The sum of the kinetic and potential energies represents the total mechanical energy of the system E:

Thus, we have established that the work of non-conservative forces is equal to the increment in the total energy of the system:

From (11) it follows that in the case when there are no non-conservative forces, the total mechanical energy of the system remains constant:

We have come to law of conservation of mechanical energy, which states that the total mechanical energy of a system of material points under the influence of only conservative forces remains constant.

If the system is closed and the interaction forces between particles are conservative, then the total energy contains only two terms: (- mutual potential energy of particles). In this case, the law of conservation of mechanical energy is the statement that the total mechanical energy of a closed system of material points, between which only conservative forces act, remains constant.

Take a look: a ball rolling along the track knocks down the pins, and they scatter to the sides. The fan that was just 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, and the farther they will fly. For example, the higher the rotation speed of the blades, the further the fan will move the air flow.

The kinetic energy of the same body can be different from the points of view of different observers. For example, from our point of view as readers of this book, the kinetic energy of a stump on the road is zero, since the stump is not moving. However, in relation to the cyclist, the stump has kinetic energy, since it is rapidly approaching, and in the event of a collision it will perform 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 the Latin “potency” - strength).

Let's look at the drawing. When ascending, the ball can perform mechanical work, for example, pushing our palm out of the water to the surface. A weight placed at a certain height can do work - crack a nut. A bow string that is pulled tight can push the arrow out. Hence, the considered bodies have potential energy because 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 - gravity pulls the weight down. The string interacts with other parts of the bow - it is pulled by the elastic force of the curved bow shaft.

The potential energy of a body depends on the force of interaction between bodies (or parts of the body) and the distance between them. For example, the greater the Archimedean force and the deeper the ball is immersed in the 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 string is pulled, the greater the potential energies of the bodies: the ball, the weight, the bow (respectively).

The potential energy of the same body can be different in relation to different bodies. Take a look at the picture. When a weight falls on each nut, you will find 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 widely uses this concept both practically and theoretically.

Work and Energy

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

The figure shows a body that can be in different mechanical states (I and II). The process of transition of a body 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. When performing 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 options for their interaction.

What is mechanical energy equal to?

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

A = ∆E

Since energy is a characteristic of the state of a 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 measurement: [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 moving bodies. When they stop, they perform mechanical work.

In different reference systems, the velocities of the same body at an arbitrary moment in time can be different. Therefore, kinetic energy is a relative quantity; it is determined by the choice of the reference system.

If a force (or several forces at the same time) acts on a 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 forces that are applied to the body will be equal to the difference in kinetic energies:

A = E k1 - E k 2 = ∆E k

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

Potential energy name the energy caused by the interaction between bodies.

When a body weighs m from high h the force of gravity does the work. Since work and energy change are related by an equation, we can write a formula for the potential energy of a body in a gravitational field:

Ep = mgh

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

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

E p = 1/2 kx 2

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

E = E p + E k

Total mechanical energy bodies call the sum of energies: kinetic and potential.

Law of conservation of mechanical energy

Some of the most accurate experiments carried out in the mid-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 during any interactions of the bodies with each other.

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

E = E p + E k = const

When the friction force between bodies acts, then a decrease in mechanical energy occurs, however, even in this case it is not lost without a trace, but turns into thermal (internal). If an external force performs work on a closed system, then the mechanical energy increases 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 completely transformed into any other type of energy.