What is the mechanical energy of the vapor, potential or kinetic. Potential and kinetic energy. Mechanical energy conservation law

In the previous paragraph, it was found that when bodies interacting with each other by elastic force or gravity do work, then the relative position of the bodies or their parts changes. And when the work is done by a moving body, then its speed changes. But when the work is done, the energy of the bodies changes. Hence, we can conclude that the energy of bodies interacting by the force of elasticity or by the force of gravity depends on the relative position of these bodies or their parts. The energy of a moving body depends on its speed.

The energy of bodies, which they possess as a result of interaction with each other, is called potential energy. The energy of bodies, which they possess due to their movement, is called kinetic energy.

Consequently, the energy possessed by the Earth and the body located near it is the potential energy of the Earth-body system. For brevity, it is customary to say that this energy is possessed by the body itself, which is near the surface of the Earth.

The energy of a deformed spring is also potential energy. It is determined by the mutual arrangement of the coils of the spring.

Kinetic energy is the energy of motion. Kinetic energy can be possessed by a body that does not interact with other bodies.

Bodies can have both potential and kinetic energy at the same time. For example, an artificial satellite of the Earth has kinetic energy because it moves and potential energy because it interacts with the Earth by the force of gravity. The falling weight also has both kinetic and potential energy.

Now let's see how you can calculate the energy that a body has in a given state, and not just its change. For this purpose, it is necessary to select one specific state from various states of the body or system of bodies, with which all the others will be compared.

Let's call this state the "zero state". Then the energy of bodies in any state will be equal to the work that is done

upon transition from this state to the bullet state. (It is obvious that in the zero state the energy of the body is equal to a bullet.) Recall that the work done by the force of gravity and the force of elasticity does not depend on the trajectory of the body. It only depends on its starting and ending positions. In the same way, the work done when the speed of the body changes depends only on the initial and final speed of the body.

It makes no difference what state of bodies to choose as zero. But in some cases, the choice of the zero state suggests itself. For example, when it comes to the potential energy of an elastically deformed spring, it is natural to assume that an undeformed spring is in a zero state. The energy of an undeformed spring is zero. Then the potential energy of the deformed spring will be equal to the work that this spring would have done, passing into an undeformed state. When we are interested in the kinetic energy of a moving body, it is natural to take for zero the state of the body in which its velocity is equal to zero. We will get the kinetic energy of a moving body if we calculate the work that it would have done while moving to a complete stop.

It is a different matter when it comes to the potential energy of a body raised to a certain height above the Earth. This energy depends, of course, on the height of the body. But there is no "natural" choice of the zero state, that is, the position of the body from which its height should be measured. You can choose for zero the state of the body when it is on the floor of the room, at sea level, at the bottom of the mine, etc. It is only necessary when determining the energy of a body at different heights to count these heights from the same level, the height of which is assumed to be zero. Then the value of the body's potential energy at a given height will be equal to the work that would have been done when the body passed from this height to the zero level.

It turns out that depending on the choice of the zero state, the energy of the same body has different values! This is no problem. Indeed, to calculate the work done by the body, we need to know the change in energy, that is, the difference between the two values \u200b\u200bof energy. And this difference does not depend in any way on the choice of the zero level. For example, in order to determine how much the top of one mountain is higher than another, it makes no difference where the height of each peak is measured from. It is only important that it is measured from the same level (for example, from sea level).

The change in both kinetic and potential energy of bodies is always equal in absolute value to the work done by the forces acting on these bodies. But there is an important difference between both types of energy. The change in the kinetic energy of a body under the action of a force on it is really equal to the work done by this force, that is, it coincides with it both in absolute value and in sign. This follows directly from the theorem on

kinetic energy (see § 76). The change in the potential energy of bodies is equal to the work done by the forces of interaction, only in absolute value, and in sign it is opposite to it. Indeed, when the body, on which the force of gravity acts, moves downward, positive work is done, and the potential energy of the body decreases. The same applies to a deformed spring: when the stretched spring contracts, the elastic force does positive work, and the potential energy of the spring decreases. Recall that a change in a quantity is the difference between the subsequent and previous value of this quantity. Therefore, when a change in any quantity consists in the fact that it increases, this change has a positive sign. Conversely, if the value decreases, its change is negative.

Exercise # 54

1. In what cases does the body have potential energy?

2. In what cases does the body have kinetic energy?

3. What energy does a freely falling body have?

4. How does the potential energy of a body, which is acted upon by the force of gravity, change during its downward movement?

5. How will the potential energy of a body, which is acted upon by the elastic force or the force of gravity, change if, following any trajectory, the body returns to its starting point?

6. How is the work done by the spring connected with a change in its potential energy?

7. How does the potential energy of a spring change when an undeformed spring is stretched? Are they squeezing?

8. The ball is suspended from the spring and vibrates. How does the potential energy of a spring change as it moves up and down?

The muscles that set the body links in motion do mechanical work.

Job in some direction - this is the product of the force (F) acting in the direction of movement of the body by the path traveled by it (S): A \u003d F S.

Doing work takes energy. Consequently, as work is done, the energy in the system decreases. Since in order for the work to be completed, a supply of energy is needed, the latter can be determined as follows: Energy – it is an opportunity to do a job, it is a certain measure of the "resource" available in a mechanical system for its performance... In addition, energy is a measure of the transition from one type of motion to another.

Biomechanics considers the following main types of energy:

Potential, depending on the relative position of the elements of the mechanical system of the human body;

Kinetic translational motion;

Kinetic rotational motion;

Potential deformation of system elements;

Thermal;

Exchange processes.

The total energy of the biomechanical system is equal to the sum of all the listed types of energy.

By raising the body, compressing the spring, one can accumulate energy in the form of a potential for its subsequent use. Potential energy is always associated with one or another force acting from one body to another. For example, the Earth acts by gravity on a falling object, a compressed spring - on a ball, a stretched bowstring - on an arrow.

Potential energy – this is the energy that a body possesses due to its position in relation to other bodies, or due to the mutual arrangement of parts of one body.

Therefore, the force of gravity and elastic force are potential.

Gravitational potential energy: Еп \u003d m g h

Where k is the stiffness of the spring; x is its deformation.

From the examples given, it can be seen that energy can be accumulated in the form of potential energy (raise a body, compress a spring) for later use.

In biomechanics, two types of potential energy are considered and taken into account: due to the mutual arrangement of body links to the Earth's surface (gravitational potential energy); associated with elastic deformation of elements of the biomechanical system (bones, muscles, ligaments) or any external objects (sports equipment, equipment).

Kinetic energy stored in the body when moving. A moving body performs work due to its loss. Since the links of the body and the human body perform translational and rotational movements, the total kinetic energy (Ek) will be equal to: , where m is the mass, V is the linear velocity, J is the moment of inertia of the system, ω is the angular velocity.

Energy enters the biomechanical system due to metabolic metabolic processes in the muscles. The change in energy, as a result of which work is performed, is not a highly efficient process in a biomechanical system, that is, not all energy is converted into useful work. Part of the energy is lost irreversibly, turning into heat: only 25% is used to do work, the remaining 75% is converted and dissipated in the body.

For a biomechanical system, the law of conservation of energy of mechanical movement is applied in the form:

Epol \u003d Ek + Epot + U,

where Epol is the total mechanical energy of the system; Ek is the kinetic energy of the system; Epot is the potential energy of the system; U is the internal energy of the system, which is mainly heat energy.

The total energy of the mechanical movement of the biomechanical system is based on the following two sources of energy: metabolic reactions in the human body and the mechanical energy of the external environment (deforming elements of sports equipment, equipment, supporting surfaces; opponents during contact interactions). This energy is transmitted through external forces.

A feature of energy production in a biomechanical system is that one part of the energy during movement is spent on performing the necessary motor action, the other goes on the irreversible dissipation of the stored energy, the third is stored and used during subsequent movement. When calculating the energy expended during movements and the mechanical work performed during this, the human body is represented as a model of a multi-link biomechanical system, similar to the anatomical structure. The movements of an individual link and the movement of the body as a whole are considered in the form of two simpler types of movement: translational and rotational.

The total mechanical energy of some i-th link (Epol) can be calculated as the sum of potential (Epot) and kinetic energy (Ek). In turn, Ek can be represented as the sum of the kinetic energy of the center of mass of the link (Ec.c.m.), in which the entire mass of the link is concentrated, and the kinetic energy of rotation of the link relative to the center of mass (Ec.c.c.).

If the kinematics of the link movement is known, this general expression for the total energy of the link will have the form:, where mi is the mass of the i-th link; ĝ - acceleration of gravity; hi - the height of the center of mass above some zero level (for example, above the Earth's surface at a given place); - the speed of the translational movement of the center of mass; Ji - moment of inertia of the ith link relative to the instantaneous axis of rotation passing through the center of mass; ω is the instantaneous angular velocity of rotation about the instantaneous axis.

The work on changing the total mechanical energy of the link (Аi) during the operation time from the moment t1 to the moment t2 is equal to the difference between the energy values \u200b\u200bat the final (Ep (t2)) and initial (Ep (t1)) moments of motion:

Naturally, in this case, the work is spent on changing the potential and kinetic energy of the link.

If the amount of work Аi\u003e 0, that is, the energy has increased, then they say that positive work has been done on the link. If Аi< 0, то есть энергия звена уменьшилась, - отрицательная работа.

The mode of work for changing the energy of a given link is called overcoming if the muscles do positive work on the link; inferior if the muscles do negative work on the link.

Positive work is done when a muscle contracts against an external load, goes to accelerate the links of the body, the body as a whole, sports equipment, etc. Negative work is done if the muscles resist stretching due to the action of external forces. This occurs when lowering a load, descending a ladder, or opposing a force that exceeds muscle strength (for example, in arm wrestling).

Interesting facts about the ratio of positive and negative muscle work have been noticed: negative muscle work is more economical than positive; preliminary execution of negative work increases the size and efficiency of the following positive work.

The greater the speed of movement of the human body (during track and field running, ice skating, cross-country skiing, etc.), the more work is spent not on a useful result - moving the body in space, but on moving the links relative to the GCM. Therefore, at high-speed modes, the main work is spent on acceleration and deceleration of the body links, since with an increase in speed, the acceleration of the body links increases sharply.

One of the characteristics of any system is its kinetic and potential energy. If any force F acts on a body at rest in such a way that the latter starts to move, then work dA is performed. In this case, the value of the kinetic energy dT becomes the higher, the more work is done. In other words, you can write equality:

Taking into account the path dR traveled by the body and the developed speed dV, we will use the second one for the force:

An important point: this law can be used if an inertial frame of reference is taken. The choice of system affects the energy value. In international terms, energy is measured in joules (joules).

It follows that a particle or body characterized by a velocity of movement V and mass m will be:

T \u003d ((V * V) * m) / 2

It can be concluded that kinetic energy is determined by velocity and mass, in fact being a function of motion.

Kinetic and potential energy allows you to describe the state of the body. If the first, as already mentioned, is directly related to motion, then the second is applied to a system of interacting bodies. It is kinetic and is usually considered for examples when the force that binds the bodies does not depend on. In this case, only the initial and final positions are important. The most famous example is gravitational interaction. But if the trajectory is also important, then the force is dissipative (friction).

In simple terms, potential energy is the ability to do work. Accordingly, this energy can be considered in the form of work that needs to be done to move a body from one point to another. I.e:

If the potential energy is denoted as dP, then we get:

A negative value indicates that work is being done due to a decrease in dP. For the known function dP, it is possible to determine not only the modulus of the force F, but also the vector of its direction.

The change in kinetic energy is always associated with potential. This is easy to understand if you remember the systems. The total value of T + dP when moving the body always remains unchanged. Thus, the change in T always occurs in parallel with the change in dP, they seem to flow into each other, transforming.

Since the kinetic and potential energies are interconnected, their sum is the total energy of the system under consideration. In relation to molecules, it is and is always present, as long as there is at least thermal motion and interaction.

When performing calculations, a reference system and any arbitrary moment taken as the initial one are selected. It is possible to accurately determine the value of potential energy only in the zone of action of such forces that, when performing work, do not depend on the trajectory of movement of any particle or body. In physics, such forces are called conservative. They are always interconnected with the law of conservation of total energy.

An interesting point: in a situation where external influences are minimal or leveled out, any studied system always tends to such a state when its potential energy tends to zero. For example, a tossed ball reaches the limit of its potential energy at the top point of the trajectory, but at the same moment begins to move downward, converting the accumulated energy into movement, into the work being performed. It is worth noting once again that for potential energy, there is always an interaction of at least two bodies: for example, in the example with a ball, it is influenced by the gravity of the planet. Kinetic energy can be calculated individually for each moving body.

The word "energy" in translation from Greek means "action". We call energetic a person who actively moves, while performing many different actions.

Energy in physics

And if in life we \u200b\u200bcan evaluate the energy of a person mainly by the consequences of his activities, then in physics, energy can be measured and studied in many different ways. Your cheerful friend or neighbor, most likely, will refuse to repeat the same action thirty to fifty times when suddenly it comes to your mind to investigate the phenomenon of his energy.

But in physics, you can repeat almost any experiment as many times as you like, making the research you need. So it is with the study of energy. Research scientists have studied and identified many types of energy in physics. These are electrical, magnetic, atomic energy and so on. But now we will talk about mechanical energy. And more specifically about kinetic and potential energy.

Kinetic and potential energy

In mechanics, the movement and interaction of bodies with each other is studied. Therefore, it is customary to distinguish between two types of mechanical energy: energy due to the movement of bodies, or kinetic energy, and energy due to the interaction of bodies, or potential energy.

In physics, there is a general rule linking energy and work. To find the energy of a body, it is necessary to find work that is necessary to transfer the body to a given state from zero, that is, one in which its energy is equal to zero.

Potential energy

In physics, potential energy is called energy, which is determined by the mutual position of interacting bodies or parts of the same body. That is, if the body is raised above the ground, then it has the ability to fall and do some work.

And the possible amount of this work will be equal to the potential energy of the body at height h. For potential energy, the formula is determined according to the following scheme:

A \u003d Fs \u003d Ft * h \u003d mgh, or Ep \u003d mgh,

where Ep is the potential energy of the body,
m body weight,
h - body height above the ground,
g acceleration of gravity.

Moreover, any position convenient for us can be taken for the zero position of the body, depending on the conditions of the experiment and measurements, not only the surface of the Earth. This can be the surface of the floor, table, and so on.

Kinetic energy

In the case when the body moves under the influence of force, it not only can, but also does some work. In physics, kinetic energy is the energy that a body possesses due to its motion. The body, moving, expends its energy and does work. For kinetic energy, the formula is calculated as follows:

A \u003d Fs \u003d mas \u003d m * v / t * vt / 2 \u003d (mv ^ 2) / 2, or Eк \u003d (mv ^ 2) / 2,

where Eк is the kinetic energy of the body,
m body weight,
v body speed.

The formula shows that the greater the mass and speed of the body, the higher its kinetic energy.

Each body has either kinetic or potential energy, or both at once, as, for example, a flying plane.