One of the characteristics of any system is its kinetic and potential energy. If any force F exerts an effect on a body at rest in such a way that the latter comes into motion, then work dA takes place. In this case, the value of kinetic energy dT becomes higher, the more work done. In other words, we can write the equality:
Taking into account the path dR traversed by the body and the speed dV developed, we will use the second one for the force:
Important point: this law can be used if taken inertial system countdown. The choice of system affects the energy value. Internationally, energy is measured in joules (J).
It follows that a particle or body characterized by movement speed V and mass m will be:
T = ((V * V)*m) / 2
We can conclude that kinetic energy is determined by speed and mass, in fact representing a function of motion.
Kinetic and potential energy help describe the state of a body. If the first, as already mentioned, is directly related to movement, then the second is applied to a system of interacting bodies. Kinetic and are usually considered for examples when the force connecting the bodies does not depend on In this case, only the initial and final positions are important. Most famous example - gravitational interaction. But if the trajectory is also important, then the force is dissipative (friction).
Speaking in simple language, potential energy represents 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. That is:
If potential energy is denoted as dP, then we get:
Negative value indicates that work is being done due to a decrease in dP. For known function dP it is possible to determine not only the magnitude of the force F, but also its direction vector.
A change in kinetic energy is always related to potential energy. This is easy to understand if you remember the systems. The total value of T+dP when moving the body always remains unchanged. Thus, a change in T always occurs in parallel with a change in dP; they seem to flow into each other, transforming.
Since kinetic and potential energy are interrelated, their sum represents 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 movement and interaction.
When performing calculations, a reference system and any arbitrary moment taken as the initial moment 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.
Interesting point: in a situation where external influences are minimal or leveled out, any studied system always tends to its state when its potential energy tends to zero. For example, a thrown ball reaches the limit of its potential energy at the top point of the trajectory, but at the same instant begins to move downward, converting the accumulated energy into movement, into work 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 the ball, it is influenced by the gravity of the planet. Kinetic energy can be calculated individually for each moving body.
The muscles that move the parts of the body perform 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 it has traversed(S): A = F S.
Doing work requires energy. Therefore, as work is performed, the energy in the system decreases. Since in order for work to be done, a supply of energy is necessary, the latter can be defined as follows: Energy – this is the opportunity to do work, this is a certain measure of the “resource” available in a mechanical system to perform it. In addition, energy is a measure of the transition from one type of motion to another.
In biomechanics, the following main principles are considered: types of energy:
Potential, depending on the relative position of the elements mechanical system human body;
Kinetic forward motion;
Kinetic rotational movement;
Potential deformation of system elements;
Thermal;
Exchange processes.
The total energy of a biomechanical system is equal to the sum of all listed types of energy.
By lifting a body, compressing a spring, you can accumulate energy in potential form for later use. Potential energy always associated with one or another force acting from one body on another. For example, the Earth acts by gravity on a falling object, a compressed spring acts on a ball, and a drawn bowstring acts 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 relative arrangement of parts of one body.
Therefore, the force of gravity and elastic force are potential.
Gravitational potential energy: En = m g h
Where k is the spring stiffness; x is its deformation.
From the above examples it is clear that energy can be stored in the form of potential energy (lifting a body, compressing a spring) for later use.
In biomechanics, two types of potential energy are considered and taken into account: conditioned relative position 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 does work due to its loss. Since the parts of the body and the human body perform translational and rotational movements, the total kinetic energy (Ek) will be equal to: 
, where m is mass, V is linear speed, J – moment inertia systems, ω – angular velocity.
Energy enters the biomechanical system due to metabolic metabolic processes occurring in the muscles. The change in energy that results in work being done is not a highly efficient process in a biomechanical system, that is, not all the energy goes into useful work. Part of the energy is lost irreversibly, turning into heat: only 25% is used to perform work, the remaining 75% is converted and dissipated in the body.
For a biomechanical system, the law of conservation of energy is applied mechanical movement in the form:
Epol = Ek + Epot + U,
where Epol is the total mechanical energy of the system; Ek – kinetic energy of the system; Epot – potential energy of the system; U – internal energy systems that represent primarily thermal energy.
The total energy of the mechanical movement of a biomechanical system is based on the following two energy sources: metabolic reactions in the human body and mechanical energy external environment(deformable 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 to the irreversible dissipation of stored energy, the third is saved and used during subsequent movement. When calculating the energy expended during movements and the mechanical work the human body is represented as a model of a multi-link biomechanical system, similar to anatomical structure. The movements of an individual link and the movements of the body as a whole are considered in the form of two more simple types 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.Vr.).
If the kinematics of movement of the link 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 free fall; hi – height of the center of mass above some zero level(for example, above the surface of the Earth in this place); - speed of translational motion of the center of mass; Ji – moment of inertia the i-th link relative to the instantaneous axis of rotation passing through the center of mass; ω – instantaneous angular velocity of rotation relative to the instantaneous axis.
Work to change the complete mechanical energy link (Ai) during operation from moment t1 to moment t2 is equal to the difference in energy values at the final (Ep(t2)) and initial (Ep(t1)) moments of movement:
Naturally, in in this case work is spent on changing the potential and kinetic energy of the link.
If the amount of work Ai > 0, that is, the energy has increased, then they say that positive work has been done on the link. If AI< 0, то есть энергия звена уменьшилась, - отрицательная работа.
The mode of work to change the energy of a given link is called overcoming if the muscles perform positive work on the link; inferior if the muscles perform negative work on the link.
Positive work is done when the muscle contracts against an external load, goes to accelerate the parts 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, going down stairs, or resisting a force that exceeds the strength of the muscles (for example, in arm wrestling).
Spotted interesting facts ratio of positive and negative muscle work: negative muscle work is more economical than positive; pre-execution negative work increases the magnitude and efficiency of the positive work that follows it.
The greater the speed of movement of a person’s body (during athletics running, skating, skiing, etc.), the most work is not spent on useful result- movement of the body in space, and the movement of links relative to the GCM. Therefore, when speed limits the main work is spent on accelerating and braking the body parts, since with increasing speed the acceleration of the movement of the body parts increases sharply.
To set any body in motion, a prerequisite is work of art. At the same time, to perform this work it is necessary to expend some energy.
Energy characterizes the body from the point of view of its ability to produce work. The unit of energy is Joule, abbreviated [J].
The total energy of any mechanical system is equivalent to the sum of the potential and kinetic energy. Therefore, it is customary to distinguish potential and kinetic energy as types of mechanical energy.
If we are talking about biomechanical systems, then the total energy of such systems additionally consists of thermal and energy of metabolic processes.
IN isolated systems bodies, when they are acted upon only by the force of gravity and elasticity, the value of the total energy is unchanged. This statement is the law of conservation of energy.
What are both types of mechanical energy?
About potential energy
Potential energy is the energy determined mutual position bodies, or components of these bodies, interacting with each other. In other words, this energy is determined the distance between the bodies.
For example, when a body falls down and sets in motion surrounding bodies along the path of the fall, gravity produces positive work. And, conversely, in the case of lifting the body upward, we can talk about the production of negative work.
Consequently, each body, when located at a certain distance from earth's surface has potential energy. How more height and body weight, the more value work done by the body. At the same time, in the first example, when a body falls down, the potential energy will be negative, and when raised, the potential energy is positive.
This is explained by the equality of the work of gravity in value, but the opposite sign of the change in potential energy.
Also, an example of the emergence of interaction energy can be an object subject to elastic deformation - compressed spring: when straightening, work will be done by the elastic force. Here we're talking about about the performance of work due to a change in the location of the components of the body relative to each other during elastic deformation.
To summarize the information, we note that absolutely every object that is affected by gravity or elasticity will have the energy of a potential difference.
About kinetic energy
Kinetic energy is the energy that bodies begin to possess as a result of movement process. Based on this, the kinetic energy of bodies at rest is equal to zero.
The amount of this energy is equivalent to the amount of work that needs to be done to remove the body from a state of rest and thereby make it move. In other words, kinetic energy can be expressed as the difference between full energy and restful energy.
The translational work done by a moving body directly depends on the mass and speed squared. The work of rotational motion depends on the moment of inertia and the square of the angular velocity.
The total energy of moving bodies includes both types of work performed; it is determined according to the following expression: . Main characteristics of kinetic energy:
- Additivity– defines kinetic energy as the energy of a system consisting of a set material points, and equal to the total kinetic energy of each point of this system;
- Invariance relative to the rotation of the reference system - kinetic energy is independent of the position and direction of the point’s velocity;
- Saving– the characteristic indicates that the kinetic energy of the systems is unchanged during any interactions, in cases where only the mechanical characteristics change.
Examples of bodies with potential and kinetic energy
All objects raised and located at some distance from the earth's surface in a stationary state are capable of possessing potential energy. As an example, this concrete slab lifted by crane, which is in a stationary state, a charged spring.
Moving things have kinetic energy vehicles, as well as, in general, any rolling object.
At the same time, in nature, everyday life and technology, potential energy can transform into kinetic energy, and kinetic energy, in turn, on the contrary, into potential energy.
Ball, which is thrown from a certain point at a height: in the highest position, the potential energy of the ball is maximum, and the value of kinetic energy is zero, since the ball does not move and is at rest. As the altitude decreases, the potential energy gradually decreases accordingly. When the ball reaches the earth's surface, it will roll; V at the moment kinetic energy increases, and potential energy will be zero.
