Kinetic energy is the energy of motion of bodies. Energy and its types Energy in physics

Conditioned by movement.

In simple terms, kinetic energy is the energy that a body has only when it moves. When the body is not moving, the kinetic energy is zero.

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  First time concept kinetic energy was introduced in the works of Gottfried Leibniz (1695), devoted to the concept of "living force" .

  physical meaning

  Consider a system consisting of one material point and write down Newton's second law:

  m a → = F → , (\displaystyle m(\vec (a))=(\vec (F)),)

  Where F → (\displaystyle (\vec (F)))- is the resultant of all forces acting on the body. Scalarly multiply the equation by the displacement of a material point d s → = v → d t (\displaystyle (\rm (d))(\vec (s))=(\vec (v))(\rm (d))t). Given that

  a → = d v → d t , (\displaystyle (\vec (a))=(\frac ((\rm (d))(\vec (v)))((\rm (d))t)),) d (m v 2 2) = F → d s → . (\displaystyle (\rm (d))\left(((mv^(2)) \over (2))\right)=(\vec (F))(\rm (d))(\vec (s )).)

  If the system is closed, that is, there are no forces external to the system, or the resultant of all forces is zero, then

  d (m v 2 2) = 0 , (\displaystyle d\left(((mv^(2)) \over (2))\right)=0,)

  and the value

  T = m v 2 2 (\displaystyle T=((mv^(2)) \over 2))

  remains constant. This value is called kinetic energy material point. If the system is isolated, then the kinetic energy is an integral of motion.

  - moment of inertia of the body

  ω → (\displaystyle (\vec (\omega ))) is the angular velocity of the body.

  The physical meaning of work

  A 12 = T 2 − T 1 . (\displaystyle \A_(12)=T_(2)-T_(1).)

  Kinetic energy of rotational motion

  Kinetic energy in hydrodynamics

  Relativism

  This formula can be rewritten in the following form.

  The word "energy" in Greek means "action". Energetic we call a person who actively moves, while performing a variety of actions.

  Energy in physics

  And if in life we ​​can evaluate the energy of a person mainly by the consequences of his activity, then in physics energy can be measured and studied in many different ways. Your cheerful friend or neighbor will most likely refuse to repeat the same action thirty or fifty times when it suddenly enters 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 labeled many types of energy in physics. These are electrical, magnetic, atomic energy and so on. But now we're talking about mechanical energy. 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 general rule linking energy and work. To find the energy of the body, it is necessary to find the work that is necessary to transfer the body to a given state from zero, that is, one in which its energy is 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, to do some work.

  And the possible value of this work will be equal to the potential energy of the body at a height h. For potential energy, the formula is defined as follows:

  A=Fs=Ft*h=mgh, or Ep=mgh,

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

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

  Kinetic energy

  In the case when the body moves under the influence of a force, it not only can, but also does some work. In physics, kinetic energy is the energy possessed by a body 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 Ek \u003d (mv ^ 2) / 2,

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

  From the formula it can be seen that the greater the mass and speed of the body, the higher its kinetic energy.

  Every body has either kinetic or potential energy, or both at the same time, like, for example, a flying plane.

  Energy is a scalar quantity. The SI unit for energy is the Joule.

  Kinetic and potential energy

  There are two types of energy - kinetic and potential.

  DEFINITION

  Kinetic energy is the energy that the body possesses due to its movement:

  DEFINITION

  Potential energy- this is the energy, which is determined by the mutual arrangement of bodies, as well as the nature of the forces of interaction between these bodies.

  Potential energy in the Earth's gravitational field is the energy due to the gravitational interaction of the body with the Earth. It is determined by the position of the body relative to the Earth and is equal to the work to move the body from this position to the zero level:

  Potential energy is the energy due to the interaction of body parts with each other. It is equal to the work of external forces in tension (compression) of an undeformed spring by the value:

  A body can have both kinetic and potential energy at the same time.

  The total mechanical energy of a body or system of bodies is equal to the sum of the kinetic and potential energies of the body (system of bodies):

  Law of energy conservation

  For a closed system of bodies, the law of conservation of energy is valid:

  In the case when external forces act on a body (or system of bodies), for example, the law of conservation of mechanical energy is not fulfilled. In this case, the change in the total mechanical energy of the body (system of bodies) is equal to the external forces:

  The law of conservation of energy makes it possible to establish a quantitative relationship between various forms of motion of matter. Just like , it is valid not only for , but for all natural phenomena. The law of conservation of energy says that energy in nature cannot be destroyed in the same way as it cannot be created from nothing.

  In its most general form, the law of conservation of energy can be formulated as follows:

  • energy in nature does not disappear and is not created again, but only transforms from one form to another.

  Examples of problem solving

  EXAMPLE 1

  Exercise	A bullet flying at a speed of 400 m / s hits an earthen rampart and travels to a stop of 0.5 m. Determine the resistance of the shaft to the movement of the bullet if its mass is 24 g.
  Solution	The resistance force of the shaft is an external force, so the work of this force is equal to the change in the kinetic energy of the bullet: Since the resistance force of the shaft is opposite to the direction of movement of the bullet, the work of this force is: Bullet kinetic energy change: Thus, one can write: whence the resistance force of the earthen rampart: Let's convert the units to the SI system: g kg. Calculate the resistance force:
  Answer	Shaft resistance force 3.8 kN.

  EXAMPLE 2

  Exercise	A load of mass 0.5 kg falls from a certain height onto a plate of mass 1 kg, mounted on a spring with a stiffness coefficient of 980 N/m. Determine the magnitude of the greatest compression of the spring, if at the moment of impact the load had a speed of 5 m/s. The impact is inelastic.
  Solution	Let's write down for the closed system cargo + plate. Since the impact is inelastic, we have: whence the speed of the plate with the load after the impact: According to the law of conservation of energy, the total mechanical energy of the load together with the plate after impact is equal to the potential energy of the compressed spring:

  Another fundamental physical concept, the concept of energy, is closely related to the concept of work. Since mechanics studies, firstly, the movement of bodies, and secondly, the interaction of bodies with each other, it is customary to distinguish between two types of mechanical energy: kinetic energy, due to the movement of the body, and potential energy due to the interaction of the body with other bodies.

  Kinetic energy mechanical system called energy,depending on the velocities of the points of this system.

  The expression for kinetic energy can be found by determining the work of the resultant force applied to a material point. Based on (2.24), we write the formula for the elementary work of the resultant force:

  Because
  , then dА = mυdυ. (2.25)

  To find the work of the resultant force when the body speed changes from υ 1 to υ 2, we integrate the expression (2.29):

  (2.26)

  Since work is a measure of the transfer of energy from one body to another, then on

  Based on (2.30), we write that the quantity is the kinetic energy

  bodies:
  whence instead of (1.44) we get

  (2.27)

  The theorem expressed by formula (2.30) is usually called kinetic energy theorem . In accordance with it, the work of forces acting on a body (or system of bodies) is equal to the change in the kinetic energy of this body (or system of bodies).

  From the kinetic energy theorem it follows physical meaning of kinetic energy : The kinetic energy of a body is equal to the work that it is capable of doing in the process of reducing its speed to zero. The more "reserve" of kinetic energy a body has, the more work it can do.

  The kinetic energy of the system is equal to the sum of the kinetic energies of the material points of which this system consists:

  (2.28)

  If the work of all forces acting on the body is positive, then the kinetic energy of the body increases, if the work is negative, then the kinetic energy decreases.

  Obviously, the elementary work of the resultant of all forces applied to the body will be equal to the elementary change in the kinetic energy of the body:

  dA = dE k. (2.29)

  In conclusion, we note that kinetic energy, like the speed of movement, has a relative character. For example, the kinetic energy of a passenger sitting on a train will be different if we consider the movement relative to the roadbed or relative to the car.

  §2.7 Potential energy

  The second type of mechanical energy is potential energy is the energy due to the interaction of bodies.

  Potential energy does not characterize any interaction of bodies, but only one that is described by forces that do not depend on speed. Most of the forces (gravity, elasticity, gravitational forces, etc.) are just that; the only exception is the force of friction. The work of the forces under consideration does not depend on the shape of the trajectory, but is determined only by its initial and final positions. The work of such forces on a closed trajectory is zero.

  Forces whose work does not depend on the shape of the trajectory, but depends only on the initial and final position of a material point (body) are called potential or conservative forces .

  If a body interacts with its environment through potential forces, then the concept of potential energy can be introduced to characterize this interaction.

  Potential called the energy due to the interaction of bodies and depending on their relative position.

  Find the potential energy of a body raised above the ground. Let a body of mass m move uniformly in a gravitational field from position 1 to position 2 along the surface, the section of which by the drawing plane is shown in Fig. 2.8. This section is the trajectory of a material point (body). If there is no friction, then three forces act on the point:

  1) force N from the side of the surface is normal to the surface, the work of this force is zero;

  2) gravity mg, the work of this force A 12;

  3) thrust force F from some driving body (internal combustion engine, electric motor, person, etc.); the work of this force will be denoted as A T .

  Consider the work of gravity when moving a body along an inclined plane of length ℓ (Fig. 2.9). As you can see from this figure, the work is equal to

  A" = mgℓ cosα = mgℓ cos(90° + α) = - mgℓ sinα

  From the triangle BCD we have ℓ sinα = h, so the last formula implies:

  The trajectory of the body (see Fig. 2.8) can be schematically represented by small sections of an inclined plane, therefore, for the work of gravity on the entire trajectory 1 -2, the expression is true

  A 12 \u003d mg (h 1 -h 2) \u003d- (mg h 2 - mg h 1) (2.30)

  So, the work of gravity does not depend on the trajectory of the body, but depends on the difference in the heights of the location of the initial and final points of the trajectory.

  the value

  e p = mg h (2.31)

  called potential energy material point (body) with mass m raised above the ground to a height h. Therefore, formula (2.30) can be rewritten as follows:

  A 12 \u003d \u003d - (En 2 - En 1) or A 12 \u003d \u003d -ΔEn (2.32)

  The work of gravity is equal to the change in the potential energy of bodies, taken with the opposite sign, i.e., the difference between its final and initialvalues (potential energy theorem ).

  Similar reasoning can be given for an elastically deformed body.

  (2.33)

  Note that the difference in potential energies has a physical meaning as a quantity that determines the work of conservative forces. In this regard, it makes no difference to what position, configuration, zero potential energy should be attributed.

  One very important consequence can be obtained from the potential energy theorem: conservative forces are always directed in the direction of decreasing potential energy. The established pattern is manifested in the fact that any system, left to itself, always tends to move into a state in which its potential energy has the smallest value. This is principle of minimum potential energy .

  If the system in a given state does not have a minimum potential energy, then this state is called energetically unfavorable.

  If the ball is at the bottom of a concave bowl (Fig. 2.10, a), where its potential energy is minimal (compared to its values ​​in neighboring positions), then its state is more favorable. The equilibrium of the ball in this case is sustainable: if you move the ball to the side and release it, it will return to its original position again.

  Energetically unfavorable, for example, is the position of the ball on top of a convex surface (Fig. 2.10, b). The sum of the forces acting in this case on the ball is equal to zero, and therefore, this ball will be in equilibrium. However, this balance is unstable: the slightest impact is enough for it to slide down and thereby move into a state of energetically more favorable, i.e. less

  P potential energy.

  At indifferent equilibrium (Fig. 2.10, c) the potential energy of the body is equal to the potential energy of all its possible nearest states.

  In figure 2.11, you can indicate some limited area of ​​\u200b\u200bspace (for example, cd), in which the potential energy is less than outside it. This area was named potential hole .

  >>Physics grade 10 >>Physics: Kinetic energy and its change

  Kinetic energy

  Kinetic energy is the energy of a body that it has as a result of its motion.

  In simple terms, the concept of kinetic energy should be understood only as the energy that a body has when it moves. If the body is at rest, that is, does not move at all, then the kinetic energy will be equal to zero.

  Kinetic energy is equal to the work that it must spend to bring the body from rest to a state of motion with some speed.

  Therefore, the kinetic energy is the difference between the total energy of the system and its rest energy. In other words, that the kinetic energy will be part of the total energy, which is due to movement.

  Let's try to understand the concept of the kinetic energy of the body. For example, let's take the movement of a puck on ice and try to understand the relationship between the amount of kinetic energy and the work that must be done to bring the puck out of rest and set it in motion with some speed.

  Example

  A hockey player playing on ice, having hit the puck with a stick, informs it of speed, as well as kinetic energy. Immediately after hitting the stick, the puck begins to move very quickly, but gradually its speed slows down and finally it stops completely. This means that the decrease in speed was the result of the friction force occurring between the surface and the puck. Then the friction force will be directed against the movement and the action of this force is accompanied by displacement. The body, on the other hand, uses the mechanical energy it has, doing work against the force of friction.

  From this example, we see that the kinetic energy will be the energy that the body receives as a result of its movement.

  Consequently, the kinetic energy of a body having a certain mass will move at a speed equal to the work that the force applied to a body at rest must do to give it a given speed:

  Kinetic energy is the energy of a moving body, which is equal to the product of the mass of the body and the square of its speed, divided in half.

  
  

  Properties of kinetic energy

  The properties of kinetic energy include: additivity, invariance with respect to the rotation of the frame of reference, and conservation.

  Such a property as additivity is the kinetic energy of a mechanical system, which is composed of material points and will be equal to the sum of the kinetic energies of all material points that are part of this system.

  The property of invariance with respect to the rotation of the frame of reference means that the kinetic energy does not depend on the position of the point and the direction of its velocity. Its dependence extends only from the module or from the square of its speed.

  The conservation property means that the kinetic energy does not change at all during interactions that change only the mechanical characteristics of the system.

  This property is unchanged with respect to the Galilean transformations. The properties of conservation of kinetic energy and Newton's second law will be quite enough to derive the mathematical formula for kinetic energy.

  Ratio of kinetic and internal energy

  But there is such an interesting dilemma as the fact that the kinetic energy can be dependent on the positions from which this system is considered. If, for example, we take an object that can only be viewed under a microscope, then, as a whole, this body is motionless, although there is also internal energy. Under such conditions, kinetic energy appears only when this body moves as a whole.

  The same body, when viewed at the microscopic level, has an internal energy due to the movement of the atoms and molecules of which it is composed. And the absolute temperature of such a body will be proportional to the average kinetic energy of such a movement of atoms and molecules.