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Kinetic and potential energy in short. Kinetic energy. Kinetic energy properties

1. A stone, falling from a certain height to the Earth, leaves a dent on the Earth's surface. During the fall, he does work to overcome the air resistance, and after touching the ground, he does the work to overcome the resistance force of the soil, since it has energy. If you pump air into a jar closed with a cork, then at a certain air pressure, the cork will fly out of the jar, while the air will do the work to overcome the friction of the cork against the neck of the jar, due to the fact that the air has energy. Thus, the body can do work if it has energy. Energy is denoted by the letter \ (E \). Unit of work - \ (\) = 1 J.

When work is done, the state of the body changes and its energy changes. The change in energy is equal to the perfect work: \ (E = A \).

2. Potential energy is the energy of interaction of bodies or body parts, depending on their mutual position.

Since bodies interact with the Earth, they have the potential energy of interaction with the Earth.

If a body of mass \ (m \) falls from a height \ (h_1 \) to a height \ (h_2 \), then the work of gravity \ (F_t \) in the section \ (h = h_1- h_2 \) is equal to: \ (A = F_th = mgh = mg (h_1 - h_2) \) Or \ (A = mgh_1 - mgh_2 \) (fig. 48).

In the resulting formula \ (mgh_1 \) characterizes the initial position (state) of the body, \ (mgh_2 \) characterizes the final position (state) of the body. The quantity \ (mgh_1 = E_ (n1) \) is the potential energy of the body in the initial state; quantity \ (mgh_2 = E_ (n2) \) is the potential energy of the body in the final state.

Thus, the work of the force of gravity is equal to the change in the potential energy of the body. The sign "-" means that when the body moves downward and, accordingly, when the force of gravity performs positive work, the potential energy of the body decreases. If the body rises up, then the work of gravity is negative, and the body's potential energy increases.

If the body is at a certain height \ (h \) relative to the surface of the Earth, then its potential energy in this state is equal to \ (E_п = mgh \). The value of potential energy depends on the level relative to which it is measured. The level at which the potential energy is zero is called zero level.

In contrast to kinetic energy, bodies at rest have potential energy. Since potential energy is the energy of interaction, it refers not to one body, but to a system of interacting bodies. V in this case this system is made up of the Earth and the body raised above it.

3. Elastically deformed bodies have potential energy. Suppose the left end of the spring is secured, and a weight is attached to the right end of the spring. If the spring is compressed by displacing its right end by \ (x_1 \), then the spring will have an elastic force \ (F_ (upr1) \), directed to the right (Fig. 49).

If we now leave the spring to itself, then its right end will move, the elongation of the spring will be \ (x_2 \), and the elastic force \ (F_ (upr2) \).

The work of the elastic force is

\ [A = F_ (cf) (x_1-x_2) = k / 2 (x_1 + x_2) (x_1-x_2) = kx_1 ^ 2/2-kx_2 ^ 2/2 \]

\ (Kx_1 ^ 2/2 = E_ (n1) \) is the potential energy of the spring in the initial state, \ (kx_2 ^ 2/2 = E_ (n2) \) is the potential energy of the spring in the final state. The work of the elastic force is equal to the change in the potential energy of the spring.

You can write \ (A = E_ (n1) -E_ (n2) \), or \ (A = - (E_ (n2) -E_ (n1)) \), or \ (A = -E_ (n) \).

The “-” sign shows that when the spring is stretched and compressed, the elastic force does negative work, the potential energy of the spring increases, and when the spring moves to the equilibrium position, the elastic force does positive work, and the potential energy decreases.

If the spring is deformed and its coils are displaced relative to the equilibrium position by a distance \ (x \), then the potential energy of the spring in this state is \ (E_п = kx ^ 2/2 \).

4. Moving bodies can also do work. For example, a moving piston compresses the gas in the cylinder, a moving projectile pierces a target, etc. Therefore, moving bodies have energy. The energy possessed by a moving body is called kinetic energy ... The kinetic energy \ (E_k \) depends on the mass of the body and its speed \ (E_k = mv ^ 2/2 \). This follows from the transformation of the work formula.

Work \ (A = FS \). Strength \ (F = ma \). Substituting this expression into the work formula, we get \ (A = maS \). Since \ (2aS = v ^ 2_2-v ^ 2_1 \), then \ (A = m (v ^ 2_2-v ^ 2_1) / 2 \) or \ (A = mv ^ 2_2 / 2- mv ^ 2_1 / 2 \), where \ (mv ^ 2_1 / 2 = E_ (k1) \) is the kinetic energy of the body in the first state, \ (mv ^ 2_2 / 2 = E_ (k2) \) is the kinetic energy bodies in the second state. Thus, the work of force is equal to the change in the kinetic energy of the body: \ (A = E_ (k2) -E_ (k1) \), or \ (A = E_k \). This statement - kinetic energy theorem.

If the force does positive work, then the kinetic energy of the body increases, if the work of the force is negative, then the kinetic energy of the body decreases.

5. Full mechanical energy\ (E \) bodies - physical quantity, equal to the sum of its potential \ (E_n \) and kinetic \ (E_n \) energy: \ (E = E_n + E_k \).

Let the body fall vertically downward and at point A is at a height \ (h_1 \) relative to the Earth's surface and has a speed \ (v_1 \) (Fig. 50). At point B, the height of the body \ (h_2 \) and speed \ (v_2 \) Accordingly, at point A, the body has potential energy \ (E_ (n1) \) and kinetic energy \ (E_ (k1) \), and at point B - potential energy \ (E_ (n2) \) and kinetic energy \ (E_ (k2) \).

When a body moves from point A to point B, gravity performs work equal to A. As was shown, \ (A = - (E_ (n2) -E_ (n1)) \), as well as \ (A = E_ ( k2) -E_ (k1) \). Equating the right-hand sides of these equalities, we get: \ (- (E_ (n2) -E_ (n1)) = E_ (k2) -E_ (k1) \) From where \ (E_ (k1) + E_ (n1) = E_ (n2) + E_ (k2) \) or \ (E_1 = E_2 \).

This equality expresses the law of conservation of mechanical energy: the total mechanical energy of a closed system of bodies between which conservative forces act (gravitational or elastic forces) is conserved.

In real systems, friction forces act that are not conservative, therefore, in such systems, the total mechanical energy is not conserved, it turns into internal energy.

Part 1

1. The two bodies are at the same height above the Earth's surface. The mass of one body \ (m_1 \) is three times the mass of another body \ (m_2 \). Potential energy relative to the Earth's surface

1) the first body is 3 times the potential energy of the second body
2) the second body is 3 times the potential energy of the first body
3) the first body is 9 times the potential energy of the second body
4) the second body is 9 times the potential energy of the first body

2. Compare potential energy ball at the pole \ (E_n \) of the Earth and at the latitude of Moscow \ (E_m \), if it is at the same height relative to the surface of the Earth.

1) \ (E_n = E_m \)
2) \ (E_n> E_m \)
3) \ (E_п 4) \ (E_n \ geq E_m \)

3. The body is thrown vertically upward. Its potential energy

1) is the same at any moments of body movement
2) maximum at the moment of the beginning of movement
3) is maximum at the upper point of the trajectory
4) is minimal at the top point of the trajectory

4. How will the potential energy of the spring change if its elongation is reduced by 4 times?

1) will increase by 4 times
2) will increase 16 times
3) will decrease by 4 times
4) decrease 16 times

5. An apple weighing 150 g lying on a table 1 m high was raised relative to the table by 10 cm. What is the potential energy of the apple relative to the floor?

1) 0.15 J
2) 0.165 J
3) 1.5 J
4) 1.65 J

6. The speed of the moving body has decreased by 4 times. Moreover, its kinetic energy

1) increased 16 times
2) decreased 16 times
3) increased by 4 times
4) decreased by 4 times

7. The two bodies are moving at the same speed. The mass of the second body is 3 times the mass of the first. In this case, the kinetic energy of the second body

1) 9 times more
2) less than 9 times
3) 3 times more
4) less than 3 times

8. The body falls to the floor from the surface of the teacher's demonstration table. (Disregard air resistance.) Kinetic energy of the body

1) is minimal at the moment of reaching the floor surface
2) is minimal at the moment of the start of movement
3) is the same at any moments of body movement
4) maximum at the moment of the beginning of movement

9. A book that fell from the table to the floor possessed a kinetic energy of 2.4 J at the moment it touched the floor. The table height was 1.2 m. What is the weight of the book? Neglect air resistance.

1) 0.2 kg
2) 0.288 kg
3) 2.0 kg
4) 2.28 kg

10. At what speed should a body with a mass of 200 g be thrown from the surface of the Earth vertically upwards so that its potential energy at the highest point of motion is 0.9 J? Neglect air resistance. Measure the potential energy of the body from the surface of the earth.

1) 0.9 m / s
2) 3.0 m / s
3) 4.5 m / s
4) 9.0 m / s

11. Set the correspondence between the physical quantity (left column) and the formula by which it is calculated (right column). In the answer, write down the numbers of the selected answers in a row.

PHYSICAL QUANTITY
A. Potential energy of interaction of the body with the Earth
B. Kinetic energy
B. Potential energy of elastic deformation

NATURE OF ENERGY CHANGE
1) \ (E = mv ^ 2/2 \)
2) \ (E = kx ^ 2/2 \)
3) \ (E = mgh \)

12. The ball was thrown vertically upward. Establish a correspondence between the energy of the ball (left column) and the nature of its change (right column) when the dynamometer spring is stretched. In the answer, write down the numbers of the selected answers in a row.

PHYSICAL QUANTITY
A. Potential energy
B. Kinetic energy
B. Total mechanical energy

NATURE OF ENERGY CHANGE
1) Decreases
2) Increases
3) Does not change

Part 2

13. A bullet weighing 10 g, moving at a speed of 700 m / s, pierced a board 2.5 cm thick and, when exiting the board, had a speed of 300 m / s. Determine the average resistance force acting on the bullet in the board.

Answers

The world around us is in constant motion. Any body (object) is capable of performing a certain job, even if it is at rest. But any process requires make some effort, sometimes considerable.

Translated from Greek, this term means "activity", "strength", "power". All processes on Earth and outside our planet occur due to this force possessed by the surrounding objects, bodies, objects.

In contact with

Among the wide variety, there are several main types of this force, differing primarily in their sources:

  • mechanical - this type is typical for bodies moving in a vertical, horizontal or other plane;
  • heat - released as a result disordered molecules in substances;
  • - the source of this type is the movement of charged particles in conductors and semiconductors;
  • light - it is transported by light particles - photons;
  • nuclear - arises as a result of spontaneous chain fission of the nuclei of atoms of heavy elements.

This article will discuss what the mechanical force of objects is, what it consists of, what it depends on and how it is transformed during various processes.

Thanks to this type of objects, bodies can be in motion or at rest. The possibility of such activities due to the presence two main components:

  • kinetic (Ek);
  • potential (En).

It is the sum of the kinetic and potential energies that determines the overall numerical indicator of the entire system. Now about what formulas are used to calculate each of them, and how the energy is measured.

How to calculate energy

Kinetic energy is a characteristic of any system that is in motion... But how do you find kinetic energy?

This is easy to do, since the calculation formula for the kinetic energy is very simple:

The specific value is determined by two main parameters: the speed of movement of the body (V) and its mass (m). The more these characteristics are, the greater the value of the described phenomenon is possessed by the system.

But if the object does not move (i.e. v = 0), then the kinetic energy is equal to zero.

Potential energy – this is a characteristic depending on positions and coordinates of bodies.

Any body is subject to gravity and elastic forces. Such interaction of objects with each other is observed everywhere, therefore the bodies are in constant motion, change their coordinates.

It has been established that the higher the object is from the surface of the earth, the greater its mass, the greater the indicator of this magnitude it possesses.

Thus, the potential energy depends on the mass (m), height (h). The value of g is the acceleration due to gravity, equal to 9.81 m / s2. The function for calculating its quantitative value looks like this:

The unit of measurement of this physical quantity in the SI system is joule (1 J)... This is exactly how much effort it takes to move the body 1 meter, while applying an effort of 1 newton.

Important! The joule as a unit of measurement was approved at the International Congress of Electricians, which was held in 1889. Until that time, the British Thermal Unit BTU was the standard of measurement, which is currently used to determine the power of thermal installations.

Basics of conservation and transformation

It is known from the foundations of physics that the total force of any object, regardless of the time and place of its stay, always remains constant, only its constant components (En) and (Ek) are transformed.

The transition of potential energy to kinetic and vice versa occurs under certain conditions.

For example, if an object does not move, then its kinetic energy is zero, and only the potential component will be present in its state.

Conversely, what is the potential energy of an object, for example, when it is on the surface (h = 0)? Of course, it is zero, and the E of the body will consist only of its component Ek.

But potential energy is driving power... One has only to raise the system to some height, after what its En will immediately begin to increase, and Ek by such an amount, accordingly, will decrease. This pattern can be seen in the above formulas (1) and (2).

For clarity, we will give an example with a stone or a ball that is thrown. During the flight, each of them possesses both potential and kinetic components. If one increases, then the other decreases by the same amount.

The flight of objects upward continues only as long as there is enough reserve and strength in the component of the movement Ek. As soon as it runs out, the fall begins.

But what the potential energy of objects is equal to at the highest point is not difficult to guess, it is maximum.

When they fall, the opposite happens. When it touches the ground, the kinetic energy level is at its maximum.

KINETIC ENERGY

KINETIC ENERGY, the energy possessed by a moving object. Receives it by starting to move. Depends on the mass () of the object and its speed ( v), according to equality: K. e. = 1/2 mv 2. Upon impact, it is converted into another form of energy, such as heat, sound or light. see alsoPOTENTIAL ENERGY.

Kinetic energy. A moving truck has kinetic energy (A). In order to increase its speed, it needs to be supplied with additional energy, sufficient to overcome the friction and air resistance, and increase the speed. In order to lower the kinetic energy of the truck, necessary for the kinetic energy to be converted into thermal energy of the brakes and tires (B), the kinetic energy of a loaded truck moving at the same speed will be greater due to the greater mass (C) and it it will take more braking force to waste kinetic energy and stop at the same distance as an unloaded truck.


Scientific and technical encyclopedic dictionary.

Kinetic energy a mechanical system is the energy of the mechanical movement of this system.

Force F acting on a resting body and causing it to move, performs work, and the energy of the moving body increases by the amount of work expended. So work dA strength F on the path that the body has traveled during the increase in speed from 0 to v, goes to increase the kinetic energy dT body, i.e.

Using Newton's Second Law F= md v/ dt

and multiplying both sides of the equality by the displacement d r, we get

F d r= m (d v/ dt) dr = dA

Thus, a body with a mass T, moving at speed v, has kinetic energy

T = tv 2 /2. (12.1)

From formula (12.1) it can be seen that the kinetic energy depends only on the mass and velocity of the body, that is, the kinetic energy of the system is a function of the state of its motion.

When deriving formula (12.1), it was assumed that the motion is considered in an inertial frame of reference, since otherwise it would be impossible to use Newton's laws. In different inertial frames of reference moving relative to each other, the speed of the body, and, consequently, its kinetic energy will not be the same. Thus, the kinetic energy depends on the choice of the frame of reference.

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

Let the interaction of bodies be carried out by means of force fields (for example, the field of elastic forces, the field of gravitational forces), characterized by the fact that the work performed by the acting forces when the body moves from one position to another does not depend on the trajectory along which this movement took place, and only depends on the start and end positions. Such fields are called potential and the forces acting in them - conservative. If the work done by the force depends on the trajectory of the body moving from one point to another, then such a force is called dissipative; friction is an example.

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

Work d A expressed as the dot product of the force F to move d r and expression (12.2) can be written as

F d r= -dП. (12.3)

Therefore, if the function П ( r), then from formula (12.3) one can find the force F modulo and direction.

The potential energy can be determined based on (12.3) as

where C is the constant of integration, that is, the potential energy is determined up to some arbitrary constant. This, however, does not affect the physical laws, since they include either the difference in potential energies in two positions of the body, or the derivative of P with respect to coordinates. Therefore, the potential energy of the body in a certain position is considered equal to zero (the zero level of reference is chosen), and the energy of the body in other positions is counted relative to the zero level. For conservative forces

or in vector form

F= -gradП, (12.4) where

(i, j, k- unit vectors of the coordinate axes). The vector defined by expression (12.5) is called scalar gradient P.

For it, along with the notation grad П, the notation П is also used.  ("nabla") means a symbolic vector called operatorHamilton or by the nabla operator:

The specific form of the function P depends on the nature of the force field. For example, the potential energy of a body with a mass T, raised to a height h above the surface of the Earth, is

NS = mgh,(12.7)

where is the height h is counted from the zero level, for which P 0 = 0. Expression (12.7) follows directly from the fact that the potential energy is equal to the work of gravity when the body falls from a height h to the surface of the Earth.

Since the origin is chosen arbitrarily, the potential energy can have a negative value (kinetic energy is always positive. !} If we take for zero the potential energy of a body lying on the surface of the Earth, then the potential energy of a body located at the bottom of the mine (depth h "), P = - mgh ".

Let us find the potential energy of an elastically deformed body (spring). The elastic force is proportional to the deformation:

F NS control = -kx,

where F x control - elastic force projection on the axis NS;k- coefficient of elasticity(for a spring - rigidity), and the minus sign indicates that F x control directed in the opposite direction to deformation NS.

According to Newton's third law, the deforming force is equal in modulus to the elastic force and is directed opposite to it, i.e.

F x = -F x control = kx Elementary work dA, by force F x at infinitesimal deformation dx, is equal to

dA = F x dx = kxdx,

and full work

goes to increase the potential energy of the spring. Thus, the potential energy of an elastically deformed body

NS = kx 2 /2.

The potential energy of a system, 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.

Total mechanical energy of the system- energy of mechanical movement and interaction:

that is, it is equal to the sum of the kinetic and potential energies.