Mechanical energy and its types. Total mechanical energy of bodies and systems What is the mechanical energy of a system of bodies

1. Consider a free fall of a body from a certain height h relative to the surface of the Earth (Fig. 77). At the point A the body is motionless, therefore it has only potential energy. At the point B on high h 1 the body has both potential energy and kinetic energy, since the body at this point has a certain speed v 1 . At the moment of touching the Earth's surface, the potential energy of the body is zero, it has only kinetic energy.

Thus, during the fall of the body, its potential energy decreases, and its kinetic energy increases.

full mechanical energy E called the sum of potential and kinetic energies.

E = E n+ E To.

2. Let us show that the total mechanical energy of the system of bodies is conserved. Consider once again the fall of a body onto the surface of the Earth from a point A exactly C(see fig. 78). We will assume that the body and the Earth are a closed system of bodies, in which only conservative forces act, in this case gravity.

At the point A the total mechanical energy of a body is equal to its potential energy

E = E n = mgh.

At the point B the total mechanical energy of the body is

E = E n1 + E k1 .
E n1 = mgh 1 , E k1 = .

Then

E = mgh 1 + .

body speed v 1 can be found using the kinematics formula. Since the movement of the body from the point A exactly B equals

s = h – h 1 = , then= 2 g(h – h 1).

Substituting this expression into the formula for the total mechanical energy, we obtain

E = mgh 1 + mg(h – h 1) = mgh.

Thus, at the point B

E = mgh.

At the moment of touching the Earth's surface (point C) the body has only kinetic energy, therefore, its total mechanical energy

E = E k2 = .

The speed of the body at this point can be found by the formula = 2 gh, given that the initial velocity of the body is zero. After substituting the expression for the velocity into the formula for the total mechanical energy, we obtain E = mgh.

Thus, we have obtained that at the three considered points of the trajectory, the total mechanical energy of the body is equal to the same value: E = mgh. We will arrive at the same result by considering other points of the body's trajectory.

The total mechanical energy of a closed system of bodies, in which only conservative forces act, remains unchanged for any interactions of the bodies of the system.

This statement is the law of conservation of mechanical energy.

3. Friction forces act in real systems. So, with a free fall of a body in the considered example (see Fig. 78), the force of air resistance acts, therefore, the potential energy at the point A more total mechanical energy at a point B and at the point C by the amount of work done by the force of air resistance: D E = A. In this case, the energy does not disappear, part of the mechanical energy is converted into the internal energy of the body and air.

4. As you already know from the 7th grade physics course, various machines and mechanisms are used to facilitate human labor, which, having energy, perform mechanical work. Such mechanisms include, for example, levers, blocks, cranes, etc. When work is performed, energy is converted.

Thus, any machine is characterized by a value showing what part of the energy transmitted to it is used usefully or what part of the perfect (total) work is useful. This value is called efficiency(efficiency).

The efficiency h is called the value equal to the ratio of useful work A n to full work A.

The efficiency is usually expressed as a percentage.

h = 100%.

5. Problem solution example

A parachutist weighing 70 kg separated from a stationary helicopter and, having flown 150 m before opening the parachute, acquired a speed of 40 m/s. What is the work done by the air resistance force?

The thermal energy at a given altitude is zero. Flying distance s= h, the skydiver acquired kinetic energy, and his potential energy at this level became equal to zero. Thus, in the second position, the total mechanical energy of the parachutist is equal to his kinetic energy:

E = E k = .

Potential energy of a skydiver E n when separated from the helicopter is not equal to the kinetic E k, since the force of air resistance does work. Hence,

A = E To - E P;

A =– mgh.

A\u003d - 70 kg 10 m / s 2 150 m \u003d -16 100 J.

The work has a minus sign, since it is equal to the loss of total mechanical energy.

Answer: A= -16 100 J.

Questions for self-examination

1. What is total mechanical energy?

2. Formulate the law of conservation of mechanical energy.

3. Does the law of conservation of mechanical energy hold true if a friction force acts on the bodies of the system? Explain the answer.

4. What does the efficiency ratio show?

Task 21

1. A ball of mass 0.5 kg is thrown vertically upwards with a speed of 10 m/s. What is the potential energy of the ball at its highest point?

2. An athlete weighing 60 kg jumps from a 10-meter tower into the water. What are equal to: the potential energy of the athlete relative to the surface of the water before the jump; its kinetic energy when entering the water; its potential and kinetic energy at a height of 5 m relative to the surface of the water? Ignore air resistance.

3. Determine the efficiency of an inclined plane 1 m high and 2 m long when a load of 4 kg is moved along it under the action of a force of 40 N.

Chapter 1 Highlights

1. Types of mechanical movement.

2. Basic kinematic quantities (Table 2).

table 2

3. Basic equations of motion (Table 3).

Table 3

4. Basic traffic charts.

Table 4

5. Basic dynamic quantities.

Table 5

6. Basic laws of mechanics

Table 6

7. Forces in mechanics.

8. Basic energy quantities.

Table 7

Take a look: a ball rolling along the lane knocks down the skittles, and they scatter around. The fan that was just turned off continues to rotate for some time, creating a stream of air. 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, the further they will scatter. For example, the faster the blades rotate, the farther the fan will move the airflow.

The kinetic energy of the same body can be different from the point of view of different observers. For example, from our perspective as readers of this book, the kinetic energy of a stump on a road is zero because 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 turn to the drawing. As the ball floats, it can perform mechanical work, such as pushing our palm out of the water to the surface. A weight located at a certain height can do work - crack a nut. A stretched bowstring can push an arrow out. Hence, considered bodies have potential energy, as 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 bowstring interacts with other parts of the bow - it is pulled by the elastic force of the curved shaft of the bow.

The potential energy of a body depends on the force of interaction of 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 water, the greater the gravity and the farther the weight is from the Earth, the greater the elastic force and the farther the bowstring is pulled, the greater the potential energies of the bodies: ball, weight, 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 of the nuts, it will be found 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 motion 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 makes extensive use of this concept both practically and theoretically.

Work and energy

Mechanical work can be determined if the force acting on the body and the displacement of the body are known. There is another way to calculate mechanical work. Consider an example:

The figure shows a body that can be in various 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, when moving from state I to state II, the body can perform work. When work is carried out, 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 matter motion and variants of their interaction.

What is mechanical energy

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

A = ∆E

Since energy is a characteristic of the state of the 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] \u003d [E] \u003d 1 J.

Types of mechanical energy

Mechanical free energy is divided into two types: kinetic and potential.

Kinetic energy- is the mechanical energy of the body, which is determined by the speed of its movement.

E k \u003d 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 point in time can be different. Therefore, kinetic energy is a relative quantity, it is determined by the choice of a reference frame.

If a force (or several forces simultaneously) 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 was given the name - kinetic energy theorem.

Potential energy called the energy due to the interaction between bodies.

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

Ep = mgh

Unlike kinetic energy E k potential Ep can be negative when h<0 (for example, a body lying at the bottom of a well).

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

E p = 1/2 kx 2

The energy of deformation has found wide application in practice (toys), in technology - automata, relays and others.

E = Ep + Ek

full mechanical energy bodies are called the sum of energies: kinetic and potential.

Law of conservation of mechanical energy

Some of the most accurate experiments conducted in the middle of the 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 for 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 the forces of interaction of charges, and others. One form of energy can be converted into another, for example, kinetic energy is converted into thermal energy during the braking 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 = Ep + Ek = const

When the force of friction between bodies acts, then there is a decrease in mechanical energy, however, in this case, it is not lost without a trace, but goes into thermal (internal). If an external force performs work on a closed system, then there is an increase in mechanical energy by the amount of work performed by this force. If a closed system performs work on external bodies, then there is a reduction in the mechanical energy of the system by the amount of work done by it.
Each type of energy can be completely transformed into any other type of energy.

The word "energy" comes from the Greek language and means "action", "activity". The concept itself was first introduced by an English physicist at the beginning of the 19th century. By "energy" is meant the ability of a body possessing this property to do work. The body is able to do the more work, the more energy it has. There are several types of it: internal, electrical, nuclear and mechanical energy. The latter is more common than others in our daily life. Since ancient times, man has learned to adapt it to his needs, transforming it into mechanical work using a variety of devices and structures. We can also transform one form of energy into another.

Within the framework of mechanics (one of the mechanical energy is a physical quantity that characterizes the ability of a system (body) to perform mechanical work. Therefore, an indicator of the presence of this type of energy is the presence of a certain speed of the body, having which it can do work.

Types of mechanical In each case, kinetic energy is a scalar quantity, consisting of the sum of the kinetic energies of all material points that make up a particular system. While the potential energy of a single body (system of bodies) depends on the relative position of its (their) parts within the external force field. The indicator of change in potential energy is the perfect work.

The body has kinetic energy if it is in motion (otherwise it can be called the energy of motion), and potential energy if it is raised above the earth's surface to some height (this is the energy of interaction). Mechanical energy is measured (like other types) in Joules (J).

To find the energy that a body has, you need to find the work spent on transferring this body to the current state from the zero state (when the body's energy is equal to zero). The following are formulas according to which mechanical energy and its types can be determined:

Kinetic - Ek=mV 2 /2;

Potential - Ep = mgh.

In the formulas: m is the mass of the body, V is its speed, g is the acceleration of the fall, h is the height to which the body is raised above the earth's surface.

Finding for a system of bodies is to identify the sum of its potential and kinetic components.

Examples of how mechanical energy can be used by man are the tools invented in ancient times (knife, spear, etc.), and the most modern watches, airplanes, and other mechanisms. As sources of this type of energy and the work performed by it, the forces of nature (wind, sea currents of rivers) and the physical efforts of a person or animals can act.

Today, very often systems (for example, the energy of a rotating shaft) are subject to subsequent conversion in the production of electrical energy, for which current generators are used. Many devices (motors) have been developed that are capable of continuously converting the potential of the working fluid into mechanical energy.

There is a physical law of its conservation, according to which in a closed system of bodies, where there is no action of friction and resistance forces, the constant value will be the sum of both types of it (Ek and Ep) of all its constituent bodies. Such a system is ideal, but in reality such conditions cannot be achieved.

The value that equates to half of the product of the mass of a given body and the speed of this body squared is called in physics the kinetic energy of the body or the energy of action. The change or inconstancy of the kinetic or driving energy of the body for some time will be equal to the work that has been done for a given time by a certain force acting on a given body. If the work of any force along a closed trajectory of any type is equal to zero, then a force of this kind is called a potential force. The work of such potential forces will not depend on the trajectory along which the body moves. Such work is determined by the initial position of the body and its final position. The starting point or zero for the potential energy can be chosen absolutely arbitrarily. The value that will be equal to the work done by the potential force to move the body from a given position to the zero point is called in physics the potential energy of the body or the energy of the state.

For different types of forces in physics, there are different formulas for calculating the potential or stationary energy of a body.

The work done by potential forces will be equal to the change in this potential energy, which must be taken in the opposite sign.

If you add the kinetic and potential energy of the body, you get a value called the total mechanical energy of the body. In a position where a system of several bodies is conservative, the law of conservation or constancy of mechanical energy is valid for it. A conservative system of bodies is such a system of bodies that is subject to the action of only those potential forces that do not depend on time.

The law of conservation or constancy of mechanical energy is as follows: "During any processes that occur in a certain system of bodies, its total mechanical energy always remains unchanged." Thus, the total or all mechanical energy of any body or any system of bodies remains constant if this system of bodies is conservative.

The law of conservation or constancy of total or all mechanical energy is always invariant, that is, its form of writing does not change, even when the starting point of time is changed. This is a consequence of the law of homogeneity of time.

When dissipative forces begin to act on the system, for example, such as, then a gradual decrease or decrease in the mechanical energy of this closed system occurs. This process is called energy dissipation. A dissipative system is a system in which the energy can decrease over time. During dissipation, the mechanical energy of the system is completely converted into another. This is fully consistent with the universal law of energy. Thus, there are no completely conservative systems in nature. One or another dissipative force will necessarily take place in any system of bodies.