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 the body (or system of bodies), for example, the conservation law mechanical energy is not performed. 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 allows you to establish a quantitative relationship between various forms the 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 shaft resistance force is an external force, so the work of this force is equal to the change kinetic energy bullets: 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 value highest compression springs, 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:

Lab #3

Topic:"Conservation of mechanical energy when a body moves under the action of gravity and elasticity"

Target: 1) learn how to measure potential energybody raised above the ground and elastically deformed springs;

2) compare two quantities - a decrease in the potential energy of a body attached to a spring when it falls and an increase in the potential energy of a stretched spring.

Devices and materials: 1) a dynamometer with a spring stiffness of 40 N/m; 2) measuring ruler; 3) cargo from the mechanics kit; the weight of the load is (0.100 ±0.002) kg; 4) retainer; 5) a tripod with a clutch and foot.

Basic information.

If a body is capable of doing work, then it is said to have energy.

mechanical energy of the bodyit is a scalar value equal to the maximum work that can be done under given conditions.

Denoted E SI unit of energy

Kinetic energy - is the energy of a body due to its motion.

A physical quantity equal to half the product of the body's mass and the square of its speed is called kinetic energybody:

Kinetic energy is the energy of motion. Kinetic energy of a body of mass m moving at a speed is equal to the work that must be done by the force applied to a body at rest to tell it this speed:

Along with kinetic energy or energy of motion in physics important role plays concept potential energy or interaction energies of bodies.

Potential energy– the energy of a body due to the mutual arrangement of interacting bodies or parts of one body.

Potential energy bodies in the field of gravity(potential energy of a body raised above the ground).

Ep = mgh

It is equal to the work done by gravity when the body is lowered to the zero level.

A stretched (or compressed) spring is capable of setting in motion a body attached to it, that is, imparting kinetic energy to this body. Therefore, such a spring has a reserve of energy. The potential energy of a spring (or any elastically deformed body) is the quantity

Where k is the stiffness of the spring, x is the absolute elongation of the body.

Potential energy of an elastically deformed body is equal to the work of the elastic force during the transition from a given state to a state with zero deformation.

Potential energy during elastic deformation is the energy of interaction of individual parts of the body with each other by elastic forces.

If the bodies that make up closed mechanical system, interact with each other only by the forces of gravity and elasticity, then the work of these forces is equal to the change in the potential energy of the bodies, taken with the opposite sign:

A = -(Ep2 - Ep1).

According to the kinetic energy theorem, this work is equal to the change in the kinetic energy of bodies:

Hence Ek2 – Ek1 = –(Ep2 – Ep1) or Ek1 + Ep1 = Ek2 + Ep2.

The sum of the kinetic and potential energy of the bodies that make up a closed system and interact with each other by gravitational and elastic forces remains unchanged.

This statement expresses law of energy conservation in mechanical processes. It is a consequence of Newton's laws.

The sum E = Ek + Ep is called full mechanical energy.

The total mechanical energy of a closed system of bodies interacting with each other only by conservative forces does not change with any movements of these bodies. There are only mutual transformations of the potential energy of bodies into their kinetic energy, and vice versa, or the transfer of energy from one body to another.

E = Ek + Ep = const

The law of conservation of mechanical energy is fulfilled only when bodies in a closed system interact with each other by conservative forces, that is, forces for which the concept of potential energy can be introduced.

In real conditions, almost always moving bodies, along with gravitational forces, elastic forces and other conservative forces, are affected by friction forces or resistance forces of the medium.

The friction force is not conservative. The work of the friction force depends on the length of the path.

If friction forces act between the bodies that make up a closed system, then mechanical energy is not conserved. Part of the mechanical energy is converted into internal energy of bodies (heating).

Description of the installation.

For work, the installation shown in the figure is used. It is a dynamometer mounted on a tripod with lock 1.

The dynamometer spring ends with a wire rod with a hook. The latch (on an enlarged scale it is shown separately - marked with the number 2) is a light cork plate (5 X 7 X 1.5 mm in size), cut with a knife to its center. It is mounted on the wire rod of the dynamometer. The retainer should move along the rod with little friction, but the friction must still be sufficient so that the retainer does not fall down on its own. You need to make sure of this before starting work. To do this, the latch is installed at the lower edge of the scale on the restrictive bracket. Then stretch and release.

The latch together with the wire rod should rise up, marking the maximum elongation of the spring, equal to the distance from the stop to the latch.

If we raise the load hanging on the hook of the dynamometer so that the spring is not stretched, then the potential energy of the load with respect to, for example, the surface of the table is equal to mgh. When the load falls (lowering a distance x = h) the potential energy of the load will decrease by

E 1 \u003d mg

and the energy of the spring when it is deformed increases by

E 2 \u003d kx 2 / 2

Work order

1. Attach the weight from the mechanics kit firmly to the hook of the dynamometer.

2. Raise the load by hand, unloading the spring, and install the latch at the bottom of the bracket.

3. Release the load. As the weight falls, it stretches the spring. Remove the load and measure the maximum elongation with a ruler by the position of the latch X springs.

4. Repeat the experiment five times. Find the average of h and x

5. Count E 1sr \u003d mgh and E 2cp \u003d kx 2 / 2

6. Enter the results in the table:

experience number	h \u003d x max, m	h cf = x cf, m	E 1sr, J	E 2sr, J	E 1sr / E 2sr
experience number	h \u003d x max, m					h cf = x cf, m	E 1sr, J	E 2sr, J	E 1sr / E 2sr
	0,048
	0,054
	0,052
	0,050
	0,052

2. We perform calculations according to the manual.

1. You met the concept of energy in the 7th grade physics course. Let's remember him. Let us suppose that some body, for example a trolley, slides down an inclined plane and moves a bar lying at its base. The cart is said to do work. Indeed, it acts on the bar with a certain elastic force, and the bar moves in this case.

Another example. The driver of a car moving at a certain speed applies the brakes, and the car stops after some time. In this case, the car also does work against the friction force.

They say that if a body can do work, then it has energy.

Energy is denoted by the letter E. SI unit of energy - joule (1 J).

2. There are two types of mechanical energy - potential and kinetic.

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

All interacting bodies have potential energy. So, any body interacts with the Earth, therefore, the body and the Earth have potential energy. The particles that make up bodies also interact with each other, and they also have potential energy.

Since potential energy is the energy of interaction, it does not refer to one body, but to a system of interacting bodies. In the case when we are talking about the potential energy of a body raised above the Earth, the system consists of the Earth and the body raised above it.

3. Let's find out what the potential energy of a body raised above the Earth is. To do this, we will find the relationship between the work of gravity and the change in the potential energy of the body.

Let the body mass m falls from a height h 1 to height h 2 (Fig. 72). In this case, the displacement of the body is h = h 1 – h 2. The work of gravity in this area will be equal to:

A = F heavy h = mgh = mg(h 1 – h 2), or
A = mgh 1 – mgh 2 .

Value mgh 1 = E n1 characterizes the initial position of the body and represents its potential energy in the initial position, mgh 2 = E n2 - potential energy of the body in the final position. The formula can be rewritten as follows:

A = E p1 - E n2 = -( E p2 - E n1).

When the position of the body changes, its potential energy changes. In this way,

the work of gravity is equal to the change in the potential energy of the body, taken with the opposite sign.

The minus sign means that when the body falls, the force of gravity does positive work, and the potential energy of the body decreases. If the body moves up, then the force of gravity does negative work, and the potential energy of the body increases.

4. When determining the potential energy of a body, it is necessary to indicate the level relative to which it is measured, called zero level.

So, the potential energy of a ball flying over a volleyball net has one value relative to the net, and another value relative to the floor of the gym. It is important that the difference between the potential energies of the body at two points does not depend on the chosen zero level. This means that the work done due to the potential energy of the body does not depend on the choice of the zero level.

Often, the surface of the Earth is taken as the zero level when determining potential energy. If a body falls from a certain height onto the surface of the Earth, then the work done by gravity is equal to the potential energy: A = mgh.

Consequently, The potential energy of a body raised to a certain height above the zero level is equal to the work done by gravity when the body falls from this height to the zero level.

5. Any deformed body has potential energy. When a body is compressed or stretched, it deforms, the forces of interaction between its particles change and an elastic force arises.

Let the right end of the spring (see Fig. 68) move from the point with coordinate D l 1 to the point with coordinate D l 2. Recall that the work of the elastic force in this case is equal to:

A =– .

Value = E n1 characterizes the first state of the deformed body and represents its potential energy in the first state, the value = E n2 characterizes the second state of the deformed body and represents its potential energy in the second state. You can write:

A = –(E p2 - E n1), i.e.

the work of the elastic force is equal to the change in the potential energy of the spring, taken with the opposite sign.

The minus sign shows that as a result of the positive work done by the elastic force, the potential energy of the body decreases. When a body is compressed or stretched under the action of an external force, its potential energy increases, and the elastic force does negative work.

Questions for self-examination

1. When can we say that the body has energy? What is the unit of energy?

2. What is potential energy?

3. How to calculate the potential energy of a body raised above the Earth?

4. Does the potential energy of a body raised above the Earth depend on the zero level?

5. How to calculate the potential energy of an elastically deformed body?

Task 19

1. What work must be done in order to shift a bag of flour weighing 2 kg from a shelf located at a height of 0.5 m relative to the floor to a table located at a height of 0.75 m relative to the floor? What is the potential energy of the bag of flour lying on the shelf, and its potential energy when it is on the table, relative to the floor?

2. What work must be done to transfer a spring with a stiffness of 4 kN/m to the state 1 , stretching it by 2 cm? What additional work must be done to bring the spring to the state 2 , stretching it another 1 cm? What is the change in the potential energy of the spring when it is transferred to the state 1 and from the state 1 into a state 2 ? What is the potential energy of the spring in the state 1 and able 2 ?

3. Figure 73 shows a graph of the force of gravity acting on the ball versus the height of the ball. Calculate, using the graph, the potential energy of the ball at a height of 1.5 m.

4. Figure 74 shows a graph of the dependence of the elongation of the spring on the force acting on it. What is the potential energy of the spring when it is extended 4 cm?

Work and kinetic energy

Kinetic energy is the energy of a mechanical system, which depends on the speed of movement of its points in the chosen frame of reference. Often allocate the kinetic energy of translational and rotational motion. in plain language, kinetic energy is the energy that a body has only when moving. When the body is not moving, the kinetic energy is zero. Work and change in the speed of the body. Let's establish a connection between the work of a constant force and a change in the speed of a body. In this case, the work done by the force can be defined as . The modulus of force according to Newton's second law is , and the modulus of displacement for uniformly accelerated rectilinear motion

. (19.3) The work of the resultant forces applied to the body is equal to the change in the kinetic energy of the body. This statement is called the kinetic energy theorem.

Since the change in kinetic energy is equal to the work of the force (19.3), the kinetic energy is expressed in the same units as the work, i.e. in joules.

If the initial speed of a body with mass is zero and the body increases its speed to the value , then the work of the force is equal to the final value of the kinetic energy of the body:

. (19.4) Since the displacement coincides in direction with the vector of gravity, the work of gravity is equal to

. (20.1) what the work of gravity does not depend on the trajectory of the body and is always equal to the product of the modulus of gravity and the difference in heights in the initial and final positions. When moving down, the work of gravity is positive, when moving up, it is negative. The work of gravity on a closed trajectory is zero. The value of the potential energy of a body raised above the Earth depends on the choice of the zero level, i.e. the height at which the potential energy is assumed to be zero. It is usually assumed that the potential energy of a body on the surface of the Earth is zero.

Solutions, osmotic pressure. Humidity: relative and absolute humidity, dew point. Osmotic pressure(denoted by π) is the excess hydrostatic pressure on a solution separated from a pure solvent by a semipermeable membrane, at which diffusion of the solvent through the membrane stops (osmosis). This pressure tends to equalize the concentrations of both solutions due to the counter diffusion of the solute and solvent molecules. The value of the osmotic pressure created by the solution depends on the amount, and not on the chemical nature of the substances dissolved in it (or ions, if the molecules of the substance dissociate), therefore, the osmotic pressure is a colligative property of the solution.

The greater the concentration of a substance in a solution, the greater the osmotic pressure it creates. This rule, called the law of osmotic pressure, is expressed by a simple formula, very similar to some ideal gas law: , where i is the isotonic coefficient of the solution; C is the molar concentration of the solution, expressed in terms of a combination of basic SI units, that is, in mol / m 3, and not in the usual mol / l; R is the universal gas constant; T is the thermodynamic temperature of the solution.

Absolute air humidity (f) is the amount of water vapor actually contained in 1m 3 of air: f = m (mass of water vapor contained in the air) / V (volume of humid air). Commonly used absolute humidity unit: (f) = g / Relative humidity: φ = (absolute humidity) / (maximum humidity). Relative humidity is usually expressed as a percentage. These values ​​are interconnected by the following relationship: φ = (f × 100) / fmax. The dew point is the temperature to which the air must be cooled in order for the vapor it contains to reach saturation and begin to condense into dew.

Crystalline and amorphous solids. liquid crystals. Deformation of solid bodies. Types of deformation.

Solid- the state of aggregation of matter, characterized by the constancy of the form and the nature of the movement of atoms, which make small vibrations around the equilibrium positions. Crystalline bodies. Solid body in normal conditions difficult to compress or stretch. To give solids the desired shape or volume in plants and factories, they are processed on special machines: turning, planing, grinding. Amorphous bodies. In addition to crystalline, amorphous bodies are also referred to as solids.

AT- These are solid bodies, which are characterized by a disordered arrangement of particles in space. Amorphous bodies include glass, amber, various other resins, and plastics. Although at room temperature these bodies retain their shape, but with increasing temperature they gradually soften and begin to flow like liquids: amorphous bodies do not have a certain temperature, melting. Liquid crystals - This is a phase state into which some substances pass under certain conditions (temperature, pressure, concentration in solution).

LCD possess simultaneously the properties of both liquids (fluidity) and crystals (anisotropy). Solid body deformation- change in linear dimensions or shapes of a solid body under the action of external forces. Types of deformations : Deformation sprains or compression- change of any linear size of the body (length, width or height). Deformation shear- displacement of all layers of a solid body in one direction parallel to a certain shear plane. Deformation bending- compression of some parts of the body while stretching others. Deformation torsion- rotation of parallel sections of the sample around some axis under the action of an external force.

Mechanical properties of solids. Hooke's Law. Deformation curve. Limits of elasticity and strength. Plastic deformation.

Under the action of applied external forces, solid bodies change their shape and volume - they are deformed. If after the termination of the force, the shape and volume of the body are completely restored, then the deformation is called elastic, and the body is perfectly elastic. Deformations that do not disappear after the cessation of the forces are called plastic, and the bodies are plastic. There are the following types of deformations: tension, compression, shear, torsion and bending. Tensile strain is characterized by absolute elongation delta l and elongation e: where l 0- initial length, l- the final length of the rod. Mechanical stress is the ratio of the modulus of elasticity F to the cross-sectional area of ​​the body S: b=F/S.

In SI, 1Pa \u003d 1N / m 2 is taken as a unit of mechanical stress. Hooke's Law: at small strains, the stress is directly proportional to the relative elongation (b= E. e). elastic deformation is called such, in which, after the termination of the force, the body restores its original shape and size. plastic deformation name one in which, after the termination of the load, the body does not restore its original shape and size. Plastic deformation is always preceded by elastic.

Basic equation of the molecular kinetic theory of gases.

The ideal gas model is used to explain the properties of matter in the gaseous state. The ideal gas model assumes the following: the molecules have a negligible volume compared to the volume of the vessel, there are no attractive forces between the molecules, and when molecules collide with each other and with the walls of the vessel, repulsive forces act. The pressure of an ideal gas. One of the first and important successes of the molecular kinetic theory was the qualitative and quantitative explanation of the phenomenon of gas pressure on the walls of a vessel. Qualitative explanation of pressure with the walls of the vessel interact with them according to the laws of mechanics as elastic bodies. When a molecule collides with the wall of the vessel, the projection of the velocity vector onto the OX axis, perpendicular to the wall, changes its sign to the opposite, but remains constant in modulus

Therefore, as a result of a collision of a molecule with a wall, the projection of its momentum on the OX axis changes from to . The change in the momentum of the molecule shows that a force acts on it during a collision, directed from the wall. The change in the momentum of the molecule is equal to the momentum of the force: During the collision, the molecule acts on the wall with a force equal, according to Newton's third law, to the force in absolute value and directed oppositely. There are a lot of gas molecules, and their impacts against the wall follow one after another with a very high frequency. The average value of the geometric sum of the forces acting on the part of individual molecules in their collisions with the vessel wall is the gas pressure force. The gas pressure is equal to the ratio of the modulus of the pressure force to the area of ​​the wall S: Based on the use of the basic provisions of the molecular kinetic theory, an equation was obtained that made it possible to calculate the gas pressure if the mass m0 of the gas molecule, the average value of the square of the velocity of molecules and the concentration n of molecules are known: - this is the equation is called the basic equation of molecular kinetic theory. Denoting the average value of the kinetic energy of the translational motion of molecules of an ideal gas : we get . The pressure of an ideal gas is equal to two-thirds of the average kinetic energy of the translational motion of the molecules contained in a unit volume.

Internal energy of the system as a function of state. Equivalence of heat and work. First law of thermodynamics.

Internal energy - thermodynamic function of the state of the system, its energy, determined by the internal state. It consists mainly of the kinetic energy of the movement of particles (atoms, molecules, ions , electrons) and the interaction energy between them (intra- and intermolecular). Internal energy is affected by a change in the internal state of the system under the action of an external field; the internal energy includes, in particular, the energy associated with the polarization of the dielectric in an external electric field and the magnetization of the paramagnet in an external magnetic field.

The kinetic energy of the system as a whole and the potential energy due to the spatial arrangement of the system are not included in the internal energy. In thermodynamics, only the change in internal energy in various processes is determined. Therefore, the internal energy is set up to a certain constant term, depending on the energy taken as the reference zero. Internal energy U as a state function is introduced by the first law of thermodynamics, according to which the difference between the heat Q transferred to the system and the work W performed by the system depends only on the initial and final states of the system and does not depend on the transition path, i.e. represents the change in the state function Δ U where U 1 and U 2- internal energy of the system in the initial and final states, respectively. Equation (1) expresses the law of conservation of energy as applied to thermodynamic processes, i.e. processes in which heat is transferred. For a cyclic process that returns the system to its initial state, Δ U= 0. In isochoric processes, i.e. processes at a constant volume, the system does not perform work due to expansion, W= 0 and the heat transferred to the system is equal to the increment of internal energy: Q v= Δ U. For adiabatic processes, when Q= 0, Δ U= -W. Internal energy system as a function of its entropy S, volume V, and the number of moles m i of the i-th component is the thermodynamic potential. This is a consequence of the first and second laws of thermodynamics and is expressed by the relationship:

Relative permittivity. Electrical constant. Electric field strength.

The dielectric constant medium - a physical quantity that characterizes the properties of an insulating (dielectric) medium and shows the dependence of electrical induction on tension electric field. The relative permittivity ε is dimensionless and shows how many times the force of interaction of two electric charges in a medium is less than in vacuum. This value for air and most other gases under normal conditions is close to unity (because of their low density).

For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. The electrical constant (e 0) is a physical constant included in the equations of the laws of electric. fields (eg. Coulomb's law) when writing these ur-tions in a rationalized form, in accordance with a swarm formed by electric. and magn. units International system of units; according to the old terminology, E. p. is called a dielectric. vacuum permeability. where m 0 - magnetic constant. Unlike the dielectric permeability e, depending on the type of substance, temperature, pressure, and other parameters, E. p. e 0 depends only on the choice of a system of units.

For example, in a Gaussian cgs system of units electric field strength in classical electrodynamics ( E) - vector characteristic of electric. fields, the force acting on a unit electric at rest in a given reference frame. charge. It is assumed that the introduction of a charge (charged test body) in the external. field E does not change it. Sometimes instead of H. e. etc. just say "electric field". Dimension N. e. n. in the Gaussian system - L -1/2 M 1/2 T -1, in SI - LMT -3 I -1; unit H. e. p. in SI is the volt per meter (1 CGSE = 3.10 4 V/m). Distribution of H. e. n. in space is usually characterized using a family of lines E(field lines of the electric field), tangents to k-rsh at each point coincide with the directions of the vector E.

Like any vector field, the field E is divided into two components: potential ([ E n) = 0, E n = - j e) and vortex ( E B = 0 E B=[ A m]). In particular, electric the field created by a system of fixed charges is purely potential. Electric radiation field, including field E in transverse el.-magp. waves, is purely vortex. Together with the vector magn. induction AT H. e. n. constitutes a single 4-tensor of the electromagnetic field.

Therefore, purely electric. the field of a given system of charges exists only in the "chosen" frame of reference, where the charges are motionless. In other inertial frames of reference, moving relative to the "chosen" from the post. speed u, there is also a magnetic field AT" = = [uE]/ , due to the appearance of convections. currents j= r u/ (r is the charge density in the "chosen" system).

Objective: Compare the decrease in the potential energy of the stretched spring with the increase in the kinetic energy of the body associated with the spring.

Equipment: two tripods for frontal work; training dynamometer; ball; threads; sheets of white and carbon paper; measuring ruler; scales for training with a tripod; weights.

Theoretical basis work

Based on the law of conservation and transformation of energy during the interaction of bodies by elastic forces, the change in the potential energy of a stretched spring must be equal to the change in the kinetic energy of the body associated with it, taken with the opposite sign:

For experimental verification of this statement, you can use the setup shown in Figure 1. A dynamometer is fixed in the foot of the tripod. A ball is tied to its hook on a thread 60-80 cm long. On another tripod, at the same height with a dynamometer, a chute is fixed in the foot. After placing the ball on the edge of the chute and holding it, move the second tripod away from the first by the length of the thread. If you move the ball away from the edge of the chute by X, then as a result of deformation, the spring will acquire a supply of potential energy

where k- spring stiffness.

The ball is then released. Under the action of the elastic force, the ball acquires speed v. Neglecting the losses caused by the action of the friction force, we can assume that the potential energy of the stretched spring is completely converted into the kinetic energy of the ball:

Rice. one

The speed of a ball can be determined by measuring its range. S in free fall from a height h. From the expressions and it follows that . Then

The purpose of the work is to check equality:

Taking into account equality, we get:

Work order

1. Fix the dynamometer and chute on tripods on the same
height h= 40 cm from the table surface. Hook a thread tied to the ball at the other end of the dynamometer hook. Place a sheet of white paper on the intended place where the ball will fall and a sheet of carbon paper on top of it.

The distance between the tripods should be such that the ball is on the edge of the chute with the thread stretched and the dynamometer spring not deformed.

2. Move the ball away from the edge of the chute until the reading
dynamometer will not become equal F y = 2H. Release the ball and note the place of its fall on the table according to the mark on the sheet of paper.

Repeat the experiment at least 10 times. Determine the average flight distance S c.p.

3. Measure the deformation X dynamometer springs with elastic force F y = 2 N. Calculate the potential energy of the stretched spring.

4. Measure the mass of the ball using a balance and calculate the increase in its kinetic energy.

5. Record the results of measurements and calculations in the reporting table.

Reporting table

Experience No.	F y , N	x, m	E r, J	Δ E r, J	m, kg	h, m v	S, m	E k , J	Δ E k , J

Because , then the relative error limit is:

The absolute error limit is:

Since , then the limit of the relative error is equal to:

Errors ε m, εg and ε h, compared with the error ε s can be neglected.

In this case

The conditions of the experiment on measuring the flight range are such that the deviations of the results of individual measurements from the average are much higher than the boundary of the systematic error ( ), so we can assume that ().

The boundary of the random error of the arithmetic mean with a small number of measurements N is found by the formula:

,

where is calculated by the formula

In this way,

The limit of the absolute error in measuring the kinetic energy of the ball is:

7. Conclude that the law of conservation of energy is satisfied by checking whether the common points have intervals

test questions

1. Define energy.

2. What is called kinetic energy?

3. Express the kinetic energy in terms of the momentum of the body.

4. What forces are called conservative?

5. What is called potential energy?

6. Write down the expression for the potential energy of a body raised above the Earth's surface and a compressed spring.

7. Formulate the law of conservation of total mechanical energy.

8. In what cases is the law of conservation of mechanical energy fulfilled?

9. Whether the law of conservation of total mechanical energy is fulfilled in a closed system in which only gravitational force and elastic forces act.

10. How can one explain the inaccurate equality of changes in the potential energy of the spring and the kinetic energy of the ball?

Creative workshop

Two springs with stiffness coefficients k 1 and k 2 are connected once in series and another time in parallel. What should be the stiffness k of the spring, which could replace this system of two springs? The initial length of the springs is the same.

Lab #4