Springs can be called one of the most common parts that are part of simple and complex mechanisms. In its manufacture, a special wire is used, wound along a certain trajectory. There are quite a large number of different parameters that characterize this product. The most important is the stiffness coefficient. It determines the basic properties of the part and can be calculated and used in other calculations. Let's take a closer look at the features of this parameter.

Definition and formula of spring stiffness

When considering what a spring constant is, attention should be paid to the concept of elasticity. The symbol F is used to designate it. In this case, the elastic force of the spring is characterized by the following features:

1. It appears exclusively when the body is deformed and disappears if the deformation disappears.
2. When considering what spring stiffness is, it should be taken into account that after the external load is removed, the body can restore its size and shape, partially or completely. In such a case, the deformation is considered elastic.

Do not forget that rigidity is a characteristic characteristic of elastic bodies capable of deformation. A fairly common question is how spring stiffness is indicated on drawings or in technical documentation. The letter k is most often used for this.

Too much deformation of the body causes various defects to appear. The key features are the following:

1. The part can maintain its geometric parameters during long-term use.
3. As the index increases, the compression of the spring under the influence of the same force decreases significantly.
4. The most important parameter can be called the stiffness coefficient. It depends on the geometric parameters of the product and the type of material used in manufacturing.

Red springs of another type have become quite widespread. Color designation is used in the production of automotive products. The following formula is used for the calculation: k=Gd 4 /8D 3 n. This formula contains the following notations:

1. G – used to determine the shear modulus. It is worth considering that this property largely depends on the material used in the manufacture of the coils.
2. d – diametrical indicator of the wire. It is produced by rolling. This parameter is also indicated in the technical documentation.
3. D is the diameter of the turns created when the wire is wound around the axis. It is selected depending on the tasks assigned. In many ways, the diameter determines how much load is applied to compress the device.
4. n – number of turns. This indicator can vary over a fairly wide range and also affects the basic performance characteristics of the product.

The formula under consideration is used in the case of calculating the stiffness coefficient for cylindrical springs, which are installed in a wide variety of mechanisms. This unit is measured in Newtons. The stiffness coefficient for standardized products can be found in the technical literature.

Spring connection stiffness formula

Do not forget that in some cases the body is connected by several springs. Such systems have become very widespread. Determining rigidity in this case is much more difficult. Among the features of the connection, the following points can be noted:

1. A parallel connection is characterized by the fact that the parts are placed in series. This method can significantly increase the elasticity of the created system.
2. The sequential method is characterized by the fact that the parts are connected to each other. This method of connection significantly reduces the degree of elasticity, but allows a significant increase in maximum elongation. In some cases, it is the maximum extension that is required.

In both cases, a certain formula is used that determines the characteristics of the connection. The modulus of elastic force may vary significantly depending on the characteristics of a particular product.

When connecting products in series, the indicator is calculated as follows: 1/k=1/k 1 +1/k 2 +…+1/k n. The indicator in question is considered a rather important property, in this case it decreases. The parallel connection method is calculated as follows: k=k 1 +k 2 +…k n.

Such formulas can be used in a wide variety of calculations, most often at the time of solving mathematical problems.

Spring connection stiffness coefficient

The above indicator of the stiffness coefficient of a part for a parallel or series connection determines many characteristics of the connection. Quite often it is determined what the elongation of a spring is. Among the features of a parallel or serial connection, the following points can be noted:

1. When connected in parallel, the elongation of both products will be equal. Do not forget that both options must have the same length in the free position. With sequential, the indicator doubles.
2. Free position - a situation in which the part is located without applying a load. This is what is taken into account in calculations in most cases.
3. The stiffness coefficient varies depending on the connection method used. In the case of a parallel connection, the indicator doubles, and in a serial connection it decreases.

To carry out calculations, you need to build a connection diagram for all elements. The base is represented by a hatched line, the product is indicated schematically, and the body in a simplified form. In addition, kinetic and other energy largely depends on elastic deformation.

Coil spring stiffness coefficient

In practice and in physics, it is cylindrical springs that have become quite widespread. Their key features include the following:

1. When creating, a central axis is specified, along which most of the various forces act.
2. In the production of the product in question, wire of a certain diameter is used. It is made of a special alloy or ordinary metals. Do not forget that the material must have increased elasticity.
3. The wire is wound in turns along the axis. It is worth considering that they can be the same or different diameters. The cylindrical version has become quite widespread, but the cylindrical version is characterized by greater stability; in the compressed state, the part has a small thickness.
4. The main parameters include the large, medium and small diameter of the turns, the diameter of the wire, and the pitch of the individual rings.

Do not forget that there are two types of parts: compression and tension. Their stiffness coefficient is determined by the same formula. The difference is this:

1. The compression version is characterized by a distant arrangement of turns. Due to the distance between them, compression is possible.
2. The model, designed for stretching, has rings located almost closely. This shape determines that maximum elastic force is achieved with minimal stretching.
3. There is also a design option that is designed for torsion and bending. Such a detail is calculated using certain formulas.

Calculation of the coefficient of a cylindrical spring can be carried out using the previously specified formula. It determines that the indicator depends on the following parameters:

1. Outer radius of the rings. As previously noted, when manufacturing a part, an axis is used, around which the rings are wound. At the same time, do not forget that the average and inner diameters are also distinguished. A similar indicator is indicated in the technical documentation and drawings.
2. The number of turns created. This parameter largely determines the free length of the product. In addition, the number of rings determines the stiffness coefficient and many other parameters.
3. The radius of the wire used. The starting material is wire, which is made from various alloys. In many ways, its properties influence the quality of the product in question.
4. Shear modulus, which depends on the type of material used.

The stiffness coefficient is considered one of the most important parameters, which is taken into account when carrying out a variety of calculations.

Units

When carrying out calculations, the units of measurement in which the calculations are carried out must also be taken into account. When considering what the elongation of a spring is, attention is paid to the unit of measurement in Newtons.

In order to simplify the selection of a part, many manufacturers indicate it by color designation.

The division of springs by color is carried out in the automotive industry.

Among the features of such marking we note the following:

1. Class A is indicated by white, yellow, orange and brown shades.
2. Class B is available in blue, cyan, black and yellow.

As a rule, a similar property is noted on the outside of the coil. Manufacturers apply a small strip, which greatly simplifies the selection process.

Features of calculating the stiffness of spring connections

The above information indicates that the stiffness coefficient is a fairly important parameter that must be calculated when choosing the most suitable product and in many other cases. That is why a fairly common question is how to find the spring stiffness. Among the features of the connection, we note the following:

1. The spring stretch can be determined during the calculation, as well as at the time of the test. This indicator may depend on the wire and other parameters.
2. A variety of formulas can be used for calculations, and the resulting result will be practically error-free.
3. It is possible to conduct tests, during which the main parameters are identified. This can only be determined by using special equipment.

As previously noted, there are serial and parallel connection methods. Both are characterized by their own specific characteristics that must be taken into account.

In conclusion, we note that the part in question is an important part of the design of various mechanisms. An incorrect design will not last for a long period. At the same time, we should not forget that too much deformation causes deterioration in performance characteristics.

Definition and formula of spring stiffness coefficient

The elastic force (), which arises as a result of deformation of a body, in particular a spring, directed in the direction opposite to the movement of particles of the deformed body, is proportional to the elongation of the spring:

It depends on the shape of the body, its size, and the material from which the body is made (spring).

Sometimes the stiffness coefficient is denoted by the letters D and c.

The value of the spring stiffness coefficient indicates its resistance to loads and how great its resistance is when exposed.

Spring connection stiffness coefficient

If a certain number of springs are connected in series, then the total stiffness of such a system can be calculated as:

In the event that we are dealing with n springs that are connected in parallel, then the resulting stiffness is obtained as:

Coil spring stiffness coefficient

Let's consider a spring in the form of a spiral, which is made of wire with a circular cross-section. If we consider the deformation of a spring as a set of elementary shifts in its volume under the influence of elastic forces, then the stiffness coefficient can be calculated using the formula:

where is the radius of the spring, is the number of turns in the spring, is the radius of the wire, is the shear modulus (a constant that depends on the material).

Units

The basic unit of measurement of the stiffness coefficient in the SI system is:

Examples of problem solving

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Elasticity coefficient - Chemist's Handbook 21

Rice. 61. Coefficient of elastic expansion of coke obtained in a cube from the cracking residue of sulfurous Devonian oil and calcined at 1300 °C for 5 hours

mylink" data-url="http://chem21.info/info/392465/">chem21.info Elements of the theory of elasticity | Welding world Introduction Under the influence of external forces, any solid body changes its shape - it is deformed. Deformation that disappears when the forces stop acting is called elastic. When a body undergoes elastic deformation, internal elastic forces arise that tend to return the body to its original shape. The magnitude of these forces is proportional to the deformation of the body. Tensile and compressive strain The resulting elongation of the sample (Δl) under the influence of an external force (F) is proportional to the magnitude of the acting force, the initial length (l) and inversely proportional to the cross-sectional area (S) - Hooke's law: The quantity E is called the elastic modulus of the first kind or Young’s modulus and characterizes the elastic properties of the material. The quantity F/S = p is called voltage. The deformation of rods of any length and cross-section (specimens) is characterized by a value called relative longitudinal deformation, ε = Δl/l. Hooke's law for samples of any shape: 2) Young's modulus is numerically equal to the voltage that doubles the length of the samples. However, sample rupture occurs at significantly lower stresses. Figure 1 graphically shows the experimental dependence of p on ε, where pmax is the ultimate strength, i.e. the stress at which a local narrowing (neck) is obtained on the rod, ptek is the yield strength, i.e. the stress at which yielding occurs (i.e., an increase in deformation without an increase in the deforming force), pel is the elastic limit, i.e. voltage below which Hooke's law is valid (meaning short-term action of force). Materials are divided into brittle and ductile. Brittle substances break at very low relative elongations. Brittle materials usually withstand, without breaking, greater compression than tension. Together with tensile deformation, a decrease in the diameter of the sample is observed. If Δd is the change in the diameter of the sample, then ε1 = Δd/d is usually called the relative transverse strain. Experience shows that |ε1/ε| Absolute value μ = |ε1/ε| is called the transverse strain ratio or Poisson's ratio. Shear is a deformation in which all layers of a body parallel to a certain plane are displaced relative to each other. During shear, the volume of the deformed sample does not change. The segment AA1 (Fig. 2), by which one plane has shifted relative to the other, is called the absolute shift. At small shear angles, the angle α ≈ tan α = AA1/AD characterizes the relative deformation and is called the relative shear. where the coefficient G is called the shear modulus. Compressibility of matter All-round compression of the body leads to a decrease in the volume of the body by ΔV and the emergence of elastic forces tending to return the body to its original volume. Compressibility (β) is a quantity numerically equal to the relative change in the volume of a body ΔV/V when the stress (p) acting normal to the surface changes by one. The reciprocal of compressibility is called the bulk modulus (K). The change in body volume ΔV with a comprehensive increase in pressure by ΔP is calculated by the formula Relationships between elastic constants Young's modulus, Poisson's ratio, bulk modulus and shear modulus are related by the equations: which, based on two known elastic characteristics, allow, to a first approximation, to calculate the rest. The potential energy of elastic deformation is determined by the formula Units of elastic modulus: N/m2 (SI), dyne/cm2 (SGS), kgf/m2 (MKGSS) and kgf/mm2. 1 kgf/mm2 = 9.8 106 N/m2 = 9.8 107 dyne/cm2 = 10-6 kgf/m2 Application Table 1 - Strength limits of some materials (kg/mm2) Material Tensile strengthin tension in compression Layered aminoplasts 8 20 Bakelite 2–3 8–10 Concrete - 0,5–3,5 Viniplast 4 8 Getinax 15–17 15–18 Granite 0,3 15–26 Graphite 0,5–1,0 1,6–3,8 Oak (at 15% humidity) along the grain 9,5 5 Oak (at 15% humidity) across the grain - 1,5 Brick - 0,74–3 Brass, bronze 22–50 - Ice (0 °C) 0,1 0,1–0,2 Polystyrene tiles 0,06 - Polyacrylate (plexiglass) 5 7 Polystyrene 4 10 Pine (at 15% humidity) along the grain 8 4 Pine (at 15% humidity) across the grain - 0,5 Steel for structures 38–42 - Silicon-chrome-manganese steel 155 - Carbon steel 32–80 - Rail steel 70–80 - Textolite PTK 10 15–25 Textolite phenoplast 8–10 10–26 Ftoroplast-4 2 - Cellon 4 16 Celluloid 5–7 - White cast iron - up to 175 Gray cast iron fine-grained 21–25 up to 140 Gray ordinary cast iron 14–18 60–100 Table 2 - Elastic moduli and Poisson's ratios Name of material Young's modulus E, 107 N/m2 Shear modulus G, 107 N/m2 Poisson's ratio μ Aluminum 6300–7000 2500–2600 0,32–0,36 Concrete 1500–4000 700–1700 0,1–0,15 Bismuth 3200 1200 0,33 Aluminum bronze, casting 10300 4100 0,25 Rolled phosphor bronze 11300 4100 0,32–0,35 Granite, marble 3500–5000 1400–4400 0,1–0,15 Rolled duralumin 7000 2600 0,31 Limestone is dense 3500 1500 0,2 Invar 13500 5500 0,25 Cadmium 5000 1900 0,3 Rubber 0,79 0,27 0,46 Quartz thread (fused) 7300 3100 0,17 Constantan 16000 6100 0,33 Rolled ship brass 9800 3600 0,36 Manganin 12300 4600 0,33 Rolled copper 10800 3900 0,31–0,34 Cold drawn copper 12700 4800 0,33 Nickel 20400 7900 0,28 Plexiglass 525 148 0,35 Soft vulcanized rubber 0,15–0,5 0,05–0,15 0,46–0,49 Silver 8270 3030 0,37 Alloy steels 20600 8000 0,25–0,30 Carbon steel 19500–20500 800 0,24–0,28 Glass 4900–7800 1750–2900 0,2–0,3 Titanium 11600 4400 0,32 Celluloid 170–190 65 0,39 Rolled zinc 8200 3100 0,27 Cast iron white, gray 11300–11600 4400 0,23–0,27 Table 3 - Compressibility of liquids at different temperatures Substance Temperature, °C In the pressure range, atm Compressibility β, 10-6 atm-1 Acetone 14,2 9–36 111 0 100–500 82 0 500–1000 59 0 1000–1500 47 0 1500–2000 40 Benzene 16 8–37 90 20 99–296 78,7 20 296–494 67,5 Water 20 1–2 46 Glycerol 14,8 1–10 22,1 Castor oil 14,8 1–10 47,2 Kerosene 1 1–15 67,91 16,1 1–15 76,77 35,1 1–15 82,83 52,2 1–15 92,21 72,1 1–15 100,16 94 1–15 108,8 Sulfuric acid 0 1–16 302,5 Acetic acid 25 92,5 81,4 Kerosene 10 1–5,25 74 100 1–5,25 132 Nitrobenzene 25 192 43,0 Olive oil 14,8 1–10 56,3 20,5 1–10 63,3 Paraffin (melting point 55 °C) 64 20–100 83 100 20–400 24 185 20–400 137 Mercury 20 1–10 3,91 Ethanol 20 1–50 112 20 50–100 102 20 100–200 95 20 200–300 86 20 300–400 80 100 900–1000 73 Toluene 10 1–5,25 79 20 1–2 91,5 weldworld.ru Elasticity coefficient - WiKi ru-wiki.org Elasticity coefficient - Wikipedia RU In a series connection there are n(\displaystyle n) springs with stiffnesses k1,k2,...,kn.(\displaystyle k_(1),k_(2),...,k_(n).) From Hooke's law ( F=−kl(\displaystyle F=-kl) , where l is the elongation) it follows that F=k⋅l.(\displaystyle F=k\cdot l.) The sum of the elongations of each spring is equal to the total elongation of the entire connection l1+l2+ ...+ln=l.(\displaystyle l_(1)+l_(2)+...+l_(n)=l.) Each spring is acted upon by the same force F.(\displaystyle F.) According to Hooke's law, F=l1⋅k1=l2⋅k2=...=ln⋅kn.(\displaystyle F=l_(1)\cdot k_(1)=l_(2)\cdot k_(2)=...=l_(n)\cdot k_(n).) From the previous expressions we derive: l=F/k,l1=F/k1,l2 =F/k2,...,ln=F/kn.(\displaystyle l=F/k,\quad l_(1)=F/k_(1),\quad l_(2)=F/k_(2 ),\quad ...,\quad l_(n)=F/k_(n).) Substituting these expressions into (2) and dividing by F,(\displaystyle F,) we get 1/k=1/k1+ 1/k2+...+1/kn,(\displaystyle 1/k=1/k_(1)+1/k_(2)+...+1/k_(n),) which is what needed to be proven. http-wikipedia.ru Poisson's ratio, formula and examples Definition and formula of Poisson's ratio Let us turn to the consideration of the deformation of a solid body. In the process under consideration, a change in the size, volume and often shape of the body occurs. Thus, relative longitudinal stretching (compression) of an object occurs with its relative transverse narrowing (expansion). In this case, the longitudinal deformation is determined by the formula: where is the length of the sample before deformation, is the change in length under load. However, during tension (compression), not only the length of the sample changes, but the transverse dimensions of the body also change. Deformation in the transverse direction is characterized by the magnitude of the relative transverse narrowing (expansion): where is the diameter of the cylindrical part of the sample before deformation (transverse size of the sample). It has been empirically found that under elastic deformations the equality holds: Poisson's ratio, together with Young's modulus (E), is a characteristic of the elastic properties of a material. Poisson's ratio for volumetric strain If the volumetric deformation coefficient () is taken equal to: where is the change in the volume of the body, is the initial volume of the body. Then, for elastic deformations, the following relation holds: Often in formula (6) terms of small orders are discarded and used in the form: For isotropic materials, Poisson's ratio should be within: The existence of negative Poisson's ratio values ​​means that when stretched, the transverse dimensions of an object could increase. This is possible in the presence of physicochemical changes during the deformation of the body. Materials with Poisson's ratio less than zero are called auxetics. The maximum value of Poisson's ratio is a characteristic of more elastic materials. Its minimum value applies to fragile substances. So steels have a Poisson's ratio from 0.27 to 0.32. Poisson's ratio for rubber varies between 0.4 - 0.5. Poisson's ratio and plastic deformation Expression (4) is also true for plastic deformations, but in this case the Poisson’s ratio depends on the magnitude of the deformation: With increasing deformation and the occurrence of significant plastic deformations, it has been experimentally established that plastic deformation occurs without changing the volume of the substance, since this type of deformation occurs due to shifts of layers of material. Units Poisson's ratio is a physical quantity that has no dimension. Examples of problem solving www.solverbook.com Poisson's ratio - WiKi This article is about a parameter characterizing the elastic properties of a material. For the concept in thermodynamics, see Adiabatic exponent. Poisson's ratio (denoted as ν(\displaystyle \nu ) or μ(\displaystyle \mu )) is the ratio of relative transverse compression to relative longitudinal tension. This coefficient does not depend on the size of the body, but on the nature of the material from which the sample is made. Poisson's ratio and Young's modulus fully characterize the elastic properties of an isotropic material. Dimensionless, but can be indicated in relative units: mm/mm, m/m. A homogeneous rod before and after tensile forces are applied to it. Let us apply tensile forces to a homogeneous rod. As a result of the influence of such forces, the rod will generally be deformed in both the longitudinal and transverse directions. Let l(\displaystyle l) and d(\displaystyle d) be the length and transverse size of the sample before deformation, and let l′(\displaystyle l^(\prime )) and d′(\displaystyle d^(\prime )) be the length and the transverse size of the sample after deformation. Then longitudinal elongation is a value equal to (l′−l)(\displaystyle (l^(\prime )-l)) , and transverse compression is a value equal to −(d′−d)(\displaystyle -(d^( \prime )-d)) . If (l′−l)(\displaystyle (l^(\prime )-l)) is denoted as Δl(\displaystyle \Delta l) , and (d′−d)(\displaystyle (d^(\prime )- d)) as Δd(\displaystyle \Delta d) , then the relative longitudinal elongation will be equal to the value Δll(\displaystyle (\frac (\Delta l)(l))), and the relative transverse compression will be equal to the value −Δdd(\displaystyle - (\frac (\Delta d)(d))) . Then, in the accepted notation, Poisson’s ratio μ(\displaystyle \mu ) has the form: μ=−ΔddlΔl.(\displaystyle \mu =-(\frac (\Delta d)(d))(\frac (l)(\Delta l)).) Typically, when tensile forces are applied to a rod, it elongates in the longitudinal direction and contracts in the transverse directions. Thus, in such cases, Δll>0(\displaystyle (\frac (\Delta l)(l))>0) and Δdd<0{\displaystyle {\frac {\Delta d}{d}}<0} , так что коэффициент Пуассона положителен. Как показывает опыт, при сжатии коэффициент Пуассона имеет то же значение, что и при растяжении. For absolutely brittle materials, Poisson's ratio is 0, for absolutely incompressible materials it is 0.5. For most steels this coefficient is around 0.3, for rubber it is approximately 0.5. There are also materials (mainly polymers) with a negative Poisson's ratio; such materials are called auxetics. This means that when a tensile force is applied, the cross-section of the body increases. For example, paper made from single-walled nanotubes has a positive Poisson's ratio, and as the proportion of multi-walled nanotubes increases, there is a sharp transition to a negative value of −0.20. Many anisotropic crystals have a negative Poisson's ratio, since the Poisson's ratio for such materials depends on the angle of orientation of the crystal structure relative to the tensile axis. A negative coefficient is found in materials such as lithium (the minimum value is −0.54), sodium (−0.44), potassium (−0.42), calcium (−0.27), copper (−0.13) and others. 67% of cubic crystals from the periodic table have a negative Poisson's ratio.

A load suspended on a spring causes its deformation. If a spring is able to restore its original shape, then its deformation is called elastic.

For elastic deformations, Hooke's law is satisfied:

where F control ¾ elastic force; k¾ coefficient of elasticity (stiffness); D l- spring extension.

Note: The “-” sign determines the direction of the elastic force.

If the load is in equilibrium, then the elastic force is numerically equal to the force of gravity: k D l = m g, then you can find the spring elasticity coefficient:

Where m¾ weight of cargo; g¾ acceleration of free fall.

Fig.1		Rice. 2

When springs are connected in series (see Fig. 1), the elastic forces arising in the springs are equal to each other, and the total elongation of the spring system is the sum of the elongations in each spring.

The rigidity coefficient of such a system is determined by the formula:

Where k 1 - stiffness of the first spring; k 2 - stiffness of the second spring.

When springs are connected in parallel (see Fig. 2), the elongation of the springs is the same, and the resulting elastic force is equal to the sum of the elastic forces in the individual springs.

The stiffness coefficient for parallel connection of springs is found by the formula:

k res = k 1 + k 2 . (3)

Work order

1. Attach the spring to the tripod. Suspending weights from each spring in order of increasing mass, measure the elongation of the spring D l.

2. According to the formula F = mg calculate the elastic force.

3. Construct graphs of the dependence of the elastic force on the magnitude of the spring elongation. By the appearance of the graphs, determine whether Hooke's law is satisfied.

5. Find the absolute error of each measurement

D k i = ê k i - k Wed ê.

6. Find the arithmetic mean value of the absolute error D k Wed

7. Enter the results of measurements and calculations into the table.

1. Carry out measurements (as described in task 1) and calculate the elasticity coefficients of series and parallel connected springs.

2. Find the average value of the coefficients and the error of their measurements. Enter the results of measurements and calculations into the table.

4. Find the experimental error by comparing the theoretical values ​​of the elasticity coefficient with the experimental ones using the formula:

.

m, kg
F, N
First spring
D l 1m
k 1 , N/m							k avg =
D k 1 , N/m							D k avg =
Second spring
D l 2 , m
k 2 , N/m							k avg =
D k 2 , N/m							D k avg =
Series connection of springs
D l, m
k, N/m							k avg =
D k, N/m							D k avg =
Parallel connection of springs
D l, m
k, N/m							k avg =
D k, N/m							D k avg =

Control questions

Formulate Hooke's law.

Define deformation and elasticity coefficient. Name the units of measurement of these quantities in SI.

How is the elasticity coefficient found for parallel and series connection of springs?

Laboratory work No. 1-5

Studying the laws of dynamics

Forward movement

Theoretical information

Dynamics studies the causes of mechanical movement.

Inertia- the ability of a body to maintain a state of rest or rectilinear uniform motion if other bodies do not act on this body.

Weight m (kg)- a quantitative measure of body inertia.

Newton's first law:

There are reference systems in which a body is at rest or in a state of linear uniform motion if other bodies do not act on it.

Frames of reference in which Newton's first law is satisfied are called inertial.

Force (N) is a vector quantity characterizing the interaction between bodies or parts of the body.

The principle of superposition of forces:

If forces and act simultaneously on a material point, then they can be replaced by the resultant force.

I. Spring stiffness

What is spring stiffness ?
One of the most important parameters related to elastic metal products for various purposes is the spring stiffness. It implies how resistant the spring will be to the influence of other bodies and how strongly it resists them when exposed. The resistance force is equal to the spring constant.

What does this indicator affect?
A spring is a fairly elastic product that ensures the transmission of translational rotational movements to the devices and mechanisms in which it is located. It must be said that you can find springs everywhere; every third mechanism in the house is equipped with a spring, not to mention the number of these elastic elements in industrial devices. In this case, the reliability of the operation of these devices will be determined by the degree of spring stiffness. This value, called the spring constant, depends on the force that must be applied to compress or stretch the spring. The straightening of the spring to its original state is determined by the metal from which it is made, but not by the degree of rigidity.

What does this indicator depend on?
Such a simple element as a spring has many varieties depending on the degree of purpose. According to the method of transferring deformation to the mechanism and shape, spiral, conical, cylindrical and others are distinguished. Therefore, the rigidity of a particular product is also determined by the method of transferring deformation. The deformation characteristic will divide spring products into torsion, compression, bending and tension springs.

When using two springs in a device at once, the degree of their stiffness will depend on the method of fastening - with a parallel connection in the device, the stiffness of the springs will increase, and with a serial connection, it will decrease.

II. Spring stiffness coefficient

Spring stiffness coefficient and spring products is one of the most important indicators that determines the service life of the product. To calculate the stiffness coefficient manually, there is a simple formula (see Fig. 1), and you can also use our spring calculator, which will quite easily help you make all the necessary calculations. However, the spring stiffness will only indirectly influence the service life of the entire mechanism - other qualitative features of the device will be of greater importance.

6. Sound research methods in medicine: percussion, auscultation. Phonocardiography.

Auscultation

Percussion

Phonocardiography

7. Ultrasound. Receiving and recording ultrasound based on the inverse and direct piezoelectric effect.

8. Interaction of ultrasound of various frequencies and intensities with matter. Application of ultrasound in medicine.

Electromagnetic oscillations and waves.

4.Scale of electromagnetic waves. Classification of frequency intervals adopted in medicine

5.Biological effect of electromagnetic radiation on the body. Electrical injuries.

6.Diathermy. UHF therapy. Inductothermy. Microwave therapy.

7. Depth of penetration of non-ionizing electromagnetic radiation into the biological environment. Its dependence on frequency. Methods of protection against electromagnetic radiation.

Medical optics

1. The physical nature of light. Wave properties of light. Light wavelength. Physical and psychophysical characteristics of light.

2. Reflection and refraction of light. Total internal reflection. Fiber optics, its application in medicine.

5. Resolution and resolution limit of the microscope. Ways to increase resolution.

6. Special microscopy methods. Immersion microscope. Dark field microscope. Polarizing microscope.

The quantum physics.

2. Line spectrum of atomic radiation. Its explanation is in the theory of N. Bohr.

3. Wave properties of particles. De Broglie's hypothesis, its experimental justification.

4. Electron microscope: principle of operation; resolution, application in medical research.

5. Quantum mechanical explanation of the structure of atomic and molecular spectra.

6. Luminescence, its types. Photoluminescence. Stokes' law. Chemiluminescence.

7. Application of luminescence in biomedical research.

8. Photoelectric effect. Einstein's equation for the external photoelectric effect. Photodiode. Photomultiplier tube.

9. Properties of laser radiation. Their connection with the quantum structure of radiation.

10. Coherent radiation. Principles of obtaining and restoring holographic images.

11. Operating principle of a helium-neon laser. Inverse population of energy levels. The emergence and development of photon avalanches.

12. Application of lasers in medicine.

13. Electron paramagnetic resonance. EPR in medicine.

14. Nuclear magnetic resonance. Use of NMR in medicine.

Ionizing radiation

1. X-ray radiation, its spectrum. Bremsstrahlung and characteristic radiation, their nature.

3. Application of X-ray radiation in diagnostics. X-ray. Radiography. Fluorography. CT scan.

4. Interaction of X-ray radiation with matter: photoabsorption, coherent scattering, Compton scattering, pair formation. Probabilities of these processes.

5. Radioactivity. Law of radioactive decay. Half life. Units of activity of radioactive drugs.

6 Law of attenuation of ionizing radiation. Linear attenuation coefficient. Half attenuation layer thickness. Mass attenuation coefficient.

8. Production and use of radioactive drugs for diagnosis and treatment.

9. Methods for recording ionizing radiation: Geiger counter, scintillation sensor, ionization chamber.

10. Dosimetry. The concept of absorbed, exposure and equivalent dose and their power. Their units of measurement. The non-systemic unit is the X-ray.

Biomechanics.

1. Newton's second law. Protecting the body from excessive dynamic loads and injuries.

2. Types of deformation. Hooke's law. Hardness coefficient. Elastic modulus. Properties of bone tissue.

3. Muscle tissue. The structure and functions of muscle fiber. Energy conversion during muscle contraction. Efficiency of muscle contraction.

4. Isotonic mode of muscle work. Static muscle work.

5. General characteristics of the circulatory system. The speed of blood movement in the vessels. Stroke blood volume. Work and power of the heart.

6. Poiseuille's equation. The concept of hydraulic resistance of blood vessels and methods of influencing it.

7. Laws of fluid movement. Continuity equation; its connection with the features of the capillary system. Bernoulli's equation; its connection with the blood supply to the brain and lower extremities.

8. Laminar and turbulent fluid movement. Reynolds number. Blood pressure measurement using the Korotkoff method.

9. Newton's equation. Viscosity coefficient. Blood is like a non-Newtonian fluid. Blood viscosity is normal and in pathologies.

Biophysics of cytomembranes and electrogenesis

1. The phenomenon of diffusion. Fick's equation.

2. Structure and models of cell membranes

3. Physical properties of biological membranes

4. Concentration element and Nernst equation.

5. Ionic composition of the cytoplasm and intercellular fluid. Permeability of the cell membrane to various ions. Potential difference across the cell membrane.

6. Cell resting potential. Goldman-Hodgkin-Katz equation

7. Excitability of cells and tissues. Excitation methods. The "all or nothing" law.

8. Action potential: graphical appearance and characteristics, mechanisms of occurrence and development.

9. Voltage-dependent ion channels: structure, properties, functioning

10. The mechanism and speed of propagation of the action potential along the non-pulpate nerve fiber.

11. The mechanism and speed of propagation of the action potential along the myelinated nerve fiber.

Biophysics of reception.

1. Classification of receptors.

2. Structure of receptors.

3. General mechanisms of reception. Receptor potentials.

4. Encoding of information in the senses.

5. Features of light and sound perception. Weber-Fechner law.

6. Main characteristics of the hearing analyzer. Mechanisms of auditory reception.

7. Main characteristics of the visual analyzer. Mechanisms of visual reception.

Biophysical aspects of ecology.

1. Geomagnetic field. Nature, biotropic characteristics, role in the life of biosystems.

2. Physical factors of environmental significance. Natural background levels.

Elements of probability theory and mathematical statistics.

Properties of a sample mean

2. Types of deformation. Hooke's law. Hardness coefficient. Elastic modulus. Properties of bone tissue.

Deformation- change in the size, shape and configuration of the body as a result of the action of external or internal forces. types of deformation:

tension-compression is a type of deformation of a body that occurs when a load is applied to it along its longitudinal axis

shear – deformation of a body caused by shear stresses

bending is a deformation characterized by curvature of the axis or gray surface of a deformable object under the influence of external forces.

torsion occurs when a load is applied to a body in the form of a pair of forces in its transverse plane.

Hooke's law- an equation of the theory of elasticity that relates the stress and strain of an elastic medium. In verbal form the law reads as follows:

The elastic force that arises in a body during its deformation is directly proportional to the magnitude of this deformation

For a thin tensile rod, Hooke's law has the form:

Here F is the tension force of the rod, Δl is the absolute elongation (compression) of the rod, and k is called the elasticity (or rigidity) coefficient.

Elasticity coefficient depends both on the properties of the material and on the dimensions of the rod. We can distinguish the dependence on the dimensions of the rod (cross-sectional area S and length L), writing the elasticity coefficient as

The stiffness coefficient is the force that causes a single displacement at a characteristic point (most often at the point of application of force).

Elastic modulus- a general name for several physical quantities that characterize the ability of a solid body (material, substance) to deform elastically when a force is applied to it.

There are no absolutely solid bodies in nature; real solid bodies can “spring” a little - this is elastic deformation. Real solids have a limit of elastic deformation, i.e. such a limit after which the mark from the pressure will already remain and will not disappear on its own.

Properties of bone tissue. Bone is a solid body whose main properties are strength and elasticity.

Bone strength is the ability to withstand external destructive forces. Strength is quantitatively determined by the tensile strength and depends on the design and composition of the bone tissue. Each bone has a specific shape and complex internal structure that allows it to withstand the load in a certain part of the skeleton. Changes in the tubular structure of the bone reduce its mechanical strength. The composition of the bone also significantly affects strength. When minerals are removed, the bone becomes rubbery, and when organic matter is removed, it becomes brittle.

Bone elasticity is the property of regaining its original shape after the cessation of exposure to environmental factors. It, just like strength, depends on the design and chemical composition of the bone.

3. Muscle tissue. The structure and functions of muscle fiber. Energy conversion during muscle contraction. Efficiency of muscle contraction.

Muscle tissue call tissues that are different in structure and origin, but similar in their ability to undergo pronounced contractions. They provide movement in space of the body as a whole, its parts and the movement of organs within the body and consist of muscle fibers.

A muscle fiber is an elongated cell. The composition of the fiber includes its shell - sarcolemma, liquid contents - sarcoplasm, nucleus, mitochondria, ribosomes, contractile elements - myofibrils, and also containing Ca 2+ ions - sarcoplasmic reticulum. The surface membrane of the cell forms transverse tubes at regular intervals through which the action potential penetrates into the cell when it is excited.

The functional unit of muscle fiber is the myofibril. The repeating structure within the myofibril is called a sarcomere. Myofibrils contain 2 types of contractile proteins: thin filaments of actin and twice as thick filaments of myosin. Muscle fiber contraction occurs due to the sliding of myosin filaments along actin filaments. In this case, the overlap of filaments increases and the sarcomere shortens.

home muscle fiber function- ensuring muscle contraction.

Energy conversion during muscle contraction. To contract a muscle, energy is used that is released during the hydrolysis of ATP by actomyosin, and the hydrolysis process is closely associated with the contractile process. By the amount of heat generated by the muscle, one can evaluate the efficiency of energy conversion during contraction. When a muscle shortens, the rate of hydrolysis increases in accordance with the increase in work performed. The energy released during hydrolysis is sufficient to ensure only the work performed, but not the full energy production of the muscle.

Efficiency(efficiency) of muscle work ( r) is the ratio of the magnitude of external mechanical work ( W) to the total amount released in the form of heat ( E) energy:

The highest efficiency value of an isolated muscle is observed with an external load of about 50% of the maximum external load. Work productivity ( R) in humans is determined by the amount of oxygen consumption during work and recovery using the formula:

where 0.49 is the proportionality coefficient between the volume of oxygen consumed and the mechanical work performed, i.e. at 100% efficiency for performing work equal to 1 kgf․m(9,81J), required 0.49 ml oxygen.

Motor action / efficiency

Walking/23-33%; Running at average speed/22-30%; Cycling/22-28%; Rowing/15-30%;

Shot put/27%; Throwing/24%; Barbell lift/8-14%; Swimming/ 3%.

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