Spring compression force. Serial connection of the spring system

Encyclopedia of Plants 20.09.2019

Encyclopedia of Plants

Instruction

Attach a dynamometer to the body and pull it, deforming the body. The force that the dynamometer will show will be equal in absolute value to the elastic force acting on the body. Find the stiffness coefficient using Hooke, which says that the elastic force is directly proportional to its elongation and is directed in the opposite direction to deformation. Calculate the stiffness coefficient by dividing the value of the force F by the elongation of the body x, which is measured with a ruler or tape measure k=F/x. To find the elongation of a deformed body, subtract the length of the deformed body from its original length. Stiffness coefficient in N/m.

If there is no dynamometer, hang a load of known mass from the deformable body. Make sure that the body is deformed elastically and does not collapse. In this case, the weight of the load will be equal to strength elasticity acting on a body whose stiffness coefficient needs to be found, for example, . Calculate the stiffness coefficient by dividing the product of the mass m and the gravitational acceleration g≈9.81 m/s² by the elongation of the body x, k=m g/x. Measure the elongation according to the method proposed in the previous one.

Example. Under a load of 3 kg, a spring 20 cm long became 26 cm, determine it. First find the extension of the spring at . To do this, from the length of the elongated spring, subtract its length in the normal state x=26-20=6 cm=0.06 m. Calculate the stiffness using the appropriate formula k=m g/x=3 9.81/0.06≈500 N / m.

And now a few tips. To reduce rigidity water in your , add distilled or clean rainwater to it, use special plants, such as elodea and hornwort. In addition, water can be frozen or boiled well. In the first case, it is poured into a low basin and exposed to frost. As soon as it freezes to half the capacity, the ice is broken through and, having melted, is used. In the second, water is boiled in enameled water for an hour, after which it is allowed to cool and two thirds of the “top” are used. water.

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As a result of deformation physical body there is always a force that counteracts it, trying to return the body to its original position. Define this force elasticity in the simplest case, according to Hooke's law.

Instruction

Strength elasticity, acting on a deformed body, arises as a result of the electromagnetic interaction between its atoms. Exist different kinds deformations: /stretching, shearing, bending. Under the influence of external forces, different parts of the body move differently, hence the distortion and force elasticity, which is directed towards the previous state.

Tensile/compressive deformation by direction external force along the axis of the object. It can be a rod, a spring, and another body that has a long shape. When distorted, the cross section changes, and the force elasticity is proportional to the mutual displacement of body particles: Fcontrol = -k ∆x.

This is called Hooke's law, but it is not always applied, but only for relatively small values of ∆x. The value k is called stiffness and is expressed in N/m. This coefficient depends on the initial material of the body, as well as the shape and dimensions, it is proportional to the cross section.

During shear deformation, the volume of the body does not change, but its layers change their relative to each other. Strength elasticity is equal to the product of the coefficient elasticity in shear, which is directly dependent on the cross section of the body, by the angle between the axis and the tangent, in the direction of which the external force acts: Fupr \u003d D α.

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Spring stiffness formula - perhaps the most important point in the topic of these elastic elements. After all, it is rigidity that plays a very important role in why these components are used so widely.

Today, practically no branch of industry can do without springs; they are used in instrument and machine tool building, agriculture, production of mining and railway equipment, energy, and other industries. They faithfully serve in the most important and critical places of various units, where their inherent characteristics are required, primarily the stiffness of the spring, the formula of which is general view very simple and familiar to children from school.

Features of work

Any spring is an elastic product, which is subjected to static, dynamic and cyclic loads during operation. The main feature of this part is that it deforms under external force, and when the impact stops, it restores its original shape and geometric dimensions. During the period of deformation, energy is accumulated, during restoration - its transfer.

It is this property to return to its original form that has brought widespread use of these parts: they are excellent shock absorbers, valve elements that prevent excess pressure, components for measuring instruments. In these and other situations, due to the ability to deform elastically, they perform important work therefore high quality and reliability are required from them.

Types of springs

There are many types of these parts, the most common are tension and compression springs.

The first of them without load have a zero pitch, that is, the coil is in contact with the coil. In the process of deformation, they stretch, their length increases. The termination of the load is accompanied by a return to its original form - again coil to coil.
The latter, on the contrary, initially wind with a certain step between the turns, and shrink under load. The contact of the turns is a natural limiter for continued exposure.

Initially, it was for the tension spring that the ratio of the mass of the load suspended on it and its change was found geometric size, which became the basis for the formula for the stiffness of the spring in terms of mass and length.

What other types of springs are

The dependence of deformation on the applied external force is also valid for other types of elastic parts: torsion, bending, disk-shaped, and others. It does not matter in which plane forces are applied to them: in the one where the axial line is located, or perpendicular to it, the deformation produced is proportional to the force under which it occurred.

Main characteristics

Regardless of the type of springs, the features of their work associated with constant deformation require the following parameters:

The ability to maintain a constant value of elasticity for a given period.
plasticity.
Relaxation resistance, due to which deformations do not become irreversible.
Strength, that is, the ability to withstand various types of loads: static, dynamic, shock.

Each of these characteristics is important, however, when choosing an elastic component for a particular job, its stiffness is primarily interested in its rigidity as an important indicator of whether it is suitable for this case and how long it will work.

What is stiffness

Stiffness is a characteristic of a part that indicates how easy or easy it will be to compress it, how much great power need to apply for this. It turns out that the deformation that occurs under load is the greater, the greater the applied force (after all, the elastic force that arises in opposition to it has the same value in modulus). Therefore, it is possible to determine the degree of deformation, knowing the force of elasticity (applied force) and vice versa, knowing the necessary deformation, it is possible to calculate what force is required.

Physical foundations of the concept of rigidity / elasticity

The force acting on the spring changes its shape. For example, tension/compression springs shorten or lengthen under the influence of an external force. According to Hooke's law (this is the name of the formula that allows you to calculate the coefficient of spring stiffness), force and deformation are proportional to each other within the limits of elasticity of a particular substance. In opposition to the load applied from the outside, a force arises that is the same in magnitude and opposite in sign, which is aimed at restoring the original dimensions of the part and its shape.

The nature of this elastic force is electromagnetic, it arises as a result of a special interaction between building blocks(molecules and atoms) of the material from which the part is made. Thus, the greater the rigidity, that is, the more difficult it is to stretch / compress the elastic part, the more ratio elasticity. This indicator is used, in particular, when choosing a particular material for the manufacture of springs for use in various situations.

How did the first version of the formula come about

The formula for calculating the stiffness of a spring, which is called Hooke's law, was established experimentally. In the course of experiments with loads of different masses suspended on an elastic element, the magnitude of its stretching was measured. So it turned out that the same test item under different loads undergoes various deformations. Moreover, the suspension of a certain number of weights, identical in mass, showed that each added/removed weight increases/reduces the length of the elastic element by the same amount.

As a result of these experiments, the following formula appeared: kx \u003d mg, where k is a coefficient constant for a given spring, x is the change in the length of the spring, m is its mass, and g is the acceleration of free fall (approximate value is 9.8 m / s²) .

Thus, the stiffness property was discovered, which, like the formula for determining the coefficient of elasticity, finds the most wide application in any industry.

Stiffness formula

The formula studied by modern schoolchildren, how to find the coefficient of spring stiffness, is the ratio of force and magnitude, showing the change in the length of the spring depending on the magnitude of this impact (or

equal to it in the modulus of the elastic force). This formula looks like this: F = -kx. From this formula, the stiffness coefficient of the elastic element is equal to the ratio of the elastic force to the change in its length. In the SI international system of units of physical quantities, it is measured in newtons per meter (N/m).

Another way to write the formula: Young's coefficient

Tensile/compressive deformation in physics can also be described by a slightly modified Hooke's law. The formula includes the values of relative strain (the ratio of the change in length to its initial value) and stress (the ratio of force to the cross-sectional area of the part). Relative deformation and stress according to this formula are proportional, and the coefficient of proportionality is the reciprocal of Young's modulus.

Young's modulus is interesting in that it is determined solely by the properties of the material, and does not depend in any way on either the shape of the part or its dimensions.

For example, Young's modulus for 100

whether it is approximately equal to one with eleven zeros (unit - N / sq. m).

The meaning of the concept of stiffness coefficient

Rigidity coefficient - coefficient of proportionality from Hooke's law. It is also rightfully called the coefficient of elasticity.

In fact, it shows the amount of force that must be applied to the elastic element in order to change its length by one (in the measurement system used).

The value of this parameter depends on several factors that characterize the spring:

The material used in its manufacture.
Forms and design features.
geometric dimensions.

According to this indicator, you can

to conclude how the product is resistant to the effects of loads, that is, what will be its resistance when an external influence is applied.

Features of the calculation of springs

Showing how to find the stiffness of a spring, the formula is probably one of the most used by modern designers. After all, these elastic parts are used almost everywhere, that is, it is required to calculate their behavior and choose those that will ideally cope with their duties.

Hooke's law very simplistically shows the dependence of the deformation of an elastic part on the applied force; engineers use more accurate formulas for calculating the stiffness coefficient, taking into account all the features of the ongoing process.

For example:

Modern engineering considers a cylindrical twisted spring as a spiral of wire with a circular cross section, and its deformation under the influence of the forces existing in the system is represented by a set of elementary shifts.
When bending is deformed, the deformation is considered to be the deflection of a rod located with its ends on supports.

Features of calculating the stiffness of spring connections

An important point is the calculation of several elastic elements connected in series or in parallel.

With a parallel arrangement of several parts, the overall stiffness of this system is determined by a simple sum of the coefficients of the individual components. As you can easily see, the rigidity of the system is greater than that of a single part.

With a sequential arrangement, the formula is more complex: the reciprocal of the total stiffness is equal to the sum of the reciprocals of the stiffness of each component. In this variant, the sum is less than the terms.

Using these dependencies, it is easy to determine the right choice elastic components for a specific case.

What is elastic force?

The force of elasticity is called such a force that arises through the deformation of the body and directed in the direction opposite to the movement of the particles of the body during deformation.

For more good example, in order to better understand what an elastic force is, let's take a vivid example from Everyday life. Imagine that you have an ordinary clothesline in front of you, on which you have hung wet clothes. If we hang wet clothes on a well-strung horizontally rope, we will see how, under the weight of things, this rope begins to bend and stretch.

First, you and I hang one wet thing on a rope and see how it, together with the rope, bends to the ground, and then stops. Then we hang next thing and we see that the same action is repeated and the rope bends even more.

In this case, the conclusion suggests itself that with an increase in the force that acts on the rope, deformation will occur until the forces opposing this deformation are equal to the weight of all things. And only after that the downward movement will stop.

It should be noted that the work of the elastic force is to maintain the integrity of objects that we act on by other objects. If the elastic forces are not able to cope with this, then the body is deformed irrevocably, that is, the rope can simply break.

And here a rhetorical question arises. At what point did the force of elasticity arise? And it occurs when we are just starting to hang clothes, that is, at the time of the initial impact on the body. And when the laundry is dry, and we take it off, then the force of elasticity disappears.

Varieties of deformations

Now we already know that the elastic force appears as a result of deformation.

Let's remember what deformation is? Deformation is a change in the volume or shape of a body under the action of external forces.

And the reason for the occurrence of deformation is that different parts of the body do not move in the same way, but in different ways. With the same movement, the body would always have its original shape and dimensions, that is, it would not be deformed.

Let's consider the question of what kind of deformation we can observe there.

Types of deformation can be divided according to the nature of the change in their shape.

In addition, the deformation is divided into two types. In this case, the deformation may be elastic or plastic deformation.

If, for example, you take and stretch a spring, and then release it, then after such a deformation, the spring will restore its previous size and shape. This will be an example of elastic deformation.

That is, if we see that after the termination of the action on the body, the deformation completely disappears, then such a deformation is elastic.

Now let's take another example. Let's take a piece of plasticine and squeeze it or make some figure. You and I can see that even after the termination of the action, the plasticine did not change shape, that is, it remained deformed. Such inelastic deformation is plastic.

Under plastic deformation, it persists even when external forces cease to act on it.

This type of deformation is used in addition to modeling from clay or plasticine and in the technical processes of forging and stamping.

Exercise: Describe what types of deformation you see in the image?

Elastic force and Hooke's law

The magnitude of the elastic force also depends on the magnitude of the deformation to which a body is subjected. Therefore, deformation and elastic force are closely related. If one value has undergone changes, it means that there have been changes in the other.

Therefore, if we know the deformation of the body, then we can calculate the elastic force that has arisen in this body. Conversely, if we know the force of elasticity, we can easily determine the degree of deformation of the body.

When, for example, we take a spring and hang weights of the same mass from it, we can see that with each subsequent suspended load, the spring is stretched more and more. And notice that the more this spring is deformed, the greater the elastic force becomes.

And if we take into account the fact that the weights have the same mass, then by hanging them one by one, you can see that with each new suspension, the length of the spring increases by exactly the same amount.

To find the relationship between elastic force and deformation elastic body, you need to use the formula that was discovered by the famous English scientist Robert Hooke.

The scientist established a simple relationship between the increase in body length and the elastic force that was caused by this lengthening.

In this formula, delta denotes the changes that occur to the value.

Hooke's law states that for small deformations, the elastic force is directly proportional to the elongation of the body.

That is, the more deformation appears, the greater the elastic force we can observe.

But it should also be noted that Hooke's law is valid only where elastic deformation is present.

The force of elasticity in nature

The force of elasticity plays a rather significant role in nature. Indeed, only thanks to this force, the tissues of plants, animals and humans are able to withstand huge loads and at the same time not break or collapse.

You have probably seen more than once such a picture as plants bend under a gust of wind or tree branches bend under the weight of snow, and as a result of the action of the elastic force they return to their previous shape.

Also, each of you could observe how, under the onslaught of a strong hurricane wind, tree branches broke. And we can observe such a result when the action of the wind force exceeds the elastic forces of the tree itself.

All bodies on Earth are able to withstand the force of atmospheric pressure only due to the force of elasticity. The inhabitants of deep waters are able to withstand even greater loads. Therefore, we can come to the logical conclusion that only thanks to the force of elasticity, all living organisms in nature have the opportunity not only to endure mechanical loads, but also to maintain their shape intact.

Flocks of birds sitting on the branches of trees, bunches of grapes hanging on the bushes, huge caps of snow on spruce paws - this is a clear demonstration of the forces of elasticity in nature.

The famous Hooke's law applies in almost all areas of our lives. It is impossible to do without it either in everyday life or in architecture. This law is used in the construction of houses and cars. Ego is even used in trading.

But, probably, not every one of you could imagine that the force of elasticity can be applied in the circus arena. Back in the century before last, a number called “Bomb Man” was demonstrated in the famous Franconi Circus.

For this, a huge cannon was installed in the circus arena, from which a man shot was fired. The audience was shocked by this number, as they did not suspect that the shot was fired not with powder gases, but with the help of a spring. A powerful elastic spring was placed in the barrel of the gun, and after the command “please!” from the muzzle, the spring threw the artist into the arena. Well, the roar, smoke and fire only enhanced the effect of this number and terrified the audience.

Subjects > Physics > Physics Grade 7

You and I know that if some force acts on a body, then the body will move under the influence of this force. For example, a leaf falls to the ground because it is attracted by the Earth. But if a leaf falls on a bench, it does not continue to fall, and does not fall through the bench, but is at rest.

And if the leaf suddenly stops moving, it means that a force must have appeared that counteracts its movement. This force acts in the direction opposite to the attraction of the Earth, and is equal to it in magnitude. In physics, this force, which opposes the force of gravity, is called the force of elasticity.

What is elastic force?

Puppy Antoshka loves to watch the birds.

For an example explaining what the force of elasticity is, let us also remember the birds and the rope. When the bird sits on the rope, the support, previously stretched horizontally, sags under the weight of the bird and slightly stretches. The bird first moves to the ground along with the rope, then stops. And this happens when another bird is added to the rope. And then another. That is, it is obvious that with an increase in the force of impact on the rope, it is deformed until the moment when the forces of counteraction to this deformation become equal to the weight of all the birds. And then the downward movement stops.

When the suspension is stretched, the elastic force will be equal to the force of gravity, then the stretching stops.

In simple terms, the work of the elastic force is to maintain the integrity of objects that we act on by other objects. And if the force of elasticity does not cope, then the body is deformed irrevocably. The rope breaks under the abundance of snow, the handles of the bag break if it is overloaded with food, with large harvests, the branches of the apple tree break, and so on.

When does the force of elasticity arise? At the moment of the beginning of the impact on the body. When the bird sat on the rope. And disappears when the bird takes off. That is, when the impact stops. The point of application of the elastic force is the point at which the action occurs.