Ticket 10. Elastic forces: the nature of elastic forces, types of elastic deformations, Hooke's law in the form Fx = -kx, stress, relative and absolute elongation, Young's modulus, Hooke's law for tensile deformation, limits of applicability of Hooke's law, tension diagram.
Elastic forces arise during deformations of bodies. Deformation is a change in the shape and size of the body. Deformations include tension, compression, torsion, shear, and bending. Deformations are elastic and plastic. The elastic deformation completely disappears after the cessation of the action of the external forces causing it, so that the body completely restores its shape and size. Plastic deformation persists (perhaps partially) after the removal of the external load, and the body does not return to its previous size and shape.
Particles of a body (molecules or atoms) interact with each other by the forces of attraction and repulsion, which are of electromagnetic origin (these are the forces acting between the nuclei and electrons of neighboring atoms). The forces of interaction depend on the distance between the particles. If there is no deformation, then the forces of attraction are compensated by the forces of repulsion. During deformation, the distances between the particles change, and the balance of interaction forces is disturbed.
For example, when a rod is stretched, the distances between its particles increase, and the forces of attraction begin to prevail. On the contrary, when the rod is compressed, the distances between the particles decrease, and repulsive forces begin to prevail. In any case, a force arises that is directed in the direction opposite to the deformation, and seeks to restore the original configuration of the body.
The elastic force is the force that arises during the elastic deformation of the body and is directed in the direction opposite to the displacement of the body particles in the process of deformation. Elastic force: acts from the side of a deformed body on a body in contact with it, causing deformation, and is applied at the point of contact of these bodies perpendicular to their surfaces (a typical example is a support reaction force).
Zakomn Gumka is a statement according to which the deformation arising in an elastic body (spring, rod, console, beam, etc.) is proportional to the force applied to this body
For a thin tensile rod, Hooke's law has the form:
Here is the force with which the rod is stretched (compressed), is the absolute elongation (compression) of the rod, and is the coefficient of elasticity (or stiffness).
Also, when calculating straight rods, the record of Hooke's law in relative form is used
Linear deformation (tensile deformation) is a deformation in which only one linear dimension of the body changes.
Quantitatively, it is characterized by absolute Dl and relative elongation.
Дl = | l − l0 | , where Dl - absolute elongation (m); l and l0 - final and initial body length (m).
If the body is stretched, then l> l0 and Dl = l - l0; if the body is compressed, then l< l0 и Дl = –(l – l0) = l0 – l, е=Дl/l0, где е – относительное удлинение тела, Дl – абсолютное удлинение тела (м); l0 –начальная длина тела (м).
Young's modulus (modulus of longitudinal elasticity) is a physical quantity that characterizes the properties of a material to resist tension / compression under elastic deformation.
where: F is the normal component of the force, S is the surface area over which the action of the force is distributed, l is the length of the deformed bar,
- the modulus of change in the length of the bar as a result of elastic deformation (measured in the same units as the length l).
Mechanical stress is a measure of the internal forces that arise in a deformable body, under the influence of various factors. Mechanical stress at a point of the body is defined as the ratio of the internal force to the unit area at a given point of the section under consideration.
Stresses are the result of the interaction of body particles when it is loaded. External forces tend to change the mutual arrangement of particles, and the resulting stresses prevent the displacement of particles, limiting it in most cases to some small value.
... - mechanical stress. F is the force generated in the body during deformation. S - area.
Hooke's law in a different form, mechanical stress is directly proportional to the relative elongation.
To study the tensile deformation, a rod made of the material under study is subjected to tension using special devices (for example, using a hydraulic press), and the elongation of the sample and the stress arising in it are measured. Based on the results of the experiments, a graph of the dependence of the stress y on the relative elongation e is drawn. This graph is called the tensile diagram (Fig. 1).
As you can see from the figure, the diagram has four characteristic sections:
I - proportionality plot;
II - area of fluidity;
III - self-hardening area;
IV - area of destruction.
At the very beginning of the tensile test, the tensile force F and, consequently, the deformation Dl of the bar are equal to zero, so the diagram starts from the point of intersection of the corresponding axes (point O).
On section I to point A, the diagram is drawn in the form of a straight line. This suggests that on this segment of the diagram, the deformations of the bar Dl grow in proportion to the increasing load F.
After passing point A, the diagram sharply changes its direction and on part II, which starts at point B, the line for some time goes almost parallel to the DL axis, that is, the deformations of the bar increase at practically the same load value.
At this moment, irreversible changes begin to occur in the metal of the sample. The crystal lattice of the metal is being rearranged. In this case, the effect of its self-strengthening is observed.
After increasing the strength of the sample material, the diagram "goes up" again (section III) and at point D the tensile force reaches its maximum value. At this moment, a local thinning appears in the working part of the test specimen (Fig. 2), the so-called "neck" caused by disturbances in the structure of the material (the formation of voids, microcracks, etc.).
Rice. 2 Steel sample with a "neck"
Due to the thinning, and consequently, the decrease in the cross-sectional area of the sample, the tensile force required to stretch it decreases, and the curve of the diagram "goes down".
At point E, the sample breaks. The sample breaks, of course, in the section where the "neck" was formed
All bodies located near the Earth are influenced by its attraction. Under the influence of gravity, raindrops and snowflakes fall on the Earth.
But when the drops lie on the roof, he is attracted by the Earth, but he does not pass or fall through the roof, but remains at rest. What prevents him from falling? Roof. It acts on the drops with a force equal to the force of gravity, but directed in the opposite direction.
Let's take a look at one example. Shown is a board lying on two supports. If a body is placed in its middle, then under the action of gravity the body will begin to push the board, but after a few minutes, it will stop. In this case, the force of gravity will become a balanced force acting on the body from the side of the curved board and directed vertically upward. This power is called force of elasticity.
The force of elasticity arises from deformation. Deformation is a change in the shape or size of the body. One of the types of deformation is bending. The more the support deflects, the greater the elastic force acting from this support on the body. Before the body (weight) was placed on the board, this force was absent. As the weight moved, which flexed its support more and more, the elastic force also increased. At the moment the weights stopped, the elastic force reached the force of gravity, and their resultant became equal to zero.
If a sufficiently light object is placed on the support, then its deformation may turn out to be so insignificant that we will not notice any change in the shape of the support. But there will still be deformation! And together with it, the elastic force will act, preventing the body from falling on the given support. In such cases (when the deformation of the body is invisible and the change in the dimensions of the support can be neglected), the elastic force is called support reaction force.
If, instead of a support, you use some kind of suspension (thread, rope, wire, rod, etc.), then the object attached to it can also be kept at rest. Here, too, the force of gravity will be balanced by the oppositely directed elastic force. In this case, the elastic force arises due to the fact that the suspension is stretched under the action of the load attached to it. Stretching another kind of deformation.
The scientist R. Hooke made a great contribution to the study of the elastic force. Hooke's Law states:
Elastic force that arises when a body is stretched or compressed is proportional to its elongation.
If the lengthening of the body, i.e. the change in its length is denoted by x, and the elastic force is denoted by F (control), then according to Hooke's law the following mathematical form can be given:
where k is the coefficient of proportionality, called the stiffness of the body. Each body has its own rigidity. The greater the rigidity of the body (spring, wire, rod, etc.), the less it changes its length under the action of a given force.
The SI unit of stiffness is the newton per meter (1 N / m).
Any body, when it is deformed and exerted an external influence, resists and strives to restore its previous shape and size. This is due to the electromagnetic interaction in the body at the molecular level.
Deformation - a change in the position of body particles relative to each other. The result of deformation is a change in interatomic distances and a rearrangement of atomic blocks.
Definition. What is elastic force?
Elastic force is a force arising from deformation in a body and tending to return the body to its initial state.
Consider the simplest deformations - tension and compression
The figure shows how the elastic force acts when we compress or stretch the bar.
For small deformations x ≪ l, Hooke's law is valid.
The deformation that occurs in an elastic body is proportional to the force applied to the body.
F y p p = - k x
Here k is a coefficient of proportionality called stiffness. The SI unit of stiffness is Newton per meter. Stiffness depends on the material of the body, its shape and size.
The minus sign shows that the elastic force opposes the external force and seeks to return the body to its original state.
There are other forms of recording Hooke's law. The relative deformation of the body is the ratio ε = x l. The stress in the body is the ratio σ = - F y p p S. Here S is the cross-sectional area of the deformed body. The second formulation of Hooke's law: the relative deformation is proportional to the stress.
Here E is the so-called Young's modulus, which does not depend on the shape and size of the body, but depends only on the properties of the material. Young's modulus for different materials varies widely. For example, for steel E ≈ 2 10 11 N m 2, and for rubber E ≈ 2 10 6 N m 2
Hooke's law can be generalized to the case of complex deformations. Consider the bending deformation of the bar. With such a bending deformation, the elastic force is proportional to the deflection of the bar.
The ends of the rod lie on two supports, which act on the body with a force N → called the normal reaction force of the support. Why normal? Because this force is directed perpendicularly (normally) to the contact surface.
If the rod is on the table, the normal reaction force of the support is directed vertically upward, opposite to the force of gravity, which it balances.
The weight of the body is the force with which it acts on the support.
Elastic force is often viewed in the context of the tension or compression of a spring. This is a common example that often occurs not only in theory, but also in practice. Springs are used to measure the magnitude of forces. The device designed for this is a dynamometer.
Dynamometer - a spring, the tension of which is graduated in units of force. A characteristic property of springs is that Hooke's law is applicable to them with a sufficiently large change in length.
When the spring is compressed and stretched, Hooke's law acts, elastic forces arise that are proportional to the change in the length of the spring and its stiffness (coefficient k).
Unlike springs, rods and wires obey Hooke's law within very narrow limits. So, with a relative defomation of more than 1%, irreversible changes occur in the material - fluidity and destruction.
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Pavlova Daria
This work was carried out by a 7th grade student of the main secondary school on the topic "The force of elasticity"
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Slide captions:
MOU OOSH №3, Kameshkovo The force of elasticity in the development of technology and in human life Prepared by a 7-b grade student Pavlova Daria 2011
Solids easily change their shape ... It is easy to squeeze a rubber toy or a washing machine ...
Elasticity is the property of bodies to restore their shape and size after removal of the load
The use of elasticity by man for his own purposes Hunting of an ancient tribe Shooting sports
Inflatable mattresses, beds ...
Resilient shoe sole ...
The use of springs in everyday life
Shock absorbers
In the architecture of the arch Columns beams
Steel structures bridges frame buildings greenhouses fences
Applications of Brass and Bronze Pipe Parts, Tableware Decorations
Making skis, golf clubs
Increased strength and resilience Increased stress Increased service life Saving materials and energy
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Report on the topic:
“The power of elasticity. Its importance in the development of technology and in human life "
Prepared by a student of grade 7
Pavlova Daria.
2011
It is known from experiments that solid bodies under the action of applied forces can change their shape and size, that is, deform. It is easy to squeeze a rubber toy, washer or bend a ruler. If the load is removed, then these bodies will regain their shape. The property of bodies to restore their original position after removing the load is called elasticity. The force that resists the external load and restores the shape of the body is called the elastic force.
Solids, liquids and gases are characterized by elasticity. Man has long been using elasticity for his own purposes: a bow for hunting and for sports, long bridges, car tires, various springs, air mattresses, shoe soles and much, much more.
From the point of view of environmental problems, the following is important: knowledge of physics allows you to change the properties of materials, changing their elasticity and strength in the way that is convenient and necessary for us.
The elasticity of the metal, and at the same time the strength, can be changed by introducing impurities of other elements into it. We already know how iron is made of steel. Likewise, soft copper turns into hard brass and elastic bronze if zinc, tin, aluminum and other metals are added to it.
The idea of combination, combination is also used in construction when using reinforced materials, such as reinforced concrete. When making skis, gluing layers of different types of wood improves their elasticity. The same effect is achieved when reinforcing plastics and metals with various fibers. Such materials are called composite materials.
By increasing the strength and elasticity of parts, it is possible to increase the load and extend their service life. Less materials and energy are spent on their manufacture. This means that the need for ore and oil decreases. Improving the properties of steel and other materials made it possible to build powerful locomotives and increase the carrying capacity of aircraft.
Literature
A.P. Ryzhenkov. Physics. Human. Environment. M. Enlightenment, 1996
We continue to review some of those from the "Mechanics" section. Our meeting today is dedicated to the force of elasticity.
It is this force that underlies the operation of mechanical watches, towing ropes and cables of cranes, shock absorbers of cars and trains are exposed to it. It is tested by a ball and a tennis ball, a racket and other sports equipment. How does this force arise, and what laws does it obey?
How elastic force is born
A meteorite falls to the ground under the influence of gravity and ... freezes. Why? Does gravity disappear? No. Power cannot just disappear. At the moment of contact with the ground counterbalanced by another force equal to it in magnitude and opposite in direction. And the meteorite, like other bodies on the surface of the earth, remains at rest.
This balancing force is the elastic force.
The same elastic forces appear in the body for all types of deformation:
- stretching;
- compression;
- shift;
- bending;
- torsion.
The forces resulting from deformation are called elastic.
The nature of the elastic force
The mechanism of the emergence of elastic forces was explained only in the XX century, when the nature of the forces of intermolecular interaction was established. Physicists called them "the short-handed giant." What is the meaning of this witty comparison?
The forces of attraction and repulsion act between molecules and atoms of a substance. This interaction is due to the smallest particles that are part of them, carrying positive and negative charges. These forces are great enough(hence the word giant), but appear only at very small distances(with short arms). At distances equal to three times the diameter of a molecule, these particles are attracted, "joyfully" rushing towards each other.
But, having come into contact, they begin to actively repel each other.
Under tensile deformation, the distance between the molecules increases. Intermolecular forces tend to reduce it. When compressed, the molecules come closer together, which gives rise to the repulsion of the molecules.
And, since all types of deformations can be reduced to compression and tension, the appearance of elastic forces for any deformations can be explained by these considerations.
Hooke's Law
A compatriot and contemporary was engaged in the study of elastic forces and their relationship with other physical quantities. He is considered the founder of experimental physics.
Scientist continued his experiments for about 20 years. He carried out experiments on deformation of tension of springs, hanging various weights from them. The suspended load caused the spring to stretch until the elastic force generated in it balanced the weight of the load.
As a result of numerous experiments, the scientist concludes: the applied external force causes the appearance of an elastic force equal to it in magnitude, acting in the opposite direction.
The law he formulated (Hooke's law) sounds like this:
The force of elasticity arising from the deformation of the body is directly proportional to the magnitude of the deformation and is directed in the direction opposite to the movement of the particles.
The formula for Hooke's law is:
- F - modulus, i.e. the numerical value of the elastic force;
- x - change in body length;
- k is the stiffness coefficient depending on the shape, size and material of the body.
The minus sign indicates that the elastic force is directed in the direction opposite to the displacement of the particles.
Each physical law has its own limits of application. The law established by Hooke can only be applied to elastic deformations, when, after removing the load, the shape and size of the body are completely restored.
In plastic bodies (plasticine, wet clay), such restoration does not occur.
All solid bodies possess elasticity to one degree or another. The first place in elasticity is taken by rubber, the second -. Even very elastic materials can exhibit plastic properties under certain loads. This is used for the manufacture of wire, cutting out parts of complex shapes with special stamps.
If you have a manual kitchen scale (steelyard), then the maximum weight for which they are designed is probably written on them. Let's say 2 kg. When you suspend a heavier load, the steel spring in them will never regain its shape.
Elastic force work
Like any force, elastic force, able to do work. Moreover, it is very useful. She protects the deformable body from destruction. If she does not cope with this, the destruction of the body sets in. For example, a crane cable breaks, a string on a guitar, an elastic band on a slingshot, a spring on a scale. This work always has a minus sign, since the elastic force itself is also negative.
Instead of an afterword
Armed with some knowledge about elastic forces and deformations, we can easily answer some questions. For example, why do large human bones have a tubular structure?
Bend a metal or wood ruler. Its convex part will undergo tensile deformation, and its concave part will undergo compression. The middle part does not bear the load. Nature took advantage of this circumstance, providing humans and animals with tubular bones. In the process of movement, bones, muscles and tendons experience all kinds of deformations. The tubular structure of bones greatly lightens their weight, without affecting their strength at all.
The stalks of cereal crops have the same structure. Gusts of wind bend them to the ground, and elastic forces help to straighten. By the way, the bicycle frame is also made of tubes, not rods: the weight is much less and the metal is saved.
The law established by Robert Hooke served as the basis for the creation of the theory of elasticity. Calculations performed according to the formulas of this theory allow ensure the durability of high-rise buildings and other structures.
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