many of us wondered how wonderfully things behave when exposed to?
example, why the cloth, if we stretch it in different directions, may be a long stretch, and at one point suddenly break?And why did the same experiment is much more difficult to hold a pencil?What determines the resistance of the material?How can I determine the extent to which it lends itself to deformation or stretching?
All these and many other questions are more than 300 years ago asking myself British researcher Robert Hooke.And I found the answers, now united under the title "Hooke's Law".
According to its research, each material has a so-called coefficient of elasticity .This property, which allows the material to stretch to a certain extent.The coefficient of elasticity - a constant.This means that each material can only sustain a certain level of resistance, after which he reaches the irreversible deformation.
In general, Hooke's law can be expressed by the formula:
F = k / x /,
where F - the force of elasticity, k - coefficient of elasticity of the aforementioned and / x / - change in the length of the material.What is meant by a change in this index?Under the influence of a force studied the subject, whether it is a string, rubber or any other change, stretching or shrinking.Changing the length in this case is the difference between the original and final length of the studied subject.That is to say, how much stretched / shrunk spring (rubber, string, etc.)
Hence, knowing the length and constant coefficient of elasticity for the material, you can find the force with which the material is stretched or elastic force, likeMore often referred to as Hooke's law.
There are also special cases in which the law, in its standard form can not be used.It is the measurement of force in a shear deformation, i.e. in situations where deformation produces a force acting on the material at an angle.Hooke's law in shear can be expressed thus:
τ = Gy,
where τ - required force, G- constant factor, known as shear modulus, y - angle shear is the amount by which the angle has changedtilting the object.
linear elastic force (Hooke's law) is applicable only in a small contractions and dilations.If the force continues to have an impact on the studied subject, then there comes a time when it loses its quality of elasticity, ie reaches its elastic limit.Provided the force exceeds the force of resistance.Technically, this can be seen not only as a change of the visible material parameters, but also as a decrease in its resistance.The force required to change the material is now reduced.In such cases, a change in the properties of the object, that is, the body no longer able to resist.In ordinary life, we see that it breaks, breaks, breaks, etc.Not necessarily, of course, the violation of integrity, but quality while significantly affected.And the coefficient of elasticity of the material, or just the body in an undistorted form, ceases to be significant in a distorted form.
This case allows us to say that the linear system (directly proportional relationship of one parameter from another) become nonlinear when the interdependence of parameters is lost, and the change takes place on a different principle.
On the basis of these observations, Thomas Young created the formula of the elastic modulus, which was later named after him and became a base for the creation of the theory of elasticity.The elastic modulus of deformation can be considered in cases where significant changes in elasticity.The law has the form:
E = σ / η,
where σ - the force applied to the cross-sectional area of the studied body, η - module extension and contraction of the body, E - modulus of elasticity, which determines the degree of expansion or contraction of the body under the influence of mechanical stress.
