Stress, strain and hookes law lesson teachengineering. If the deformation, or strain the ratio of the change in length to the initial length, is. The modern theory of elasticity generalizes hookes law to say that the strain deformation. This topic is beyond this text, but through the use of compatibility and equilibrium equations, complex 3d stresses can be determined by numerical methods. Robert hooke, english physicist who discovered the law of elasticity, known as hookes law, and who did research in a remarkable variety of fields. The modern theory of elasticity generalizes hooke s law to say that the strain deformation of an elastic object or material is proportional to the stress applied to it. Some treatment of this neg lected, yet fundamental, facet of the history of the theory of elasticity seems called for. Stated by theory the total time period of a pendulum can be calculated through the following equation. When studying springs and elasticity, the 17 century physicist robert hooke noticed that the stress vs strain curve for many materials has a. We will focus on materials following the linear material law. We will discuss the fundamental concepts of stress and strain, and the equations describing the deformation of an elastic object in equilibrium.
Here, is the restoring force, is the displacement from equilibrium or deformation, and is a constant related to the difficulty in deforming the system. Hookes law applies essentially to onedimensional deformations, but it can be extended to more general threedimensional deformations by the. Hookes law relates the stretching force and extension produced. Objects that quickly regain their original shape after being deformed by a force, often obey hookes law. Hookes law of elasticity project gutenberg selfpublishing. George ferdinand becker, the finite elastic stressstrain function, the american. The law is named after 17th century british physicist robert hooke. Students are introduced to hooke s law as well as stressstrain relationships. This lecture is the summary of the basics of the elasticity theory. Hooke s law states that the force needed to stretch or compress a spring is directly. Robert hooke a renaissance man, jackofalltrades and master of many. The modulus of the elasticity is classified into three types as young s modulus, bulk modulus of elasticity and modulus of rigidity.
Since we intend to study elastic bodies, we now present an experimental foundation that serves as a basis for mathematical description of. The spring constant is measured in nm and is different for different objects and. As noted above, for small deformations, most elastic materials such as springs exhibit linear elasticity and can be described by a linear relation between the stress and strain. Fke, where k is the constant of proportionality called spring constant. It expresses, in terms of macroscopic quantities, something about the nature or constitution of the material. Foundation for seismology, acoustics and molecular mechanics. Thus, the experiments indicate that prima facie a linear theory of elas ticity such as hookes law does not obtain because of the complicated form of the. From the straight line graph oa, we deduced that the extension is proportional to the load or tension in the wire when the elastic limit is not exceeded. The dotted line shows what the actual experimental plot of force might look like. Ee is known as hookes law and is an example of a constitutive law. The slope of this line corresponds to the spring constant k. At least, he was the first one who hypothesized that gravity follows an inverse square law. Since we intend to study elastic bodies, we now present an experimental foundation that serves as a basis for mathematical description of elastic bodies.
Physics lab report 2 hookes law and simple harmonic. Dec 24, 2017 hookes law it states that within the limit of elasticity, the stress induced. Hookes law article about hookes law by the free dictionary. Model to demonstrate hookes law and illustrate that physiological phenomena, such as lengthtension relationships of the heart starling mechanism, aortic recoil, and lung recoil, share. Learn about elasticity and how to determine the force exerted by a spring. A brief overview of springs, hookes law, and elastic potential energy for algebrabased physics students. Here we will continue with that discussion and gradually cover the hookes law and modulus of elasticity. The cognitive law expressed by equation 4 is formally identical to hookes law of elasticity. The resulting generalized hookes law, upon which the linear theory of elasticity is based, provides a good description of the elastic properties of all materials, provided that the deformations correspond to extensions not exceeding about 5 percent.
Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. This proportionality is called hooke s law and the force is equal to the spring constant times the extension. Hypothesis the change in length of spring is directly proportional to the applied so that it will cause greater change in length of the spring for greater force applied. On the other hand, hooke s law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. No molecular theory of matter is essential to the mechanical.
F kx, where k is a constant factor characteristic of the spring, its stiffness. Use this interactive quiz to test your knowledge of hooke s law and elasticity. Materials for which hookes law is a useful approximation are known as linearelastic or hookean materials. Theory hookes law an ideal spring is remarkable in the sense that it is a system where the generated force is linearly dependent on how far it is stretched. Elastic materials have internal forces which restore the size and shape of the object when the stress is removed. In continuous elastic materials hookes law implies that strain is a linear function of stress. May 12, 2017 he practiced his law on elasticity in his development of the balance spring, or hairspring, which made possible a portable timepiece for the first time the watch. Hookes law experiment report done by yovaphine wijaya 11 science 1 aim to investigate hookes law for simple strings or rubber. The accompanying worksheet can help you identify important study. To verify hooke s law hooke s law states that the extent to which an elastic material will change size and shape under stress is directly proportional to the amount of stress applied to it theory. A brief overview of springs, hookes law, and elastic potential energy for algebrabased physics students many materials obey this law of elasticity as long as the load does not exceed the materials elastic limit. Finally we will cover a youngs modulus 2 shear modulus 3 bulk modulus.
In the elastic limit, the magnitude of the elastic force of the spring is proportional to the deformation of the spring. Todays lab will allow you to test the accuracy of hookes law for a simple object, a spring. Hookes law holds up to a maximum stress called the proportional limit. It states that for a helical spring or any other elastic material, extension is directly proportional to the stretching force,provided elastic limit is not exceeded i. This behavior is described by hookes law, and you would like to verify this in lab today. Our present interest is in whether or not the data will fit on a linear trend line.
Here f is the restoring force or the force exerted by the spring on the external agent and k is a. Hookes law, law of elasticity that relates the size of the deformation of an object to the deforming force or load. To call dr robert hooke a genius is too small a word to describe such a man. Hookes law states that to extend a string by an amount. A formal lab report should include a title page like this one, with all of the appropriate information a descriptive title, your name, the course title, the date, and an abstract. An ideal spring is remarkable in the sense that it is a system where the generated force is linearly dependent on how far it is stretched, this behavior is described by hookes law. Hookes law is a basic relationship applicable in calculating the strength and deformability of. Hookes law is not valid when certain stresses or deformations attain limiting values characteristic for each material and the body passes into an elasticplastic state. Nov 04, 2017 this physics video tutorial provides a basic introduction into elasticity and hooke s law. According to hookes law stated above that to extend a spring by an amount dx from its previous position, one needs a force f which is determined by f kdx. A generalization of hookes law in muscle elasticity.
He first stated the law in 1660 as a latin anagram. When a force is applied to an elastic object, the object will be stretched. Hookes law is the statement that the restoring force acting on an object is proportional to the negative of the displacement deformation of the object. He was the first man to state in general that all matter expands when heated and that air is made up of particles separated from each other by relatively large distances. Hooke s law is a principle of physics that states that the force f needed to extend or compress a spring by some distance x is proportional to that distance. Ut tensio, sic vis meaning as the extension, so the force, a linear relationship commonly referred to as hooke s law.
Theory the shape of a body will distort when a force is applied to it. He first stated the law in 1660 as a latin anagram, and then. When a spring is stretched by an applied force, a restoring force is produced. Hookes law in simple terms says that strain is directly proportional to stress. An ideal spring is remarkable in the sense that it is a system where the generated force is linearly dependent on how far it is stretched, this behavior is described by hooke s law.
The case raises questions about the nature of discovery, credit and priority, and the contributions of. The modern theory of elasticity is a generalized variation on hookes law, which states that the straindeformation of an elastic object or material is proportional to the stress applied to it. In addition to the hookes law, complex stresses can be determined using the theory of elasticity. Hookes law is used all branches of science and engineering. It forms the elastic theory and appears in the range of stresses higher than rh. The modern theory of elasticity is a generalized variation on hooke s law, which states that the straindeformation of an elastic object or material is proportional to the stress applied to it. Robert hooke the english scientist who discovered the. The analysis presented so far applies to all bodies that could be, with sufficient accuracy, described as continuous bodies. This is known as hookes law, after robert hooke, founder of the royal society, who discovered the relation in 1676. A geometrydependent version of the idea was first formulated by robert hooke in 1675 as a latin anagram, ceiiinosssttuv. Due to the restoring force, simple harmonic motion is caused in a straight line in which the acceleration and the restoring force are. In the video lesson, we learned about hooke s law and the spring constant.
When stress and strain were covered in newtons third law of motion, the name was given to this relationship between force and displacement was hookes law. Since material does not like to be deformed if pulls back at the string to go back to a previous state. Hookes law has an elastic potential energy that is proportional to the square of the displacement from the equilibrium position of the system. Hookes law is a law of physics that states that the force f needed to extend or compress a. Hookes law and modulus of elasticity me mechanical. Many materials obey this law of elasticity as long as the load does not exceed the materials elastic limit. Our mission is to provide a free, worldclass education to anyone, anywhere. Theory measuring the stretching produced by different loads, added to the spring, tests the elasticity of a spring. Definition and application of hookes law of elasticity. Sciences and at the institute of problems of mechanics of the academy of sciences of the ussr, in the department of the theory of elasticity and plasticity of moscow state university, at the institute of crystallography, institute of. Your goal will be to extract a measure of the stiffness of one particular spring. Between 1658 and 1678 robert hooke worked on his invention of the watchspring and developed his theory of elasticity, now known as hooke s law.
It is the general question that is asked in the subject strength of materials. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law. The red line in this graph illustrates how force, f, varies with position according to hookes law. The primary purpose of the lab is to study hookes law and simple harmonic motion by studying the behavior of a mass on a spring. Objective the objective of this lab is to show that the response of a spring when an external agent changes its equilibrium length by x can be described by hookes law, f. It is used as a fundamental principle behind manometer, spring scale, balance wheel of the clock. Hooke almost preceded newton in the theory of gravity. Physics 3 summer 1989 lab 7 elasticity theory all materials deform to some extent when subjected to a stress a force per unit area. This law gives us a relation between stress and strain. Hookes law and the newton spring balance by professor mac duration. Hookes law stress and strain modulus of elasticity in our last post we have discussed on elasticity and plasticity.
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