Hookes law, law of elasticity discovered by the english scientist robert hooke in 1660, which states that, for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Introduction hookes law states that the force applied by a spring, f, relates linearly to the springs displacement from equilibrium, x. English physicist robert hooke is known for his discovery of the law of elasticity hookes law, for his first use of the word cell in the sense of a basic unit of organisms describing the microscopic cavities in cork, and for his studies of microscopic fossils, which made him an early proponent of a theory of evolution. Many materials obey this law as long as the load does not exceed the materials elastic limit. Hookes law describes this behavior, and we would like to verify this in lab today. In equation form, hookes law looks like equation 1. Spring constant, displacement from equilibrium position, and restoring force are defined and demonstrated. In elementary mechanics the elasticity of a spring is expressed by hookes law which says that the amount a spring is stretched or compressed beyond its relaxed length is proportional to the force acting on it. Here f is the restoring force or the force exerted by the spring on the external agent and k is a. Many materials obey this law as long as the load does not exceed the. Mathematically, hookes law states that the applied force f n or kgms 2 equals a constant k nm or kgs 2 times the displacement or change in length x meters, or f kx.
The property is described by an equation now known as hookes law. Hookes law and simple harmonic motion rowan university. 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. This topic is beyond this text, but through the use of compatibility and equilibrium equations, complex 3d stresses can be determined by numerical methods. Hookes law of elasticity is an approximation that states that the extension of a spring is directly proportional to the load applied to it. It is essential that the theory section be written for the particular audience for which the. Some treatment of this neg lected, yet fundamental, facet of the history of the theory of elasticity seems called for. The analysis presented so far applies to all bodies that could be, with sufficient accuracy, described as continuous bodies. Hookes law says that the restoring force f produced by the spring is proportional to the distance by which the spring has been lengthened x. To verify hookes law hookes 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.
Module 3 constitutive equations learning objectives understand basic stressstrain response of engineering materials. Generate the mathematical expression of hookes law. 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. Hookes law states that the restoring force is a linear function of the displacement from equilibrium. This lab is set up for us to to be able to determine the spring constant with two different methods and the gravitational acceleration with a pendulum.
This week in class you will discuss springs in some detail. Our present interest is in whether or not the data will fit on a linear trend line. Todays lab will allow you to test the accuracy of hookes law for a simple object, a spring. Jacobs woodberry forest school woodberry forest, va 22989 abstract today, you will investigate the relationship between the force applied to a spring and the distance the spring stretches this relationship is called hookes law. As an equation, hooke s law says that the force applied in newtons or the restoring force it amounts to the same thing is equal to the negative of the spring constant, k, of the material. 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. As an equation, hookes law says that the force applied in newtons or the restoring force it amounts to the same thing is equal to the negative of the spring constant, k, of the material. This behavior is described by hookes law, and you would like to verify this in lab today. Hookes law describes the relationship between the extension of a spring and the force applied to the spring. Jacobs woodberry forest school woodberry forest, va 22989 abstract today, you will investigate the relationship between the force applied to a spring and the distance the spring stretches this relationship is called hooke s law. When studying springs and elasticity, the 17 century physicist robert hooke noticed that the stress vs strain curve for many materials has a. Introduction and theory hookes law elastic force occurs in the spring when the spring is being stretchedcompressed or deformed. Stated by theory the total time period of a pendulum can be calculated through the following equation. 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.
In this case, imagine your audience to consist of one of your classmates who had to. If hooke s law, fa kx, holds for the spring, the data points should lie along a straight line. Hookes law definition of hookes law by the free dictionary. Hooke s law states that the force applied by a spring, f, relates linearly to the spring s displacement from equilibrium, x.
If hookes law, fa kx, holds for the spring, the data points should lie. When a spring is stretched by an applied force, a restoring force is produced. Theory the motion of a body that oscillates back and forth is defined as simple harmonic motion. Theory hooke s 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. Hookes law is the statement that the restoring force acting on an object is proportional to the negative of the displacement deformation of. For any additional loads, the springs will follow hookes law with a different value of. Hookes law experiment report done by yovaphine wijaya 11 science 1 aim to investigate hookes law for simple strings or rubber.
Hookes law applies essentially to onedimensional deformations, but it can be extended to more general threedimensional deformations by the. 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. If an exterior force acts on the spring, such as the weight f w m gof a. It tries to bring the deformed end of the spring to the original equilibrium position. In order to extend a spring by an amount x from its previous position.
If hookes law, fa kx, holds for the spring, the data points should lie along a straight line. In continuous elastic materials hookes law implies that strain is a linear function of stress. This behavior is described by hooke s law, and you would like to verify this in lab today. The case raises questions about the nature of discovery, credit and priority, and the contributions of. Hookes law and the newton spring balance by professor mac. Hooke s law synonyms, hooke s law pronunciation, hooke s law translation, english dictionary definition of hooke s law. In order to adhere to the form of hookes law as stated by equation 4, plot the displacement x on the horizontal axis x axis and the applied force on the vertical axis y axis.
Jan 21, 2017 according to hookes law for a small deformation, the stress in a body is proportional to the corresponding strain. From slinkies to pinball, they bring us much joy, and now they will bring you even more joy, as they help you understand simple harmonic mo. Hypothesis the change in length of spring is directly proportional to the applied so that it will cause greater change in. Hookes law holds up to a maximum stress called the proportional limit. Because the force is proportional to displacement of the spring from its equilibrium position, a mass attached to the spring will undergo simple harmonic motion. 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.
Pdf in this note we propose an alternative approach to the experimental study of hookes law that takes into. And this law is called hookes law, and its named after ill read it a physicist in the 17th century, a british physicist. Hookes law and modulus of elasticity me mechanical. Hookes law this is a wikipedia book, a collection of wikipedia articles that can be easily saved, imported by an external electronic rendering service, and ordered as a printed book.
Hookes law objective to test hookes law by measuring the spring constants of di erent springs and spring systems to test whether all elastic objects obey hookes law equipment two nearly identical springs, long rubber band, support stand with a. The shape of a body will distort when a force is applied to it. 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. This is known as hookes law, after robert hooke, founder of the royal society, who discovered the relation in 1676. So then we can use hooke s law to note the equation for this to figure out the restorative force for this particular spring, and it would be minus 2x. Ee is known as hookes law and is an example of a constitutive law. Hookes law in terms of stress and strain is stress strain in terms of the definitions l l y a f the constant of proportionality is called the elastic modulus or youngs modulus. Well i, displaced it by 1 meter, so then we multiply both sides by negative 1, and we get k is equal to minus 2. The modern theory of elasticity is a generalized variation on hookes law, which states that the straindeformation of an elastic object or material. Theory the shape of a body will distort when a force is applied to it. 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. And he figured out that the amount of force necessary to keep a spring compressed is proportional to how much youve compressed it. Theory of elasticity for scientists and engineers download book pdf theory of elasticity for scientists and engineers pp 85111 cite as.
In fact, the use of springs to demonstrate the hookes law is an integral part of every elementary physics lab. If hookes law holds for the spring and the data fits a straight line, then the motion of masses vibrating up and down on the spring should be simple harmonic motion. This document is highly rated by class 10 students and has been viewed 1778 times. Since we intend to study elastic bodies, we now present an experimental foundation that serves as a basis for mathematical description of. In addition to the hookes law, complex stresses can be determined using the theory of elasticity. Depending upon the nature of force applied on the body, the modulus of the elasticity is classified in the following three types. Open or add a new excel worksheet and prepare it to record your new data by. Elastic force acts in the opposite direction of the external force. Your goal will be to extract a measure of the stiffness of one particular spring. With hookes law apparatus for physical science and physics, students can measure and prove that the stretch of a spring is proportional to its load. Hookes law is a law of physics that states that the force f needed to extend or compress a spring by some distance x scales linearly with respect to that distancethat is, where k is a constant factor characteristic of the spring i.
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. Theory it is essential that the theory section be written for the particular audience for which the report is intended. 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. Definition and application of hookes law of elasticity. Intro to springs and hookes law video khan academy. Hookes law utk department of physics and astronomy. Physics lab report 2 hookes law and simple harmonic. The two springs will obey hookes law until the upper spring has been stretched to its limit. Due to the restoring force, simple harmonic motion is caused in a straight line in which the acceleration and the restoring force are. 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. Quantify the linear elastic stressstrain response in terms of tensorial quantities and in particular the fourthorder elasticity or sti ness tensor describing hookes law.
Theory measuring the stretching produced by different loads, added to the spring, tests the elasticity of a spring. This is hookes law or the linear law of forces, where the proportionality constant d, which is a general magnitude of reference, is called the spring constant in the case of a helical spring. At equilibrium, the spring is under two forces, the restoring force that proportional to the elongation, given by hookes law f r k l, and newtons second law, f g mg. Physics lab report 2 hookes law and simple harmonic motion. It expresses, in terms of macroscopic quantities, something about the nature or constitution of the material. For help with downloading a wikipedia page as a pdf, see help. Hookes law synonyms, hookes law pronunciation, hookes law translation, english dictionary definition of hookes law. Under these conditions the object returns to its original shape and size upon removal.