Waves and Vibrations. Search for:. Key Terms elasticity : The property by virtue of which a material deformed under the load can regain its original dimensions when unloaded. Elastic Potential Energy If a force results in only deformation, with no thermal, sound, or kinetic energy, the work done is stored as elastic potential energy. Learning Objectives Express elastic energy stored in a spring in a mathematical form. Key Takeaways Key Points In order to produce a deformation, work must be done.
Deformation can also be converted into thermal energy or cause an object to begin oscillating. Key Terms deformation : A transformation; change of shape. Also, because it is a close approximation of all solid bodies as long as the forces of deformation are small enough , numerous branches of science and engineering as also indebted to Hooke for coming up with this law. These include the disciplines of seismology, molecular mechanics and acoustics. However, like most classical mechanics, Hooke's Law only works within a limited frame of reference.
Because no material can be compressed beyond a certain minimum size or stretched beyond a maximum size without some permanent deformation or change of state, it only applies so long as a limited amount of force or deformation is involved.
In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. Still, in its general form, Hooke's Law is compatible with Newton's laws of static equilibrium. Together, they make it possible to deduce the relationship between strain and stress for complex objects in terms of the intrinsic materials of the properties it is made of.
For example, one can deduce that a homogeneous rod with uniform cross section will behave like a simple spring when stretched, with a stiffness k directly proportional to its cross-section area and inversely proportional to its length. Another interesting thing about Hooke's law is that it is a a perfect example of the First Law of Thermodynamics. Any spring when compressed or extended almost perfectly conserves the energy applied to it.
The only energy lost is due to natural friction. In addition, Hooke's law contains within it a wave-like periodic function.
A spring released from a deformed position will return to its original position with proportional force repeatedly in a periodic function. The wavelength and frequency of the motion can also be observed and calculated.
However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number. A good example of this would be when dealing with wind, where the stress applied varies in intensity and direction. In cases like these, it is best to employ a linear map aka. If you enjoyed this article there are several others that you will enjoy on Universe Today. Here is one about Sir Isaac Newton's contributions to the many fields of science.
Here is an interesting article about gravity. There are also some great resources online, such as this lecture on Hooke's Law that you can watch on academicearth. There is also a great explanation of elasticity on howstuffworks. Explore further. More from Other Physics Topics.
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Add a comment. Active Oldest Votes. Improve this answer. If you distort an object beyond the elastic limit, you are likely to cause permanent distortion or to break the object.
The elastic properties of linear objects, such as wires, rods, and columns which can be stretched or compressed, can be described by a parameter called the Young's modulus of the material.
This is an equation relating magnitudes. All quantities are positive. Young's modulus is a property of the material. It be used to predict the elongation or compression of an object before the elastic limit is reached. Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain.
How much would such a string stretch under a tension of N? Consider a point object, i. If this object is at rest and the net force acting on the object is zero, the object is at an equilibrium position.
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