scholarly journals Elasticity of Solids

2020 ◽  
pp. 179-233
Author(s):  
Steven L. Garrett
Keyword(s):  
Relaxation Time ◽  
Elastic Solid ◽  
Maxwell Model ◽  
Elastic Behavior ◽  
Second Law ◽  
Vibration Isolators ◽  
Applied Forces ◽  
Newton's Second Law ◽  
Definition Of ◽  
Shape And Size

Abstract If a solid is initially at rest and equal and opposing forces are applied to that object, Newton’s Second Law guarantees that the object will remain at rest because the net force on the sample is zero. If that object is an elastic solid, then those forces will cause the solid to deform by an amount that is directly proportional to those applied forces. When the forces are removed, the sample will return to its original shape and size. That reversibility is the characteristic that is required if we say the behavior of the solid is “elastic.” This chapter will quantify the elastic behavior of solids by introducing the concepts of stress and strain and expressing their linear relationship through the definition of elastic moduli that depend only upon the material and the nature of the deformation and not upon the shape of the object. Those concepts allow us to generalize Hooke’s law. As before, the combination of a linear equation of state with Newton’s Second Law will now describe wave motion in solids. The introduction of a relaxation time, through the Maxwell model, will let these results be generalized to viscoelastic materials and then be applied to rubber vibration isolators.

scholarly journals The Origin of Electromagnetic Mass (Electromagnetic Inertia)

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Electromagnetic Radiation ◽  
Special Relativity ◽  
Light Source ◽  
Universal Constant ◽  
Second Law ◽  
Perfect Equilibrium ◽  
Speed Of Light ◽  
Electromagnetic Mass ◽  
Newton's Second Law ◽  
Definition Of

Newton described in his second law of motion the classical definition of mass (inertia). However, it is impossible to calculate with Newton’s second law of motion the (electromagnetic) mass of a beam of light. Because the speed of light is a universal constant which follows from Albert Einstein’s Theory of Special Relativity, it is impossible to accelerate or to slow down a beam of light and for that reason it is impossible to determine the electromagnetic mass of a beam of light (free electromagnetic radiation) by Newton’s second law. To calculate the electromagnetic mass of free or confined electromagnetic radiation, the fundamental concept of the New Theory has been used that the Universe is in a perfect Equilibrium and that any electromagnetic field configuration is in a perfect equilibrium with itself and its surrounding. From this fundamental concept follows a different definition of (confined) electromagnetic mass. Electromagnetic mass (or inertia) has been determined by the relativistic Lorentz transformation of the radiation pressures in all different directions and the disturbance of a uniform motion (or position at rest) of confined electromagnetic radiation results in a relativistic effect which we measure (experience) as electromagnetic mass (inertia). The mass in [kg] of an object will be generally measured by acceleration (or deceleration) of the object according Newton’s second law of motion. In the theory of special relativity, the speed of light is a fundamental constant and the intensity of the light is not a universal constant. The calculate the relativistic mass of Confined Electromagnetic Radiation, we start with a thought experiment in which a beam of light is propagating between two 100 % reflecting mirrors, indicated as Mirror A and Mirror B. Both mirrors are part of a rigid construction and the relative velocity between both mirrors always equals zero. The results of this calculation will be be generalized for any kind of electromagnetic radiation which has been confined by its own electromagnetic and gravitational field. When the speed of the observer has the same speed as the speed of the light source, then the observer and the light source are relative at rest. And the same light intensity will be measured at the location of the emitter and at the location of the observer.

scholarly journals Introduction to The Origin of Electromagnetic Mass (Electromagnetic Inertia)

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
Electromagnetic Radiation ◽  
Special Relativity ◽  
Light Source ◽  
Universal Constant ◽  
Second Law ◽  
Perfect Equilibrium ◽  
Speed Of Light ◽  
Electromagnetic Mass ◽  
Newton's Second Law ◽  
Definition Of

Newton described in his second law of motion the classical definition of mass (inertia). However, it is impossible to calculate with Newton’s second law of motion the (electromagnetic) mass of a beam of light (Ref. [1], [2],[3]). Because the speed of light is a universal constant which follows from Albert Einstein’s Theory of Special Relativity, it is impossible to accelerate or to slow down a beam of light and for that reason it is impossible to determine the electromagnetic mass of a beam of light (free electromagnetic radiation) by Newton’s second law. To calculate the electromagnetic mass of free or confined electromagnetic radiation, the fundamental concept of the New Theory has been used that the Universe is in a perfect Equilibrium and that any electromagnetic field configuration is in a perfect equilibrium with itself and its surrounding. From this fundamental concept follows a different definition of (confined) electromagnetic mass. Electromagnetic mass (or inertia) has been determined by the relativistic Lorentz transformation of the radiation pressures in all different directions and the disturbance of a uniform motion (or position at rest) of confined electromagnetic radiation results in a relativistic effect which we measure (experience) as electromagnetic mass (inertia). The mass in [kg] of an object will be generally measured by acceleration (or deceleration) of the object according Newton’s second law of motion. In the theory of special relativity, the speed of light is a fundamental constant and the intensity of the light is not a universal constant. The calculate the relativistic mass of Confined Electromagnetic Radiation, we start with a thought experiment in which a beam of light is propagating between two 100 % reflecting mirrors, indicated as Mirror A and Mirror B. Both mirrors are part of a rigid construction and the relative velocity between both mirrors always equals zero. The results of this calculation will be generalized for any kind of electromagnetic radiation which has been confined by its own electromagnetic and gravitational field. When the speed of the observer has the same speed as the speed of the light source, then the observer and the light source are relative at rest. And the same light intensity will be measured at the location of the emitter and at the location of the observer.

Reactions in solution

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Phase Equilibria ◽  
Gas Phase ◽  
First Principles ◽  
Unique Feature ◽  
Life Sciences ◽  
Equilibrium Mixture ◽  
Second Law ◽  
Ideal Solution ◽  
Coupled Reactions ◽  
Definition Of

Another key chapter, examining reactions in solution. Starting with the definition of an ideal solution, and then introducing Raoult’s law and Henry’s law, this chapter then draws on the results of Chapter 14 (gas phase equilibria) to derive the corresponding results for equilibria in an ideal solution. A unique feature of this chapter is the analysis of coupled reactions, once again using first principles to show how the coupling of an endergonic reaction to a suitable exergonic reaction results in an equilibrium mixture in which the products of the endergonic reaction are present in much higher quantity. This demonstrates how coupled reactions can cause entropy-reducing events to take place without breaking the Second Law, so setting the scene for the future chapters on applications of thermodynamics to the life sciences, especially chapter 24 on bioenergetics.

Feeling Newton’s Second Law

2019 ◽  
Vol 57 (2) ◽  
pp. 88-90 ◽  
Author(s):  
Vincent P. Coletta ◽  
Josh Bernardin ◽  
Daniel Pascoe ◽  
Anatol Hoemke
Keyword(s):  
Second Law ◽  
Newton's Second Law

Scootin' with Newton: Teaching Newton's Second Law Using Motion

Strategies ◽  
2002 ◽  
Vol 16 (2) ◽  
pp. 7-11
Author(s):  
Deborah A. Stevens-Smith ◽  
Shelley W. Fones
Keyword(s):  
Second Law ◽  
Newton's Second Law

A dynamic method to measure the shear strength of snow

2010 ◽  
Vol 56 (196) ◽  
pp. 333-338 ◽  
Author(s):  
Tsutomu Nakamura ◽  
Osamu Abe ◽  
Ryuhei Hashimoto ◽  
Takeshi Ohta
Keyword(s):  
Shear Strength ◽  
Strain Rate ◽  
Reasonable Agreement ◽  
Dynamic Method ◽  
Second Law ◽  
Snow Density ◽  
Newton's Second Law

AbstractA new vibration apparatus for measuring the shear strength of snow has been designed and fabricated. The force applied to a snow block is calculated using Newton’s second law. Results from this apparatus concerning the dependence of the shear strength on snow density, overburden load and strain rate are in reasonable agreement with those obtained from the work of previous researchers. Snow densities ranged from 160 to 320 kg m−3. The overburden load and strain rate ranged from 1.95 × 10−1to 7.79 × 10−1kPa and 2.9 × 10−4to 9.1 × 10−3s−1respectively.

Relaxation Time Spectrum, Elasticity, and Viscosity of Rubber. I

1954 ◽  
Vol 27 (1) ◽  
pp. 36-54 ◽  
Author(s):  
W. Kuhn ◽  
O. Künzle ◽  
A. Preissmann
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Time Spectrum ◽  
Test Sample ◽  
Elastic Behavior ◽  
Relaxation Processes ◽  
Relaxation Time Spectrum ◽  
Restoring Force ◽  
Constant Length ◽  
Rapid Deformation

Abstract By rapid deformation of a medium in which linear molecules are present, various changes are produced simultaneously in the latter. These changes are more or less independent of one another, and can release independently and totally or partially by rearrangement of valence distances and valence angles in the chain molecules. By virtue of such relaxation processes, a portion of the stress originating in the rapid deformation disappears, with a changing time requirement for the various portions. A relaxation time spectrum is thus formed. The relaxation time spectrum consists of a finite number of restoring force mechanisms with proper relaxation times or of a continuous spectrum. Both the creep curves (the dependence of the length of a body on time at constant load), and stress relaxation (decay of the stress observed in test sample kept at constant length after rapid deformation), as well as the total visco-elastic behavior, especially the behavior at constant periodic deformation of the test sample, are determined by the relaxation time spectrum. The appropriate Quantitative relationships were derived.

Simulation of the Film Blowing Process Using a Continuum Model for Crystallization in Polymers

2000 ◽  
Author(s):  
I. J. Rao
Keyword(s):  
Viscoelastic Fluid ◽  
Crystalline Phase ◽  
Elastic Solid ◽  
Second Law Of Thermodynamics ◽  
Maxwell Model ◽  
Polymer Processing ◽  
Solid Polymer ◽  
Crystalline Solid ◽  
Film Blowing ◽  
Anisotropic Elastic

Abstract In this paper we simulate the film blowing process using a model developed to study crystallization in polymers (see Rao (1999), Rao and Rajagopal (2000b)). The framework was developed to generate mathematical models in a consistent manner that are capable of simulating the crystallization process in polymers. During crystallization the polymer transitions from a fluid like state to a solid like state. This transformation usually takes place while the polymer undergoes simultaneous cooling and deformation, as in film blowing. Specific models are generated by choosing forms for the internal energy, entropy and the rate of dissipation. The second law of thermodynamics along with the assumption of maximization of dissipation is used to determine constitutive forms for the stress tensor and the rate of crystallization. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The mixture region, where in the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. The anisotropy of the crystalline phase and consequently that of the final solid depends on the deformation in the melt during crystallization, a fact that has been known for a long time and has been exploited in polymer processing. The film blowing process is simulated using a generalized Maxwell model for the melt and an anisotropic elastic solid for the crystalline phase. The results of the simulation agree qualitatively with experimental observations and the methodology described provides a framework in which the film blowing problem can be analyzed.

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