Strain in physics

[latex]\text).[/latex] Another unit that is often used for bulk stress is the atm (atmosphere). Conversion factors are [latex]\begin[/latex] An object or medium under stress becomes deformed. The quantity that describes this deformation is called strain. Strain is given as a fractional change in either length (under tensile stress) or volume (under bulk stress) or geometry (under shear stress). Therefore, strain is a dimensionless number. Strain under a tensile stress is called tensile strain, strain under bulk stress is called bulk strain (or volume strain), and that caused by shear stress is called shear strain. The greater the stress, the greater the strain; however, the relation between strain and stress does not need to be linear. Only when stress is sufficiently low is the deformation it causes in direct proportion to the stress value. The proportionality constant in this relation is called the elastic modulus. In the linear limit of low stress values, the general relation between stress and strain is [latex]\text[/latex] Aluminum 7.0 7.5 2.5 Bone (tension) 1.6 0.8 8.0 Bone (compression) 0.9 Brass 9.0 6.0 3.5 Brick 1.5 Concrete 2.0 Copper 11.0 14.0 4.4 Crown glass 6.0 5.0 2.5 Granite 4.5 4.5 2.0 Hair (human) 1.0 Hardwood 1.5 1.0 Iron 21.0 16.0 7.7 Lead 1.6 4.1 0.6 Marble 6.0 7.0 2.0 Nickel 21.0 17.0 7.8 Polystyrene 3.0 Silk 6.0 Spider thread 3.0 Steel 20.0 16.0 7.5 Acetone 0.07 Ethanol 0.09 Glycerin 0.45 Mercury 2.5 Water 0.22 Tensile or Compressive Stress, Strain, a...

Learning Objectives By the end of this section, you will be able to: • Explain Newton’s third law of motion with respect to stress and deformation. • Describe the restoration of force and displacement. • Calculate the energy in Hook’s Law of deformation, and the stored energy in a string. Newton’s first law implies that an object oscillating back and forth is experiencing forces. Without force, the object would move in a straight line at a constant speed rather than oscillate. Consider, for example, plucking a plastic ruler to the left as shown in Figure \(\PageIndex\): (a) A graph of absolute value of the restoring force versus displacement is displayed. The fact that the graph is a straight line means that the system obeys Hooke’s law. The slope of the graph is the force constant \(k\). (b) The data in the graph were generated by measuring the displacement of a spring from equilibrium while supporting various weights. The restoring force equals the weight supported, if the mass is stationary. Example \(\PageIndex\] Discussion Note that \(F\) and \(x\) have opposite signs because they are in opposite directions—the restoring force is up, and the displacement is down. Also, note that the car would oscillate up and down when the person got in if it were not for damping (due to frictional forces) provided by shock absorbers. Bouncing cars are a sure sign of bad shock absorbers. Energy in Hooke’s Law of Deformation In order to produce a deformation, work must be done. That is...

1 Introduction: The Nature of Science and Physics • Introduction to Science and the Realm of Physics, Physical Quantities, and Units • 1.1 Physics: An Introduction • 1.2 Physical Quantities and Units • 1.3 Accuracy, Precision, and Significant Figures • 1.4 Approximation • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 2 Kinematics • Introduction to One-Dimensional Kinematics • 2.1 Displacement • 2.2 Vectors, Scalars, and Coordinate Systems • 2.3 Time, Velocity, and Speed • 2.4 Acceleration • 2.5 Motion Equations for Constant Acceleration in One Dimension • 2.6 Problem-Solving Basics for One-Dimensional Kinematics • 2.7 Falling Objects • 2.8 Graphical Analysis of One-Dimensional Motion • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 3 Two-Dimensional Kinematics • Introduction to Two-Dimensional Kinematics • 3.1 Kinematics in Two Dimensions: An Introduction • 3.2 Vector Addition and Subtraction: Graphical Methods • 3.3 Vector Addition and Subtraction: Analytical Methods • 3.4 Projectile Motion • 3.5 Addition of Velocities • Glossary • Section Summary • Conceptual Questions • Problems & Exercises • 4 Dynamics: Force and Newton's Laws of Motion • Introduction to Dynamics: Newton’s Laws of Motion • 4.1 Development of Force Concept • 4.2 Newton’s First Law of Motion: Inertia • 4.3 Newton’s Second Law of Motion: Concept of a System • 4.4 Newton’s Third Law of Motion: Symmetry in Forces • 4.5 Normal, Tension, and Other Examp...

There is nothing particularly magical about the shape of a coil spring that makes it behave like a spring. The 'springiness', or more correctly, the elasticity is a fundamental property of the wire that the spring is made from. A long straight metal wire also has the ability to ‘spring back’ following a stretching or twisting action. Winding the wire into a spring just allows us to exploit the properties of a long piece of wire in a small space. This is much more convenient for building mechanical devices. In mechanics, the force applied per unit area is what is important, this is called the stress (symbol σ \sigma σ sigma ). The extent of the stretching/compression produced as the material responds to stress is called the strain (symbol ϵ \epsilon ϵ \epsilon ). Strain is measured by the ratio of the difference in length Δ L \Delta L Δ L delta, L to original length L 0 L_0 L 0 ​ L, start subscript, 0, end subscript along the direction of the stress, i.e. ϵ = Δ L / L 0 \epsilon=\Delta L/L_0 ϵ = Δ L / L 0 ​ \epsilon, equals, delta, L, slash, L, start subscript, 0, end subscript . • Elastic deformation. When the stress is removed the material returns to the dimension it had before the load was applied. The deformation is reversible, non-permanent. • Plastic deformation. This occurs when a large stress is applied to a material. The stress is so large that when removed, the material does not spring back to its previous dimension. There is a permanent, irreversible deformation. ...

\( \newcommand\) • • • • • Learning Objectives By the end of this section, you will be able to: • State Hooke’s law. • Explain Hooke’s law using graphical representation between deformation and applied force. • Discuss the three types of deformations such as changes in length, sideways shear and changes in volume. • Describe with examples the young’s modulus, shear modulus and bulk modulus. • Determine the change in length given mass, length and radius. We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by \[F = k \Delta L, \] where \(\Delta L \) is the amount of deformation (the change in length, for example) produced by the force \(F\), and \(k\) is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function o...

• State Hooke’s law. • Explain Hooke’s law using graphical representation between deformation and applied force. • Discuss the three types of deformations such as changes in length, sideways shear and changes in volume. • Describe with examples the young’s modulus, shear modulus and bulk modulus. • Determine the change in length given mass, length and radius. We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. A change in shape due to the application of a force is a deformation. Even very small forces are known to cause some deformation. For small deformations, two important characteristics are observed. First, the object returns to its original shape when the force is removed—that is, the deformation is elastic for small deformations. Second, the size of the deformation is proportional to the force—that is, for small deformations, Hooke’s law is obeyed. In equation form, Hooke’s law is given by where is the amount of deformation (the change in length, for example) produced by the force and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Note that this force is a function of the deformation —it is not constant as a kinetic friction force is. Rearranging this to makes it clear that the deformation is proportional to...

Discussion basics Elasticity is the property of solid materials to return to their original shape and size after the forces deforming them have been removed. Recall Hooke's law — first stated formally by Robert Hooke in The True Theory of Elasticity or Springiness (1676)… ut tensio, sic vis which can be translated literally into… As extension, so force. or translated formally into… Extension is directly proportional to force. Most likely we'd replace the word "extension" with the symbol ( ∆ x), "force" with the symbol ( F), and "is directly proportional to" with an equals sign ( =) and a constant of proportionality ( k), then, to show that the springy object was trying to return to its original state, we'd add a negative sign ( −). In other words, we'd write the equation… F=− k∆ x This is Hooke's law for a spring — a simple object that's essentially one-dimensional. Hooke's law can be generalized to… Stress is proportional to strain. where strain refers to a change in some spatial dimension (length, angle, or volume) compared to its original value and stress refers to the cause of the change (a force applied to a surface). The coefficient that relates a particular type of stress to the strain that results is called an elastic modulus (plural, moduli). Elastic moduli are properties of materials, not objects. There are three basic types of stress and three associated moduli. Elastic moduli modulus (symbols) stress (symbol) strain (symbol) configuration change Young's ( E or ...