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Questions tagged [elasticity]

Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.

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Ellipsoid form of a sphere deformed by gravity of its own weight

So I have a sphere of radius $R$, and density $\rho$, elastic modulus $E$ and Poisson ratio $\nu$. With no gravity it is a sphere, but when gravity comes with a direction $(Oz)$ it becomes an ...
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How large can the change in sound velocity in a solid be?

It is known that the "speed of sound" in air is not actually constant, but varies a lot with temperature and composition, with in an ideal gas tending towards zero at $0$ K. $$v_{air} = \sqrt{\frac{\...
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Elastic potential energy

Elastic potential energy derivation For a string ...
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Elastic potential energy per unit volume,stress-strain and strain-stress curve

From what I understand, when we calculate elastic potential energy per unit volume of a material which extends linearly, we calculate the area under the graph of stress- strain OR strain- stress graph,...
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What is the resultant force acting upward on the point of contact under an elastic deformation?

The situation here is you have an elastic string (or a rubber band) fixed at two ends A and B. A•-------------------------------------------------•B An object is ...
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Why is there a difference between work done and elastic potential energy above the elastic limit?

When a spring is inelastically deformed, the work done is no longer equal to the elastic potential energy stored in the spring – what accounts for this disparity? Put another way, the spring is no ...
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Elasticity free boundary terms

Suppose I have a 2D elastic body, and $\mathbf{u}(x,y)$ is a displacement field of the body. I am trying to derive the equilibrium equations for linear elasticity; I define an elastic energy $$E[\...
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Stress v/s Strain in a heated frustum between 2 rigid walls

So consider a situation where we have a frustum b/w 2 walls. We heat it , so it wants to expand but the walls prevent it from doing so. Does the stress in the frustum remain constant or not Say we ...
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Poisson ratio and volume change

Consider a rod of 1 m diameter and 2 m length. The Poisson's ratio of the material is 0.5. Assume the rod is stretched to 2.5 m length. Now longitudinal strain is 0.5/2 = 0.25 lateral strain = ...
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Elastic wave in isotropic medium

The 2D elastic wave equation is given by: $$ \begin{align} \rho \frac{\partial^2 u}{\partial t^2} &= C_{11} \frac{\partial^2 u}{\partial x^2} + C_{44} \frac{\partial^2 u}{\partial y^2} + (C_{12} ...
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Stress acting at an internal point of a suspended rod [closed]

I've come across a question that asks to calculate the stress acting at the midpoint of a uniform rod (mass $M$, length $l$ and area $A$) suspended at one end: I know that the basic definition of ...
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How to get the height of a constrained, infinite elastic surface?

Suppose I have an infinite elastic sheet, constrained by several poles of height 1. The height of the surface would be 1 at the coordinates of each of the poles, and converge to 0 as the distance from ...
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What would be a correct/natural approximation for the curve of bended materials?

Would it be a cubic/quadratic Bezier curve? Or perhaps (part of an) ellipse? I am a computer science student who is working on a physics engine using realistic materials, meaning I would like for ...
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How to measure the mechanical vibration when a hammer hits a nail? [closed]

I want to know the exact location of the vibration sensor that can be placed to measure the vibrations created by a hammer hits the nail.
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1answer
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What limits the projectile speed and power of a ballista?

Suppose that I have arbitrary quantities of some material A, a string material B, and I make a gigantic crossbow/ballista out of it, making an arm out of A and the string out of B. What happens as I ...
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1answer
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What is the error in the potential energy calculation of an elongated rod (if any)?

When we calculate the energy stored in the rod after elongation by an external force, we only consider longitudinal expansion. My question is that according to Poisson, there is also a sideways/...
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Can I combine two shear-stresses acting on one plane?

For example, I have an axial force and a torsion force applied on a rock socket installed in bedrock. So, the socket surface will have two shear stress generated, one in axial direction, and the other ...
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Why does setting kinetic energy equal not work in inelastic collision?

From my understanding, in an inelastic collision there is no loss of kinetic energy. So if we take the following problem: A 7700kg car is traveling 18 m/s and strikes a second car. The two stick ...
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Why does my baby's feeding bottle get smashed in fewer pieces when fuller?

After and after again my baby has tossed in the air his glass made feeding bottle and get it smashed on the floor, I realized that the more the milk the bottle has the fewer fragments I had to ...
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Change in Volume of Objects on applying stress

I came across a statement that whenever any stretching or compressing is done on any object, its change in volume is always greater than $0$. This means that density always decreases (mass remaining ...
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1answer
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Description of the stress in an elastic ring

How can one describe in terms of elasticity the stress necessary to stretch an elastic ring of Young Modulus $E$ and rest radius $R_0$, and width $d$ ? My guess is that in the linear regime, the ...
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Elasticity of an object [closed]

I was studying elasticity, and I thought of certain questions that I couldn't find an answer to. I'll will try to explain my queries If in the elastic limit, the strain on say a rectangular block of ...
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How to determine two elastic tensors are similar?

A elastic tensor is a 3*3 symmetric matrix that determines some material property. I have a elastic tensor A and I want to find the most similar elastic tensor B from a collection of elastic tensors {...
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Why is the law of Hooke valid only for small displacements?

What changes when displacement exceeds a certain limit?
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Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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2answers
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Where does the half of Potential energy go? [duplicate]

We have the formula for elastic energy stored in a spring to be 1/2*Force*extension. When we have an object on a vertical spring, then the energy gained should be 1/2*mgh.(h is extension produced) ...
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Why bulk modulus of air is initial pressure?

So in the definition of bulk modulus the strain part is defined as (∆v/v) where ∆v is change in volume and v is the initial volume and while driving it for air we use the ideal gas law PV= constant ...
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How does tension work for a simple pendulum? What force is at play to keep a rigid body from stretching?

Here recently I have been working on programming a physics framework for simulations, but I've ran into a problem... I was testing forces, so I created a simple pendulum like in the photo, and I ...
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Spring Constant from a Non-Linear Force-Extension Graph

If you have a linear force-extension graph for say a spring then the spring constant is simply the gradient of the graph. However, how would you calculate the spring constant at a particular point on ...
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What does “substantial changes” in material properties mean in geometric optics?

We know that (I read it from Kip Throne's Modern Classic Physics) if a wave's wavelength is smaller than the length scale over which "substantial changes" of material properties occur, then the wave ...
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Doubts in understanding the elastic property of matter

Here the graph of potential energy and force produced due to interaction between two atoms are given . And at a particular separation between the atoms, they have their minimum potential energy. And ...
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1answer
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Doubt in the derivation of the relation between Young's modulus and Modulus of rigidity

Please refer to the image attached. My doubt is marked in red. What i don't understand in this part of the derivation is that how and why is the extension and compression is equivalent to a shear ...
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2answers
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Why is the mechanical energy lost whenever an object undergoes plastic deformation?

I have read here that "Mechanical energy is lost whenever an object undergoes plastic deformation." Why is that? I mean the object would be changing its shape, and while it's changing its shape it ...
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How can you use tensors in theory of elasticity? [closed]

I am interested in physics and Icame across the usage of tensors in elasticity. How do you do that? How can tensors be useful?
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Elastic collision between a circle and a point [duplicate]

In a 2D environment, I have a circle with velocity v, a stationary point (infinite mass), and I am trying to calculate the velocity of the circle after a perfectly elastic collision with the point. ...
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Calculating velocities of 2 squares after collision

If I have 2 squares each with random velocities, and both with the same mass, would it be possible to calculate their velocities after a collision, and how would I do so?
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Which formula for elastic collision?

When researching a bit about elastic collisions, I've been confused about how many different ways there are to do this. I've seen multiple methods, some of which are extremely complex (using sine and ...
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Why does a metal block make a shrill sound but not a wooden block upon hammering?

When hammered, a metal block makes a shrill sound but not a wooden block of identical shape. Is it that the wooden block vibrates with lesser frequency than the metal block? If so, why is that? Also ...
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Yi's Bell sound and how it relates to temperature?

Yi's Bell is an ancient chinese musical instrument that plays different sound frequencies when its heated than when its in room temperature. My question is Why does that happen? Why does higher body ...
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The relation between the spring constant and its radius [duplicate]

I've observed that the spring constant of a spring with a smaller radius is higher than that of a spring with a larger even though they are made of the same material , their thickness and all other ...
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My Elasticity Doubt

I had a question on elasticity which looked something like this. {: .center} We have small beads of mass say $m$ and Mass of rod say $M$. Now we need to find the extension in the rod after the beads ...
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1answer
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What are inelastic elastic-bands?

In the third episode of Julius Sumner Miller's physics series he sets up an experiment with two masses connected by an array of elastic-bands. He comments that the elastic-bands are inelastic. ...
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1answer
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Continuum limit for a bulk of discrete masses coupled by springs

I have a question that has been bothering me for a long time. I know very well how to take the continuum limit for a chain of masses connected by springs. But in my recent project I would like to ...
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3answers
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Hooke's full unapproximated law

It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation. That is, the equation $F=-kx$ is only ...
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Why is the partial derivative of strain energy function with respect to strain equal to stress

In Elasticity, we have a strain energy function , $W$, that is a function of strain tensor, $E$. Then the cauchy stress tensor, $T$ can be determined by: $$T_{ij}=\frac{\partial W}{\partial E_{ij}} \...
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Confusion Regarding Hookes law

I am used to seeing Hookes law in the form: $F = kx$ but in another one of my books it gives the equation: $\\ F = \frac{\lambda x}{l}$ where $l$ is the unstretched length, $x$ is the extension and $\...
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4answers
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Stress in a rod clamped between two rigid walls when the temperature is increased

The usual approach to calculate stress is to equate thermal expansion in the unclamped condition to the magnitude of contraction caused by strain produced due to the walls. I have some questions about ...
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Elongation of rod in two cases

Case 1: Suppose there is a rod hung vertically from the ceiling. It experiences gravitational force W (its weight).It's Young's Modulus is $Y$. Now I know that the end connected to the ceiling ...
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Deformation of a circle ring under tensile force

How will it deform when I apply a tensile force to a circle ring? Can I estimate the force applied on the ring by knowing the major and minor axis of the deformation elliptic ring? For simplicity we ...
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How is elastic hysteresis effected by time?

Here's how I understand the phenomenon: let's take the example of weights and rubber band, when a weight is put it does work on the band to stretch it, and heats it up, some of the heat gets ...