# 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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### Is the force $F$ in formula of longitudinal stress applied on both sides of a rod?

Suppose a force $F$ is applied on one face of a rod (with cross-sectional area $A$) and one end is fixed. And now suppose another situation with the same rod, force $F$ is applied on both faces of the ...
0answers
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### Strain rate and deformation in non-Cartesian coordinates

I have a question regarding the connection between deformation, strain, and strain rate: The deformation tensor $\textbf{F}$ is defined by $F_{ij} = \partial X_i / \partial x_j$ and its determinant ...
0answers
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### Bow and Arrow problem '2'

Several days ago I posted the next question....Bow and Arrow problem. At the beginning the question got 3 downvotes but after a certain period it stabilized at equal number of downvotes and upvotes... ...
0answers
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### Could you help me understand the notation of forces on the plate?

I am so confused about the notation in this book with the one I learned before. So could anybody help me comprehend the notation in this figure? I am not clear about is the notation of the moments. ...
1answer
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### Physics of bursting balloons?

This is a reference request for a theory of bursting balloons: Let's say I have a balloon and this balloon has an impurity along a small strip. Let's assume for example the balloon had a hole there at ...
1answer
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### Stress to make concrete stronger

In reinforced concrete steel rods are embedded in wet cement and held in tension while the mixture dries. Once fully dry the tension is removed, and the concrete should be stronger as a result of this ...
1answer
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### Why is the number of independent elements of a stiffness tensor 21?

I think that the dilatation of an elastic material is proportional to the hydrostatic pressure. That is, ${\rm{tr}}(\boldsymbol\sigma)=3k\ {\rm{tr}}(\boldsymbol\epsilon)$ for small strains. If so, ...
2answers
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### Elastic Modulus of Elastomers

For an elastomer, what could be the modulus of elasticity. My thought process is that the modulus of elasticity is the tangent of a point of the stress-strain graph. And therefore looking at the graph ...
0answers
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### Chladni plates theory

I have come upon a very old post (Theory behind patterns formed on Chladni plates?). In this post, the computation of the eigenmodes of a rectangular plate with free edges is addressed, but one point ...
1answer
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### Why do books deform?

I take a thick book, open it to the middle, put a pencil in it, and then close the book. If I then wait five minutes and take the pencil out, the book will go back to normal. If I instead wait five ...
1answer
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### Regarding the Hooke's law and how it can be described using stress and strain [closed]

Can someone kindly explain to me the how the relationship marked as (2) below is obtained from the relationship marked as (1). In our Physics class, our lecture wrote down the following relationship, ...
5answers
497 views

### In a collision shouldn't objects of different mass have same acceleration?

Suppose two objects of different mass, A and B, collide with each other. Now, during the time of collision, they both apply forces on each other according to Newton's 3rd law. Therefore, their ...
1answer
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### Impulse Time Elapsed in relation to Hardness and Momentum

I am trying to calculate the time elapsed of an impulse during a collision of two objects. I will give three examples below in hopes that they make clear what I am stuck on. Two object of the same ...
2answers
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### What is the unit for modulus of elasticity?

I've previously asked a question regarding the modulus of elasticity which I am still unsure about. I've been told various formulae to calculate the modulus of elasticity, some of which give answers ...
1answer
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### How do I calculate the modulus of elasticity of a spring when I don't know the cross-sectional area? [closed]

'An elastic spring of natural length 1.5 m has one end attached to a fixed point. A horizontal force of magnitude 4 N is applied to the other end and compresses the spring to a length of 1 m. Find the ...
0answers
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### Energy conservation of longitudinal waves

Suppose I have an elastic body described by a vector field $\pmb{\Delta} \left( \pmb{x}, t \right)$ which gives the displacement of a point from equilibrium. This field can be separeted in a ...
1answer
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### Does increasing the number of stretched elastic bands increase the total elastic potential energy?

Suppose I stretch a single elastic band to $x$ cm attached to an object like a paperclip. The elastic has potential energy modelled by $$U = \frac{1}{2}kx^2$$ where $U$ is potential energy, $k$ is the ...
0answers
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### Can tablets/capsules bounce?

I'm doing a physics lab on rotational motion tomorrow and I wanted to know whether a capsule-shaped object (other than a tic-tac, i.e. a capsule/pill, since I don't have tic tacs and don't have time ...
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### Rotational invariance of the the elastic deformation in spherical symmetry

I write the elastic deformation $E$ for an incompressible material in spherical symmetry (Have a look at here Eq.(5.32) ). Since we are incompressible, $\mathbf{det} \,E=1$, so in spherical ...
1answer
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### Chameleon's tongue as a harmonic oscillator

I was watching a documentary about reptiles, at some point, it showed how chameleons catch their prey. Approximately, their tongue has an acceleration of $2500 \frac{m}{s^2}$, length of $0.7m$. They ...
3answers
220 views

### Rule of the Work done by a force

I have been always taught that Work done = force x distance through which the force was applied. but recently in the elasticity I have been taught that W= (1/2) (F X D). why did we multiply it by a ...
1answer
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### Completely elastic and inelastic colission

I know what is preserved in completely inelastic collision: $m_1v_1+m_2v_2=(m_1+m_2)v$. Now I would like to know what is preserved in completely elastic one.
2answers
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### How much of the momentum is being transfer in case of collision relative to elastically and momentum difference?

if we take a look at two objects that has been collision ,we may use the the third law of newton to calculate the velocity of each one if we know the force they use on each other. for example if we ...
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1answer
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### Continuum Mechanics: Why would dashpot kinematics require 5 equations to specify deformation for a 2D axisymmetric problem?

I work with PEG hydrogels and use the material to recapitulate cartilage biology and I am really interested in modeling the soft tissue mechanics in COMSOL. I have been studying the work of Caccavo et ...
0answers
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### Can anyone explain how this rod (experiencing shear stress and deflection) mysteriously resists the downward force from the weight of the mass?

This fascinating and, in my opinion, very unique question came out of a competition lab I did in a general engineering course. I will leave out or change info about the lab to make this question more ...
4answers
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### Mathematical definition of elastic materials

Physically, elastic materials are materials which return to their original state upon complete removal of applied mechanical loads under isothermal conditions. In the book "Mechanics of ...
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### mechanical energy for a membrane with natural curvature of both radii

I'd like to study the following mechanical energy : $$F_{my\,energy}=\int \Big(\frac{1}{R_1}-c_1\Big)^2+\Big(\frac{1}{R_2}-c_2\Big)^2 dA$$ I noticed that this energy cannot be written as a Canham-...
1answer
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### Energy of local rotation in elasticity theory

In the theory of elasticity there is an important object, the displacement increment vector $u_i$. The derivative of such an object can be decomposed into symmetric and antisymmetric parts:  \...
1answer
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### Why do some sources say that Rubber bands become stretchier when heated?

For a physics project I'm changing the temperature of a rubber band and measuring elasticity. The rubber band will be tied to a mass and will be heated in a water bath. Some sources show data of the ...