# Tagged Questions

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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### Why is the vibration in my wire acting so oddly?

I was soldering a very thin wire today, and when I had one end firmly soldered, I accidentally bumped the wire diagonally with my tweezers. What I'd expect to happen is that the wire oscillates for a ...
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### Why is filling a balloon from your mouth much harder initially?

Why is it that when you first fill up a balloon, it's hard to get air through, but after inflating it a bit, it becomes much easier to further inflate the balloon?
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### Why can one bend glass fiber?

Why can one bend glass fibers without breaking it, whereas glasses one comes across in real life is usually solid? Is there also a good high-school level explanation of this?
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### Is an entropic force an actual force that can be explained as a fundamental interaction?

Fundamental interactions, such as electromagnetism, the strong force, the weak force, and possibly gravitation, all have something in common: They can be described in terms of relativistic quantum ...
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### Inflating a balloon (expansion resistance)

I am doing a quick calculation on how to calculate the pressure needed to inflate a perfectly spherical balloon to a certain volume, however I have difficulties with the fact that the balloon (rubber) ...
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### Aren't all collisions elastic at some level?

The more I think about it, inelastic collisions produce heat and sound which imply motion at some scale, right? Are inelastic collisions macroscopic events that ignore motion at microscopic levels? ...
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### Will a tennis ball go further if i hit it with the side of the racket?

If i hit a tennis ball 'properly' on the stringing, does it go further than if i rotate the racket 90 degrees in my hand and hit the ball with the same force, but on the side of the frame? I'm ...
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### Why does the balloon pop?

When we pierce a balloon with a sharp needle, it pops and produce a great sound. But, It doesn't pop when we open the mouth of the balloon (through which we have blown air)... So, Why doesn't the gas ...
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### Elasticity of Space; How does the expansion of Space affect gravity?

Does space have an elastic quality? What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine ...
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### What determines the bounce time of an elastic ball?

Consider an elastic ball is bounced off a hard flat surface. I would like to reconcile two different answers to the question "how does the contact time between the ball and surface depend on the speed ...
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### Why does the overhand knot jam but the figure-8 knot doesn't?

After tensioning a rope with an overhand knot in it, it is often very hard if not impossible to untie it; a figure-8 knot, on the other hand, still releases easily. Why is that so? Most "knot and ...
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### Origin of Elasticity

Why is it that not all bodies possess Elastic behavior? What is the origin of elasticity or plasticity? I mean, it's a physical property. So, how does it relate to atoms or molecules in different ...
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### gravity delayed by speed of information transfer

A few months ago I had the pleasure of listening to an episode of RadioLab (a very informative podcast I would recommend to everyone) when they had Neil deGrasse Tyson on. He was discussing the very ...
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### Physical meaning of elastic constants of a monoclinic crystal

For the elasticity of a material, Hook's law can be written in tensorial form as: $$\sigma = \mathsf{C}\, \varepsilon$$ where $\sigma$ is the Cauchy stress tensor, $\varepsilon$ is the infinitesimal ...
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### Elastic band around a cylinder

An elastic band is stretched using a known force and then placed around a cylinder. How are the forces or tensions distributed? I assume there will be two components: firstly, a tangential or ...
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### Tensorial version of Hooke's law

It is well known that $${\boldsymbol F} = k {\boldsymbol x}$$ for isotropic media. Also, according to Wikipedia $$F_k = k_{jk} x_j$$ for some elastic tensor $k_{jk}$. I'm a bit confused as to how ...
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### Does zero strain always imply zero stress?

In solid mechanics, can I always assume that if an object undergoes no strain, then no stress is applied to it? I think it's true only because I can't seem to find a counter-example.
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### What is the root cause of elasticity of a material?

I know that there exist some interatomic and intermolecular forces in the material but why does stretching a material will enhance attractive force over repulsive force and vice versa.
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### Normal modes of a flexible rod clamped at only one point

I am interested in the vibrations of a thin, flexible rod that would only be clamped at one point, properly I'd like to calculate its eigenvalue. But the way I learned it in wave mechanics doesn't ...
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### A question about surface tension of membranes and their curvature

I'm reading a review about membranes properties and I have reach a section about fluid membranes. The section discuss the principal curvatures ($c_1, c_2$) and the spontaneous curvatures ($c_0$). ...
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### Stress tensor in a cube with shear forces

I want to calculate stress matrix in a cube with two faces parallel to x axis and perpendicular to z axis (sorry I don't know how can I put a picture in this post). There are two force uniform ...
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### First-principles derivation of cutting force

I know that the amount of force required to separate a material from itself is linked to the surface energy of that material. However, looking at just the surface energy laughably underestimates the ...
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### Reference Request: Fluid dynamics/Elasticity via Lagrangians

Would there be a book that does what Landau does in Fluid Mechanics and Theory of Elasticity using Lagrangian's/Action-principles, analogous to the presentation in Landau's mechanics? I have only ...
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### (Botanical) branch bending under gravity

I'm a PhD student in maths, and attended my last physics class some 15 years ago, so you can imagine my competences in the field. My supervisor (also not a mechanist) cant tell me how to proceed ...
2k views

### Rubber Band Forces

I have a question regarding the force a band places on an object. Say I have a rubber band wrapped around 2 pegs at a certain distance, and at that distance I know the pounds of force per inch it is ...
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### A conceptual problem with Euler-Bernoulli beam theory and Euler buckling

Euler-Bernoulli beam theory states that in static conditions the deflection $w(x)$ of a beam relative to its axis $x$ satisfies $$EI\frac{\partial^4}{\partial x^4}w(x)=q(x)\ \ \ \ (1)$$ where $E$ is ...
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### How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?

This is a question about dynamics. If I have understood correctly there should be a tensor that describes the dynamics of a (solid?) body (= viscosity ?). I mean, tensor that includes the time ...
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### Good books on elasticity

Can someone suggest good books/textbooks/treatises/etc on elasticity?
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### Parabola or Catenary in this case?

Exhibit A: the flexible film sinks into the box due to lower internal pressure inside the box. question is, does the film form a paraboloid or a 3D catenary or neither? this is the usual method used ...
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### What equation predicts at what point a stretched object comes apart?

I am creating a simulation and am interested in pulling stretchy things and when they break, like taffy. I imagine this is a bit tougher then a simple equation like gravity, but I have no idea. Is ...
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### What does Hooke's law have to do with molecular forces?

In The Feynman Lectures, in the chapter Characteristics of Force, In the section entitled Molecular forces, Feynman talks about the molecular forces, and then he states afterwards: If the ...
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### origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$\sigma_{ij} = C_{ijkl} \epsilon_{kl}$$ Because $\sigma$ ...
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### Does quasi-static motion imply zero energy dissipation?

When a droplet is deposited on a surface with some surface roughness and subsequently tilted it can stick due to pinning (think of droplets on a window after rain). What I am interested in is how/...
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### What is the function of the top point of a bouncing ball?

A ball is thrown away as parallel to x axis from M(0,h) point with speed V . After each jumping on x axis , it can reach half of previous height as shown in the figure.(Assume that no any air ...
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### Young modulus and Sound Velocity in a continuus medium

In elasticity theory, general equations of motion are: $$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$$ where $\overline u$ are ...
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### Rubber band elongates like s-curve

A normal rubber band (brownish yellow) with about 1 mm^2 cross section and approximate slack length of 170 mm is suspended vertically and gradually loaded with a number of weights (each weighing 9.36 ...
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### Derivation of elastic energy per unit volume

So I basically asked this question a little while back and didn't get much help, but I really need help, so I'm coming back and asking again. Looking at the section on Continuum Systems on the ...
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### Cantilever Beam - Maximum Shear of the Beam

A cantilever beam $3\ \text{m}$ long is subjected to a moment of $10\ \text{kNm}$ at the free end. Find the maximum shear of the beam. The answer is "There is no vertical load, shear is zero" How ...
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### How to calculate the energy in thermoelastic damping?

Note - I'm not 100% sure *thermoelastic damping* is the right term here - so please feel free to correct the question in case I'm wrong! If a force is applied to an elastic rod such that it ...
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### Degree of anisotropy of crystal tensors

Does there exist a scalar that can describe how anisotropic the elasticity of a crystal is? What about other tensors such as the permittivity or susceptibility? I found a Wikipedia article that was ...
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### Consistent theory of continuum

Why is there a consistent theory of continuum mechanics in which one just consider things like differential elements and apply Newtons laws? Is there a deeper reason for it. Is it the nature of ...
2k views

### Simple elastic collision

If a particle with mass $m$ collides with a wall at right angles, and the collision is perfectly elastic. The particle hits the wall at $v\ ms^{-1}$. There is no friction or gravity. So the particle ...
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### What is the two dimensional equivalent of a spring?

I'm trying to model isotropic linear elastic deformation in two dimensions. In one dimension, I know that a linear elastic material can be thought of as a spring which obeys Hooke's law $F=-k\Delta x$...
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### Illustrating the definition of Young's modulus from spring factor

The relationship between Young's modulus $E$ and the spring factor $k$ from Hooke's law is $k=\frac{E A}{L_0}$ where $L_0$ is the initial length of the stretched material and $A$ the cross-...