# 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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### 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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### Hooke's law limitation question

Let's consider a spring. I am a strong man(well, lets assume) and I am pulling the spring. the work I do is being stored in the spring in the form of its elastic potential energy. Then suddenly, ...
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### Maximum Shear on a Beam - beam with fixed support on one end and hinge on other end

A beam $\displaystyle 3m$ long with fixed support on one end and hinge on the other end is subjected to a uniform load of $10\ kN/m$. What is the maximum shear of this beam? The solution is this one: ...
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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 do I find the force from drop shock using material properties?

I am dropping a cylindrical cast iron bar with a know elastic modulus and poisson's ratio, $E_{1}$ and $v_{1}$, onto a flat beam of elastic modulus, $E_{2}$ and $v_{2}$ so there is tangential drop ...
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### Whats the contact area for elastic contact between a cylinder and a plane surface?

I am trying to determine the contact area between a cylinder and a plane surface of two different materials so that the plane lies tangent to the cylinder. There is elastic contact between the two ...
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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 ...
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### Is shear elasticity the same as shear modulus?

I've encountered both the terms "shear elasticity" and "shear modulus". Are these the same?
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### Modeling linear spring deformation in time

Suppose I had a spring (at equilibrium) and applied a certain force $F$, causing it to undergo elastic deformation. I know that by applying this specific force, hooke's law tells me that the spring ...
24k views

### 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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### A differential equation of Buckling Rod

I tried to solve a differential equation, but unfortunately got stuck at some point. The problem is to solve the diff. eq. of hard clamped on both ends rod. And the force compresses the rod at both ...
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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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### Decomposition of elastic constants of a crystalline material

I have performed a calculation the tensor of elastic constants (or stiffness tensor) for a given crystalline material. From there, I calculated various elastic properties, such as Youngâ€™s modulus, ...
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### Modulus of Elasticity

Consider a cube of unit dimensions. Let $\alpha$ and $\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying unit tension - 1) At one edge: Young's ...
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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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### Fracture because of high-speed rotation

I was watching a rerun of an early MythBusters episode, where they look at whether CDs in high-speed drives can explode / fail simply because of being rotated too fast. The following are some ...
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### Slackline Jump Tension

So a slackline is basically a bouncy tight rope. I found a site that has a calculator for the tension of a static slackline http://www.slacklineexpress.com/force.php?linelength=40&sag=1&w=...
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### 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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### Why does a ball bounce?

If an object is acted on by equal and opposite forces then it will be in equilibrium, and it's acceleration or velocity (and so direction as well) will not be changed. So when a ball bounces, it ...
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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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### 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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### Boundary conditions of Navier-Cauchy equation

I'm having difficulties with Neumann boundary conditions in Navier-Cauchy equations (a.k.a. the elastostatic equations). The trouble is that if I rotate a body then Neumann boundary condition should ...
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### Why does elastic energy only depend on first derivatives?

Say we have an elastic material that is deformed with displacement function $u : \mathbb{R}^n \rightarrow \mathbb{R}^n$. It is reasonable to assume that the energy required for such a displacement is ...
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### At what point does a projectile leave a slingshot?

Assuming a frictionless / "perfect" environment, and given a ball held in an elastic sling (like a hand-held catapult) where the pocket is lighter than the projectile itself, what is the point at ...
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### Is there analysis library for stress-strain data?

I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield stress/...
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### Friction + Bouncing of an Object against an Elastic Wall

I am trying to create the formula for applying a bouncing effect to an element which is already slowing down by friction. At the moment I have an element which moves in one dimension at speed "S" and ...
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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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### Simplifying some math for an ant-on-rubber-band problem

OK, I've been doing this problem for fun (it's a great problem, BTW!): http://www.physics.harvard.edu/academics/undergrad/probweek/prob76.pdf Here is the solution: http://www.physics.harvard.edu/...
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### Can a wave propagate in an elastic fluid in the absence of volume forces?

A motion (wave) $\mathbf{x}: \mathcal{B}_0 \times [t_0,t_1] \to \mathcal{E}:$ such that $q-o = \mathbf{x}(p,t)=(p-o)+\mathbf{a}_0 cos(\mathbf{k}_0\cdot(p-o) - \omega_0 t)$ can propagate in an elastic ...
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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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### 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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### Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?

Assumptions: Cross terms in strain tensor are defined as equal $\varepsilon_{xy} = \varepsilon_{yx}$. pure mode I crack. Far from crack tip, material is purely elastic and we are way below yield ...
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### Determine the tensor of contraint and deformation of a cube under compression

We have a cube under compression with dimension l1*l2*l3, is put between 2 rigid plates in the axis 1 (two plates block the deformation of the cube in thÃ­ axis), the cube is also put on a rigid plate, ...
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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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### 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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### How must you spin the ball to make it alternate between 2 positions? [closed]

Assume any parameters you may need. Thanks in advance.
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### Modellng mechanical behavior of heat shrink film

Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or radiation)...