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.
921 questions
0 votes
2 answers
82 views
Confusion in finding stress in accelerated body
On the left side, my teacher shows the method for finding stress on a small element dx of a rod. He treats the tension as the restoring force. However, my question concerns the diagram on the right ...
11 votes
2 answers
3k views
If you're putting a rubber band around a sphere, when does it stay on?
A little while ago, I was fidgeting with a ball and some elastic bands, and I noticed that it seems like the elastic bands have to lie along a great circle (or near one) in order to not snap off. Is ...
- 119
3 votes
0 answers
94 views
Possible Error in Pippard's "Cavendish Problems in Classical Physics": Extension of a wire under its own weight [closed]
I am going through Brian Pippard’s Cavendish Problems in Classical Physics and came across the following exercise: Calculate the extension under its own weight of a wire $10\,\mathrm{m}$ long ...
- 75
1 vote
1 answer
150 views
Does this spring work with Hooke's law or not? [closed]
In the table is the data from the spring. In the y axis is the force in Newtons, and in the x axis is the extension in meters. Edit: I found out the reason why this spring did not work as initially ...
- 11
1 vote
0 answers
74 views
Da Vinci bridge: why outer steps stay in place?
Consider Da Vinci's famous "boltless" bridge. (See image below*) Consider in particular an implementation with a significant 'arc', i.e. both ends start with a significant incline. How to ...
- 653
2 votes
3 answers
509 views
Does the maximum amount of energy a spring can store depend on spring geometry?
I have two springs made from the same metal, one is a helical torsion spring, and one is a spiral watch spring. Both springs contain the same volume of metal in their active region. I wind up both ...
- 1,424
0 votes
0 answers
79 views
Visualising the twist produced in every segment of an axially loaded compression spring
My understanding of the mechanism of axially loaded compression springs: When loaded axially, a small twist is produced in every single element AB of the spring. To explain what I mean more clearly, ...
0 votes
0 answers
70 views
Intuitive view of structural metamaterials
A little bit of background here: I have a bachelor’s in chemistry and have broad interests in scientific topics but I am NOT a scientist. I can handle a mathematical explanation but not a specialist ...
3 votes
1 answer
191 views
Finite Speed of Propagation for 2D Elastic Green's Function
$\newcommand{\RR}{\mathbb{R}}\DeclareMathOperator{\diag}{diag}$I'm working on deriving the analytic solution for wave propagation in an infinite homogeneous 2D linear elastic material, as a warmup for ...
- 135
-1 votes
1 answer
336 views
For the stress-energy tensor, is there an analogue to Hooke's law for $\sigma_{ij}$?
Hooke's law for the Cauchy stress-tensor is: $$ \sigma_{ij} = \lambda u_{kk} \delta_{ij} + 2 \mu u_{ij} $$ with the deformation tensor $u_{ij}$ which is calculated by $u_{ij}=1/2(\partial_iu_j + \...
- 143
0 votes
3 answers
129 views
What causes road resistance of a tire?
Road loss of a bicycle tire is usually explained as the work of deformation, as the leading edge continually deforms upon contact with the pavement; i.e. the tire flattens. However, at the trailing ...
- 385
2 votes
2 answers
266 views
How do you derive the speed of a transverse wave in a solid medium? [closed]
Before I start, yes I have read Speed of a transverse wave in a solid medium but I want a proof which is more elementary and intuitive that doesn't use the full tensor theory of elasticity. I couldn't ...
- 326
7 votes
3 answers
2k views
Why the upper section falls faster than the bottom section when the line is cut?
This question is from the book Problems in Elementary physics - Bukhovtsev et al. question number 78. It goes like this: A homogeneous cube is hanging from a line. The line is then cut. Which parts ...
- 257
6 votes
3 answers
2k views
Why is the Young modulus of a gas "undefined"?
Various sources on Google state that the Young's modulus of a gas is undefined rather that zero. Why is this so? The Young's modulus(Y) of a material is defined as $$Y=\frac{\sigma \ (tensile \ stress)...
- 326
0 votes
0 answers
37 views
Understanding the mathematical definition of stress [duplicate]
I don't properly understand how this equation defines stress- $$\sigma=\lim_{\Delta A \to 0} \frac{\Delta F_{\rm internal}}{\Delta A}$$ How does it relate to the intutive defination of stress-"...
