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Physics

Questions tagged [elasticity]

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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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2answers
89views

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 ...
11votes
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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1answer
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$\newcommand{\RR}{\mathbb{R}}\DeclareMathOperator{\diag}{diag}$I'm working on deriving the analytic solution for wave propagation in an infinite homogeneous 2D linear elastic material, as a warmup for ...
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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 + \...
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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 ...
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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 ...
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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 ...
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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 $$Y=\frac{\sigma \ (tensile \ stress)...
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I don't properly understand how this equation defines stress- $$\sigma=\lim_{\Delta A \to 0} \frac{\Delta F_{\rm internal}}{\Delta A}$$How does it relate to the intutive defination of stress-"...

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