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When you cut the plastic film using the prong of a fork, it probably slightly stretched the film as it was being cut. The stretching, though, was only along the edge. The only way the stretched portion can be stretched but remain attached to the unstretched portion is for it to deform into a curve that lets the edge be longer than the straight edge that ...
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Is there any two objects that as the distance increases between them so do the forces of attraction?
Simple take the two objects and tie them together with an elastic rope (for simplicity assume unbreakable rope) then it happens that the force acting on each object increases as the distance between the two increases. Now if you are talking of a fundamental force then strong nuclear force would be a great example as it has such properties though it might not ...
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Dark field gives better contrast vs the background (no background light), bright field gives better resolution (better numerical aperture, lower depth of field).
For surface feature, oblique illumination is better because it casts shades.
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In a given element of the disk, with a distance $r$ from the centre, length $\Delta r$, and cross section $r \Delta \theta$, the balance of forces are:
$$r \Delta \theta ( \sigma_{r+\Delta r} - \sigma_{r}) = \mu r \Delta \theta \Delta r \omega^2 r$$
Dividing by $r \Delta \theta \Delta r$ and taking the limit when $\Delta r->0$:
$\frac{d\sigma}{dr} = \...
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No, it is impossible. The reason is very simple if one recalls the meaning of phonon dispersion curves. They give the set of possible frequencies, $\omega_s({\bf k})$, for the eigenmodes of the $s-$th dispersion branch.
The energy density of a harmonic crystal, at a temperature $T$ is:
$$
u = u_{static} + \frac{1}{V}\sum_{{\bf k},s} \frac{1}{2} \hbar \...
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There’s a great explanation for this here.
Essentially, you can model rubber as a mess of long, tangled molecules. When the rubber is unstretched, the molecules are more tangled, so in a higher entropy state. Stretching the rubber untangles the molecules, lowering the entropy.
At higher temperature, the change in entropy results in more heating of the ...
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