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Yes, the rod will ultimately break—barring any other failure mechanism that occurs first.
(Depending on the material and conditions, you may need to wait a very, very long time, but your mentions of "long enough" and "ultimately" suggest that you're interested even in glacially slow processes, so to speak. Read on to hear about one such ...
84
Your wire is not quite round (almost no wire is), and consequently it has a different vibration frequency along its principal axes1.
You are exciting a mixture of the two modes of oscillation by displacing the wire along an axis that is not aligned with either of the principal axes. The subsequent motion, when analyzed along the axis of initial excitation, ...
81
I think that most of the answers here are incorrect since it has nothing to do with decreasing resistance of rubber. In fact, the force required to stretch the balloon increases, not decreases while inflating. It's similar to stretching a string, ie. the reaction force is proportional to the increase in length of the string - this is why there is a point ...
65
There are two separate concepts here:
the Young's modulus, which determines the force needed to stretch the material
the elastic limit, aka yield strain, which determines how far the material can be stretched
As you say, the term elastic tends to be used in a vague way that conflates these two properties. Generally a high Young's modulus means the material ...
53
Both the OP and John Rennie have well illustrated the imperfections in the usage of the word "elastic" in physics and how the word can create confusion between "stiffness" and a material's ability to brook strain.
But an important point to be made is that the one important field where one hears the vague statement that "steel is more elastic than rubber" is ...
43
The coils of the spring are touching one another and the spring is initially under self-compression so it takes a finite force to move all the coils away from one another and for the spring to behave as you expected.
That initial part of the source vs stretch curve is real (you had obtained data whilst undertaking an experiment) and hence should not be ...
41
Colour can come from pigment particles embedded in the translucent rubber matrix absorbing light. When you pull the band the particles become separated by a longer distance, but being themselves inelastic remain the same size. Hence the amount of absorption per unit area decreases, and the band become lighter in color.
Simulated rubber band with pigment ...
36
Take a strip of balloon rubber and pull it. It will get harder the more you pull. So why is it that inflating the balloon gets easier (at least long before the breaking point)?
The balloon starts with very high curvature, so the air pressure is distorting each spot on its surface a lot relative to its 1cm neighbors for example. All the rubber's tension ...
35
Rubber bands are made of polymers (more specifically elastomers). A given polymer in the band can either be aligned with other polymers around it, or it can be misaligned. Therefore, you can end up with regions of order and regions of disorder in the band. In an unstretched band you have much more disorder, but when you stretch the rubber band you are ...
29
There is no "systematic error" in the experimental results. I have done this experiment as well when teaching a high school physics class. The effect you are seeing is due to the fact that the spring you are using requires a small amount of force before it begins to stretch, while the "theoretical" spring that is described by Hooke's Law does not. This ...
29
This paper describes scientific creep tests with some specific steel.
In a low stress (but relatively high temperature) regime, they report creep of 200 micrometers per year, for a test specimen of 200mm length, 30 micrometers for their 30mm specimens. At room temperature, you would say that yes, eventually it would break, but it may take millions of years ...
28
Great question!
First, I would note that not all flat surfaces are represented by a sheet of paper. Flat rubber sheets for example, if rolled, will usually unroll themselves flat again.
The answer will lie in an understanding of the forces at the molecular level. Rubber is made of coiled polymer chains. You can distort those chains by pulling, pushing, ...
26
I think your perplexity is understandable, and it comes from the clash between the notion of stress, which belongs to continuum mechanics, and the molecular description. Let me arrive in a roundabout but hopefully insightful way at why the factor of 2 is unnecessary.
The notion of stress (more precisely: internal pressure) was introduced by Euler around 1753 ...
23
When in doubt, use mathematics.
Imagine the balloon as a sphere (close enough for this answer) of initial radius $r_0$ and thickness $t$. Let's inflate it just a little bit from the uninflated state (to radius $r_0 + \Delta r$). Now we can take a look at what happens by taking a cut through the equator of the sphere. The total circumference at the equator ...
17
Like Dev said above, the material your typical round balloon is made from has a non-linear stress strain curve. When just starting to inflate it is fairly stiff, but then as it starts to blow up the stiffness goes down somewhat until it approaches its maximum size. We measured this in my undergraduate advanced lab class, and while I don't have the data ...
16
The volume of a balloon grows linear, while the surface (which you actually stretch) doesn't. So although you're blowing the same amount of air into a balloon, you don't stretch the surface as much as in the beginning.
16
Is it that the wooden block vibrates with lesser frequency than the
metal block? If so, why is that?
'Yes', to the first question.
Metal is stiffer than wood and produces higher frequencies (higher pitch).
This follows from the wave equation (here in one dimension):
$$u_{tt}=\frac{E}{\rho}u_{xx}$$
$E$ is Young's Modulus and $\rho$ the material's ...
15
In general the rubber from elastic bands scatters light. This explains why rubbers are opaque, but still reflect light quite a lot, in the same way as milk looks white.
In the presence of pigments, the whitening when pulled can be explained if the material scatters light more when it is stretched. More scattering means that light rays that get reflected, or ...
14
The metal block has a relatively low level of internal damping, however the wooden block has a high level of internal damping: Much of the energy imparted to the wooden block is dissipated internally as heat and deformation, also the higher frequencies are damped more than the lower frequencies (it acts like a low pass filter).
So the wooden block will ...
13
UPDATE :
After looking again at the video, I agree that Floris' explanation seems to be correct and my explanation below is wrong. Slightly different frequencies of vibration in two perpendicular planes accounts more simply for a rotation which reverses one way then the other. Kinetic energy seems to decay constantly; it does not seem to be stored in an ...
13
It is much easier to explain with a diagram than it is with a chart or equations.
Imagine threading tiny weightless disks along your length of blue wool. Twist it and hold it stretched out horizontally between your fingers. Each disk along the length of the wool is rotated a different amount (in a vertical plane) by the twist in the wool - disks at one end ...
13
Anders Sandberg explained the main effect (in fact, decreased per-area pigment concentration and the band becoming thin are the same effect).
There are two more effects that acts even for non-translucent rubbers, making them whiter:
The presence of tiny cracks on the surface. When stretched, they open wider. One can see the same effect on macro scale in ...
13
If you model the colliding objects as rigid bodies, then the collision will take zero time. Since the collision has zero duration, there is no issue with the objects having different accelerations. While this is often a reasonable approximation to make to simplify calculations, it doesn't exactly explain really going on here, so we look at what happens if we ...
11
Let's draw a comparison with ceramics, which—just as metals are generally ductile—are generally brittle.
First, note that crystals (and metals and ceramics are both generally polycrystalline) can deform through dislocation motion. A dislocation is a line defect that carries plasticity through a crystal. The classic analogy is moving a rug by kicking a ...
11
Yes, we can derive Hooke's Law from more basic continuum conditions, provided that the material be stable and at equilibrium, so that the strain energy is smoothly minimized with respect to the distance between atoms. (This energy is sometimes called the pair potential and is modeled using functions such as the Lennard-Jones potential.)
Consider just a pair ...
11
But my question is that since the rope is pulled from both the ends ,
the molecules of the considered cross section is being pulled by other
molecules from both sides of the cross sections.
True the molecules of the cross section are being pulled by the molecules of from both sides of the cross section. But the force on both sides cross section have to be ...
11
Under normal conditions structure building materials, such as steel, will not yield or break. Which is good, because all modern buildings and bridges are based on steel, even if embedded in the concrete as rebars.
For high temperatures, (at least above $300^\circ$C for steel) a constant stress can lead to plastic strain over time, even if it is below the ...
10
This called a "twist to writhe" transition. It is much studied in biology! See the Wikipedia article "DNA supercoil."
I think it is easier to explain with energy rather that by studying forces.
The basic idea is that elastic energy of a flexible cable (or fibre or DNA molecule) can be approximated by
$$
E=\int_\gamma \left\{\frac 12 \alpha ( \omega\cdot{...
10
It is very important to understand that contrary to popular belief, Sunlight is white light (not yellow).
Now you are asking why does a rubber band become lighter colored when stretched, and your question can be why does a rubber band refract/reflect more light when stretched without changing too much the (distribution of) energy levels of the photons, ...
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