Explore Elasticity: Is There a Constant Relation Between Elasticity & Density?

[Misr]

Elastic properties are those properties related to the tendency of a material to maintain its shape and not deformcordint whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material

http://www.physicsclassroom.com/Class/sound/u11l2c.cfm

according to this,rubber is not elastic

The problem is that I read before that elasticity is the physical property of the material when it deforms under stress(eg external forces),but it returns to its shape when the stress is removed.
An object is said to be elastic if it restores its original size and shape.

but rubber is elastic because it restores its original size and shape..

I'm confused
I fell that this is contradicory

Is elasticity constant for all solids?

its written in the textbook that "the speed of sound increases in solids and liquids by increasing their densities due to the increase in their elasticities"
is that true? If so ,Is there a relation between elasiticity and density?

 

[rcgldr]

wiki articles:

http://en.wikipedia.org/wiki/Elasticity_(physics)\

http://en.wikipedia.org/wiki/Rubber_elasticity

 

[Simon Bridge]

Rubber does not return to it's original shape and size very well.
In common useage the term "elastic" has a different, though related, meaning.
There are less elastic materials that rubber.

Do the following experiment:

Equipment:
A long rubber band (3-4 regular ones joined together will do)
A collection of small weights all the same (10-20 20g washers or lab weights)
Something to hang them on so you can easily add and remove weights without disturbing the system.
A ruler.

Method:
Hang the rubber band someplace handy - on a wall is good.

Part 1.
You are going to add the weights to the end of the rubber band one at a time and record the length, then plot a graph of length vs weight.

Predict: what shape will the graph be.
(just collect the data for now - keep going, you're not done yet.)

Part 2.
Start taking weights away from the rubber band one at a time and record the length.
You get to plot this data too - on the same axis as part 1.

Predict: what path will the graph of part2 follow compared with the path for part1?

OK - now do the graphs.

 

[sphyics]

in short to quantify elasticity, physics defines elasticity as "resistance to change" the greater the resistance to change greater the elasticity, the faster it comes to its original dimension, hence steel is more elastic than rubber.

Even i was confused while learning the course a long ago :) to paraphrase my professor " elasticity is normally viewed in layman terms as more a body can be stretched or deformed without breaking it. In physics terms less the body can be stretched or deformed" :)

 

[rcgldr]

rubber band ... then plot a graph of length vs weight.

That would demonstrate hysteresis, but not disprove elasticity:

http://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis

Latex rubber can be stretched 350% (total length = 450% of it's original length) without any permanent deformation, which is the normal meaning of elasticity. Perhaps there's confusion between elasticity and the term elastic, as in reference to collision. If a collision is 100% elastic, then no loss of kinetic energy occurs.

[URL]http://en.wikipedia.org/wiki/Elastic_collision[/ul]

In the case of a collision, if there is hysteresis, some of the kinetic energy is converted into heat. This is why rubber makes a good dampening material for mounting vibrating objects like automotive engines.

 

[Simon Bridge]

That would demonstrate hysteresis, but not disprove elasticity

1. elasticity is a property - all materials have it to some degree.
2. do the experiment - you'll see. Do you expect it to return to the same length it started in? The hysteresis suggests not.

In physics terms less the body can be stretched or deformed" :)

That usually works out to be the case, however, the definition allows for very wide deformation provided it returns to it's original shape quickly.

The physics use is about the energy lost in the deformation - hence the definition of an elastic collision.

 

[rcgldr]

1. elasticity is a property - all materials have it to some degree.
2. do the experiment - you'll see. Do you expect it to return to the same length it started in? The hysteresis suggests not.

Yes, when all weights are removed, it returns to the same length. It's only during the return path when weights are still present that it's longer, due to hysteresis. Once all the weights are removed, it reverts back to it's original length. I have a 4 1/4 pound, 10 foot 2 inch wing span, radio control glider that I launch with a "hi-start", which is made up of 60 feet of 2/16 inner diameter, 7/16 inch outer diameter, latex tubing and 210 feet of monofilament fishing line (there's a collapsable chute at the end to bring the line somewhat back downwind). Even when I pull it back 210 feet (stretching the 60 feet of tubing to a total length of 270 feet) (it generates 27lbs of tension at this point), it returns back to it's original 60 feet after a launch and release of the "hi-start". In case anyone is curious, this is what it looks like (video):

http://www.youtube.com/watch?v=7q4eZLBXoHQ&hd=1

 

[Simon Bridge]

Yes, when all weights are removed, it returns to the same length.

This tells me you have not done the experiment :)

It's only during the return path when weights are still present that it's longer, due to hysteresis. Once all the weights are removed, it reverts back to it's original length. I have a 4 1/4 pound, 10 foot 2 inch wing span, radio control glider that I launch with a "hi-start", which is made up of 60 feet of 2/16 inner diameter, 7/16 inch outer diameter, latex tubing and 210 feet of monofilament fishing line (there's a collapsable chute at the end to bring the line somewhat back downwind). Even when I pull it back 210 feet (stretching the 60 feet of tubing to a total length of 270 feet) (it generates 27lbs of tension at this point), it returns back to it's original 60 feet after a launch and release of the "hi-start". In case anyone is curious, this is what it looks like (video):

http://www.youtube.com/watch?v=7q4eZLBXoHQ&hd=1

Cute - how did you measure it, or are you estimating by eye?
Do it with regular rubber bands.

This is a routine experiment I set students at college level. I've seen it performed literally thousands of times and every time there is 1-2 centimeters difference at the end. By next day, the band is within a millimeter of the original length.

Try stretching your hi-start to it's max, then keeping it there for an hour or so, then release it - use a tape measure right away. I suspect the tube has been built to withstand long stretches without deforming much... it may be impractical to do the incremental weights thing with that: you'd have to hang it off a tall building!

I have another one for the Engineering school which measures this effect in bending a steel beam. In that case the beam is clamped to a bench and 10kg weights added to it and the bending is not visible to the naked eye. It has to be measured by taping a capacitor top and bottom so the plates change their separation as the bar bends.

That one take about an hour to return.

 

[rcgldr]

Cute - how did you measure it

Marked off spots on the ground, and compared before and after launch.

This is a routine experiment I set students at college level. I've seen it performed literally thousands of times and every time there is 1-2 centimeters difference at the end.

That would mean you stretched it beyond it's normal range of elasticity. Also rubber bands have other chemicals mixed in with them, so I'm not sure of their limits compared to latex tubing. You can get latex tubing from a medical supply store (the smaller diameter stuff), or from some radio control hobby shops (for the larger tubing).

Try stretching your hi-start to it's max

The max is over 400%, but at that point, near permanent deformation occurs, so a 350% limit is used to avoid permanent deformation.

It may be impractical to do the incremental weights thing with that ...

I did do that testing, but with a 1 foot length of various tubing, using a variety of weights. I ended up getting about the same curve as this archive of an old website (click on impatient if it doesn't show up), done using a fish scale to measure tension:

http://web.archive.org/web/20070425194300/http://www.hollyday.com/rich/hd/sailplanes/rubberdata.htm

This is the smoothed data I got for various sizes of latex tubing used to launch radio control gliders:

   strain versus tension: (strain == pull distance)

     0% =   0 lb / in^2
    50% =  70 lb / in^2
   100% =  95 lb / in^2
   150% = 115 lb / in^2
   200% = 135 lb / in^2
   250% = 160 lb / in^2
   300% = 175 lb / in^2
   350% = 195 lb / in^2
   400% = 205 lb / in^2  (not recommended).

 

[AlephZero]

I have another one for the Engineering school which measures this effect in bending a steel beam. In that case the beam is clamped to a bench and 10kg weights added to it and the bending is not visible to the naked eye. It has to be measured by taping a capacitor top and bottom so the plates change their separation as the bar bends.

That one take about an hour to return.

Have you demonstrated whether it takes the beam an hour to "return", or the bench, and/or the clamping arrangements, and/or the lab floor ... ?

In any case, going back to the OP, it makes little sense to say that something is "not elastic" just because it also shows some time-dependent behaviour.

 

[Simon Bridge]

The students would measure the bending in the beam by comparing the two capacitors ... so they measures the contraction inside the bend vs the expansion on the outside of the bend. This way the amount of flexing is measured with respect to the beam and not the rest of the lab.

In terms of OP ... The professors statement "rubber is not elastic" is clearly false since rubber clearly has some elasticity. However, that's not what he was trying to communicate.

It is fair to characterize a material as elastic or not elastic - especially in context of a lesson where the professor wants to make a pedagogical point. He wants to draw the students attention to the difference between commonly held notions of "elastic" and how the term is defined in materials science.

In physics we are interested in the energy "loss" in the deformation - if we look at how the rubber-band deforms vs the steel beam (a polymer mixture vs a metal-crystal) you'll see why the steel is generally much more elastic than the rubber. Not just a little bit more elastic.

To be more rigorous than the experiments I've described, you need to actually measure the youngs modulus for different elastic and steel materials (each term refers to many different substances remember) ... or just look them up.

Youngs modulus for rubber is typically on the order of 10s-100s of kPa while for steel it is more like 200,000kPa ... you can look them up in standard tables of physical properties.

It may be interesting to see if it is possible to make rubber that is more elastic than steel ... but that won't change the fair characterization.

anyone want to convert rcgldr's data into elasticity?
Back of envelope, I get around 1000psi for max extension vs 29,000,000psi for steel.
Rubber can go as high as 15000psi or so - so it is not very elastic even for rubber.

So - compared to steel, it is fair to say that rubber is inelastic.

Other experiments would involve collisions
1. build a Newton's cradle with rubber balls, compare with steel balls.
2. do a collision experiment with steel and rubber bumpers, check how well momentum and energy are conserved in the collision.

It often surprises people to find out how well steel balls bounce (off a hard surface).

Here's a nice demo (as an ad for an exotic glass)
http://www.leaderboard.com/BOUNBALL.htm

 

[rcgldr]

It is fair to characterize a material as elastic or not elastic

So can you explain how your definition differs from the one a wiki and some other web sites? From wiki:

In physics, elasticity (or stretchiness) is the physical property of a material that returns to its original shape after the stress (e.g. external forces) that made it deform or distort is removed. The relative amount of deformation is called the strain.

 

[Simon Bridge]

So can you explain how your definition differs from the one a wiki and some other web sites?

"My" definition does not differ from the wiki quoted - don't know about those "other websites", people say all kinds of things online.

http://en.wikipedia.org/wiki/Elasticity_(physics )
... describes elasticity in terms of Hookes Law - you can have a go: look to your original data and see if the short bit of latex you tested obeys Hook's law for all weights. Bet extension vs weight is not linear.

(note: looks like I didn't read your rubber data properly - you have listed the Young's moduli for different bits of rubber in psi - I misread it as force per extension.)

Also from wikipedia - youngs modulus, or the "modulus of elasticity" is the measure of elasticity of a material.
http://en.wikipedia.org/wiki/Youngs_modulus
http://en.wikipedia.org/wiki/Elastic_modulus
"An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: As such, a stiffer material will have a higher elastic modulus."

Think what this means in terms of energy.

Elasticity is a relative term - things can be elastic or inelastic in comparison to something else. So the professor was being imprecise - telling us he was using rhetoric rather than logic or mathematics. If professors restricted themselves to logical and mathematically rigorous statements, their lectures would be even more boring than usual. Steel is 2000x more elastic than rubber - the characterization is fair and the lesson has sunk in: elastic does not always mean stretchy.

Job done.

 

[sophiecentaur]

Elasticity contrasts with plasticity. After an elastic deformation, the object returns to its original shape. After plastic deformation, an object doesn't - the amount of permanent distortion can vary with the material and so can the energy lost in the process..
An elastic collision involves no loss of energy whereas a non-elastic collision involves a loss of energy.

There is no need to talk about 'how elastic' something is. The terms Modulus of Elasticity, spring constant and Hysteresis etc. exist so why not use them and there needn't be any confusion?

There are better things to do than concern oneself overmuch with challenging the popular misuse of terms and pointing inconsistencies due to this misuse. Just try to be as rigorous as possible in the choice and use of these well defined terms and get on with some more useful Science.

Any teacher who doesn't make it plain when terms are being used 'colloquially' is not doing his (her) job properly but don't lose too much sleep over it. If you've spotted the error then it won't affect your understanding.

 

[rcgldr]

... latex rubber ...

Bet extension vs weight is not linear.

It isn't linear, but elasticity only requires the object to return to it's original shape after the load is removed, and latex rubber does that unless you subject to an excessive load, the same as any elastic material that's stressed beyond it's range of elasticity. The table I listed above is the strain versus stress during the pull or holding, the strain (tension) will be less on the return path, until the strain (tension) returns to zero, in which case the latex tubing returns to it's original unstressed length.

 

[Simon Bridge]

There is no need to talk about 'how elastic' something is. The terms Modulus of Elasticity, spring constant and Hysteresis etc. exist so why not use them and there needn't be any confusion?

In practice, very little time is spent on it, and we do move on to more useful physics.

But it cannot just be ignored either. Many of the terms we use in physics have additional semantic baggage that students will happily apply. We do similar exercises with terms like work and force for eg. Students come to us thinking that words must have an intrinsic meaning that doesn't change, they need to get used to technical meanings and labels. This way, when they get to things like the colors and names of quarks they are used to it and don't batt an eye.

@rcgldr:
Further argument is pointless. Have fun.

 

[rcgldr]

Getting back to the original post:

http://www.physicsclassroom.com/Class/sound/u11l2c.cfm
according to this,rubber is not elastic

That article states Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it and later states Rigid materials such as steel are considered to have a high elasticity (Elastic modulus is the technical term). Elastic modulus is the proper term, but stating rigid materials ... have high elasticity seems to conflict with the conventional physics usage of the term elasticity, since there are several properties of elasticity (not just rigidity), at least in the articles I've found (links below) and textbooks such as Sears and Zemansky University Physics. As sophiecentaur posted previously, elasticity contrasts with plasticity.

Another elastic property is how much deformation can occur before plastic behavior occurs. For most metals, it's less than 3% (elastic limit), and the linear portion of the stress versus strain curve ends at around 1% (proportional limit). In comparason, latex rubber can be stretched 350% before plastic behavior occurs and in that sense, rubber could be considered more elastic than metal.

Example articles found doing a web search for rubber elasticity.

http://en.wikipedia.org/wiki/Rubber_elasticity

http://en.wikipedia.org/wiki/Natural_rubber

http://www.matter.org.uk/matscicdrom/manual/rb.html

http://apbrwww5.apsu.edu/robertsonr/chem3610-20/ELASTOMR.pdf

 

[sophiecentaur]

I wonder just how valuable this discussion is - seems like just another of those 'classification' things that people get so bogged down in on this Forum and elsewhere. To my mind, unless there is a defined Unit for measuring a quantity or a very strict, universally accepted, definition, it really isn't worth too much discussion. Quantities like Modulus (etc) describe the behaviour of a material in a way that is hard to mis-interpret. Why not just stick to them?
Arguing about the meanings of fuzzy words is about as useful to understanding Science as train spotting is to Railway Engineering.

 

[Misr]

hmmmm okay

its written in the textbook that "the speed of sound increases in solids and liquids by increasing their densities due to the increase in their elasticities"
is that true? If so ,Is there a relation between elasiticity and density?

Is this true?

it is said that the speed of sound is inversely proportional to the square root of the density of the medium,this is true when sound is transferred between two different media of the same state (from solid to solid) or from liquid to liquid or from gas to gas

that's okay for gases since the elasticity of gases is constant,,but is elasticity constant for solids?or is elasticity constant for liquids??
I hope you could realize my problem here..