View source for Physics and Astronomy Labs/Hooke's law and Young's modulus

This is a simple lab that can be done in almost any school.  

The hallway was used to stretch out approximately 100 ft (30 m) of string.  We used an electronic force probe from ''[[w:Vernier Software & Technology|Vernier Software & Technology]]'', but an ordinary [[w:spring scale|spring scale]] with a sensitivity of at least 0.2 Newtons could also be used.  We named our device the HLA100<ref>"HLA100" stands for the "100 ft Hooke's Law Apparatus".  If your school is big enough you might be able to have an HLA200</ref> 
==Spring 2016 effort at WSU-Lake==
===Photos===
<gallery>
Elastic hysteresis lab hallway wsulake.JPG|Elastic hysteresis lab hallway wsulake.JPG

Elastic hysteresis lab clamping wsulake.jpg|Elastic hysteresis lab clamping wsulake.jpg

File:Elastic hysteresis lab clamping2 wsulake.JPG|Elastic hysteresis lab clamping wsulake.jpg

Elastic hysteresis lab rollup1 wsulake.JPG|Elastic hysteresis lab rollup1 wsulake.JPG

Elastic hysteresis lab rollup2 wsulake.JPG|Elastic hysteresis lab rollup2 wsulake.JPG

Elastic hysteresis lab rollup3 wsulake.JPG|Elastic hysteresis lab rollup3 wsulake.JPG

</gallery>

===Data===
To measure &Delta;L we measured the various positions of the hook.  We did not carefully measure the total length because we didn't really care.  At zero Newtons, the end of the hook was at &minus;4 cm. (see first figure below).

{{cot|click to view data}}
<gallery>
Elastic hysteresis lab equilibrium wsulake.JPG|Elastic hysteresis lab equilibrium wsulake.JPG

Elastic hysteresis lab 1 N wsulake.jpg|Elastic hysteresis lab 1 N wsulake.jpg

Elastic hysteresis lab 2 N wsulake.JPG|Elastic hysteresis lab 2 N wsulake.JPG

Elastic hysteresis lab 2.8 N wsulake.JPG|Elastic hysteresis lab 2.8 N wsulake.JPG

File:Elastic hysteresis lab 4 N wsulake.JPG|File:Elastic hysteresis lab 4 N wsulake.JPG

File:Elastic hysteresis lab 4.8 N wsulake.JPG | File:Elastic hysteresis lab 4.8 N wsulake.JPG 

File:Elastic hysteresis lab d 3.2 N wsulake.JPG|File:Elastic hysteresis lab d 3.2 N wsulake.JPG

File:Elastic hysteresis lab d 2.05 N wsulake.JPG| File:Elastic hysteresis lab d 2.05 N wsulake.JPG

Elastic hysteresis lab d 1.2 N wsulake.JPG|Elastic hysteresis lab d 1.2 N wsulake.JPG

Elastic hysteresis lab d 0.2 N wsulake.JPG|Elastic hysteresis lab d 0.2 N wsulake.JPG

</gallery>
{{cob}}

:[[File:Elastic hysteresis lab 2nd order fit wsu-lake.svg|350px]][[File:Elastic hysteresis lab 4th order fit wsu-lake.svg|350px]]

*See [[Wikipedia:Overfit]]

==What rules of physics apply when you stretch a long piece of string?==
[[File:Where strain is distributed in a stretched wire.svg|thumb|The strain in stretched wire is uniformly distributed along the wire.  Each individual subsection, no matter how short, is stretched by a factor of &Delta;L/L<sub>0</sub>.  For that reason, strain, or  &Delta;L/L<sub>0</sub>, is considered an [[w:Intrinsic and extrinsic properties|intrinsic]] property of the material.]]
*When you pull on a piece of string, the molecules at each point along the string are being pulled apart.  The force at any point in the string that holds the string together is called the [[w:Tension (physics)|''tension'']].  Your teacher will try to convince you that the tension in a low-mass string is the same all along the string.
:#Is the tension the same if the string is very massive and held vertically?  Explain.
:#Is the tension the same if you are trying to hold back a horse and you wrap the rope around a tree a couple of times?  Explain.
* If &Delta;L is the extra length caused by a force of 1 Newton for a string of length L, what is the extra length if we double the length, but keep the force at 1 Newton?  
:# Sketch the situation for a simple case with L = 3 cm and &Delta;L = 1 cm.  
:# Explain the following

<nowiki><!--</nowiki>
If we are taliking about string from a particular type of string (area, thread-type), then if you tell me

:<math>\frac{\Delta L}{L}</math> 

I can tell you what the force is.  This simplest law would be that they are proportional:

:<math>\frac{\Delta L}{L}  = const.\times F</math> 

<nowiki>--></nowiki>

==Preliminary data on household string from the HLA100 indicates hysteresis==

Force was measured as a function of '''''[[w:Deformation_(mechanics)#Engineering_strain|strain]]''''' on a string that was approximately 100ft (30.5 m) long. The diameter of the string was measured with calipers to be {{nowrap|0.85 ± 0.15mm}}, but this should be considered an estimate of the diameter because we could not accurately ascertain whether or not the caliper jaws were compressing the string.  The linear density of this string is 
{{nowrap|0.512 grams/meter}}.  It is the same string used in the '''''[[Physics and Astronomy Labs/Beads on string drop|paperclip drop]]''''' experiment, and we performed this measurement to better understand whether '''''[[w:longitudinal waves|longitudinal waves]]''''' might cause an error in our measurement of Earth's '''''[[w:gravitational acceleration|gravitational acceleration]]'''''.<ref>See the  '''''[https://www.youtube.com/watch?v=wGIZKETKKdw slinky-drop video]'''''  </ref>

To check for '''''[[w:hysteresis|hysteresis]]''''' the first data point was taken at zero strain.<ref>I added a datapoint at 35 cm and zero force in the beginning.  This is how I remember it.--<nowiki>[[User:Guy vandegrift|guyvan52]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:52, 8 February 2015 (UTC)</nowiki></ref>  The string was stretched and subsequently unstretched for one cycle.

==Fact-checking Wikipedia==
Shown below are two graphs that have appeared on Wikipedia.  One graph has an '''''[[Wikipedia:inflection point|inflection point]]''''', and the other does not.  
#Which graph is more consistent with the data?
#Which graph currently appears on [[Wikipedia:Hysteresis]]?
<gallery widths = "140px" heights= "140px">
Force versus strain 0.512 gram per meter string.png|Force versus strain 0.512 gram per meter string
Incorrect Elastic Hysteresis.svg|with inflection point
Elastic Hysteresis.svg|without inflection point
</gallery>


===Raw data===
The variable ''s'' is a measure of displacement, was measured from 100 ft mark, and the force, ''F'', was measured using a Vernier force probe set to a maximum of 5 Newtons.  The knot 18.7 cm from the zero foot mark did not appear to have moved.

{{cot|click to view raw data}}
{| class="wikitable"
|-
| ''s''<br> cm||''F''<br> N
|-
| 35||0.0000
|-
| 36||0.0600
|-
| 37||0.1200
|-
| 38||0.1500
|-
| 39||0.2300
|-
| 40||0.2700
|-
| 41||0.2500
|-
| 42||0.2700
|-
| 43||0.2300
|-
| 44||0.4100
|-
| 45||0.4400
|-
| 50||0.8800
|-
| 55||1.6000
|-
| 60||2.7600
|-
| 65||5.0700
|-
| 70||8.3300
|-
| 65||3.0700
|-
| 60||1.0400
|-
| 55||0.6700
|-
| 50||0.3500
|-
| 45||0.1500
|-
| 44||0.1100
|-
| 43||0.0800
|-
| 42||0.0300
|-
| 41||0.0300
|-
| 40||0.0300
|-
| 39||0.0000
|}
{{cob}}
===Footnotes===
<references/>
[[Category:Physics and Astronomy/Labs]]
====From ''[[Wikipedia:Talk:Hysteresis]]''====
{{cot|click to view talk}}
<big>''' Elastic hysteresis diagram'''</big>

[[File:Force_versus_strain_0.512_gram_per_meter_string.png|thumb|Wikiversity has a student lab that confirms what you are saying.  Be warned that Wikiversity research is not refereed and should not be cited on Wikipedia.  --[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|talk]]) 18:27, 13 April 2015 (UTC)]]
An IP editor has claimed that the diagram in [[w:Hysteresis#Elastic hysteresis]] is incorrect: "The diagram should be a steep gradient followed by less steep and then steep." Does anyone know if that is true? I found [http://openi.nlm.nih.gov/detailedresult.php?img=2865008_ijn-5-137f2&req=4 one diagram from a publication] that looked like the one in this article, but it is just a schematic. A citation would be useful. [w:[User:RockMagnetist|RockMagnetist]] ([[User talk:RockMagnetist|talk]]) 18:00, 11 April 2014 (UTC)
:I formally tagged the image itself ([[:commons:File:Elastic Hysteresis.svg]]), including several links that support the IP's claim (the IP had also left a note in the image-description there) and a possible origin of the confusion. And I left a note for the uploader of the image at [[:commons:User talk:Tiger66]], but that account appears inactive on all wikis since December 2012. [[User:DMacks|DMacks]] ([[User talk:DMacks|talk]]) 18:33, 11 April 2014 (UTC)
::Uploader agreed with the problem and uploaded a replacement image that resolves it, so I'm going to un-tag the article. [[User:DMacks|DMacks]] ([[User talk:DMacks|talk]]) 02:12, 14 April 2014 (UTC)
<s>:::That diagram looks like the same one with a different vertical scale. I think the other editor was saying that the curve should have negative curvature at first and then positive curvature - as in [http://www.diracdelta.co.uk/science/source/h/y/hysteresis/source.html#.U0v1zOZdVrE this image].  [[w:User:RockMagnetist|RockMagnetist]] ([[w:User talk:RockMagnetist|talk]]) 14:52, 14 April 2014 (UTC)</s> Sorry, I needed to refresh the page before I could see the new image. [[w:User:RockMagnetist|RockMagnetist]] ([[w:User talk:RockMagnetist|talk]]) 14:57, 14 April 2014 (UTC)
::::If only there were some term to describe a lag between a changed input to a complex system and the resulting output we see! [[User:DMacks|DMacks]] ([[User talk:DMacks|talk]]) 15:32, 14 April 2014 (UTC)
:::::It's on the tip of my tongue. [[w:User:RockMagnetist|RockMagnetist]] ([[w:User talk:RockMagnetist|talk]]) 16:04, 14 April 2014 (UTC)

{{outdent}} [[:File:Elastic_Hysteresis.svg]] <s>does</s> '''did''' seem wrong to me. See image posted to right.  I placed it ahead of all discussion so it would fit nicely in this section.[w:User:Guy vandegrift|Guy vandegrift]] ([[w:User talk:Guy vandegrift|talk]]) 15:50, 13 April 2015 (UTC)


Also, I placed the link to this diagram in External Links at the bottom of your article to conform to WP standard practice on sisterlinks.  I am not asking you to move the link up to the section on mechanical hysteresis, but won't complain if you do.--[w:User:Guy vandegrift|Guy vandegrift]] ([[w:User talk:Guy vandegrift|talk]]) 18:27, 13 April 2015 (UTC)

{{cob}}