# 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 Vernier Software & Technology, but an ordinary spring scale with a sensitivity of at least 0.2 Newtons could also be used. We named our device the HLA100[1]

## Spring 2016 effort at WSU-Lake

### Data

To measure ΔL 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 −4 cm. (see first figure below).

click to view data

## What rules of physics apply when you stretch a long piece of string?

The strain in stretched wire is uniformly distributed along the wire. Each individual subsection, no matter how short, is stretched by a factor of ΔL/L0. For that reason, strain, or ΔL/L0, is considered an 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 tension. Your teacher will try to convince you that the tension in a low-mass string is the same all along the string.
1. Is the tension the same if the string is very massive and held vertically? Explain.
2. 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 ΔL 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?
1. Sketch the situation for a simple case with L = 3 cm and ΔL = 1 cm.
2. Explain the following

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

${\displaystyle {\frac {\Delta L}{L}}}$

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

${\displaystyle {\frac {\Delta L}{L}}=const.\times F}$

-->

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

Force was measured as a function of strain on a string that was approximately 100ft (30.5 m) long. The diameter of the string was measured with calipers to be 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 0.512 grams/meter. It is the same string used in the paperclip drop experiment, and we performed this measurement to better understand whether longitudinal waves might cause an error in our measurement of Earth's gravitational acceleration.[2]

To check for hysteresis the first data point was taken at zero strain.[3] 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 inflection point, and the other does not.

1. Which graph is more consistent with the data?
2. Which graph currently appears on Wikipedia:Hysteresis?

### 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.

click to view raw data
 s cm F 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

### Footnotes

1. "HLA100" stands for the "100 ft Hooke's Law Apparatus". If your school is big enough you might be able to have an HLA200
3. I added a datapoint at 35 cm and zero force in the beginning. This is how I remember it.--[[User:Guy vandegrift|guyvan52]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:52, 8 February 2015 (UTC)

#### From Wikipedia:Talk:Hysteresis

click to view talk

Elastic hysteresis diagram

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. --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 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]] (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. 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. DMacks (talk) 02:12, 14 April 2014 (UTC)

:::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 this image. RockMagnetist (talk) 14:52, 14 April 2014 (UTC) Sorry, I needed to refresh the page before I could see the new image. 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! DMacks (talk) 15:32, 14 April 2014 (UTC)
It's on the tip of my tongue. RockMagnetist (talk) 16:04, 14 April 2014 (UTC)

┌─────────────────────────────────┘
File:Elastic_Hysteresis.svg does 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]] (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]] (talk) 18:27, 13 April 2015 (UTC)