{"id":834,"date":"2019-10-16T13:19:10","date_gmt":"2019-10-16T20:19:10","guid":{"rendered":"https:\/\/c21-wp.phas.ubc.ca\/index.php\/stretching-rubber-bands"},"modified":"2019-10-22T10:46:13","modified_gmt":"2019-10-22T17:46:13","slug":"stretching-rubber-bands","status":"publish","type":"article","link":"https:\/\/c21.phas.ubc.ca\/article\/stretching-rubber-bands\/","title":{"rendered":"Stretching Rubber Bands"},"content":{"rendered":"<p><strong>Purpose:<\/strong><\/p>\n<p>To describe the stretching action of rubber bands, and explore the connection between Hooke&#8217;s Law and Young&#8217;s modulus.<\/p>\n<p><strong>Introduction:<\/strong><\/p>\n<p>Rubber bands stretch when we pull on them, but pulling as hard as you can on a 2-by-4 will probably have no visible effect. The stretchability of solid materials is expressed as their Young&#8217;s Modulus (a.k.a. &#8220;Elastic Constant&#8221;), $Y$. Here is the formula for Young&#8217;s modulus (Eqn.1):<\/p>\n<p>$Y=\\dfrac{\\dfrac{F}{A}}{\\dfrac{\\ \\Delta L\\ }{L_0}} \\tag{1}$<\/p>\n<ul>\n<li>$F$ = Force applied to solid [N]<\/li>\n<li>$A$ = Cross-sectional area of solid [m$^2$]<\/li>\n<li>$L$ = stretched length of solid [m]<\/li>\n<li>$L_0$ = original length of solid [m]<\/li>\n<\/ul>\n<p>A simple way to understand this formula is $Y = \\frac{\\text{stress}}{\\text{strain}}$. The stress is the amount of force applied to the object, per unit area ($F\/A$). The strain is the relative change in the length of the solid ($\\Delta L\/L_0$). Therefore, a solid with a greater value of $Y$ will stretch less than a solid with a smaller $Y$, when the same force is applied.<\/p>\n<p>Let&#8217;s return to rubber bands. Rubber bands are elastic solids and can be described with Hooke&#8217;s Law (Eqn.2). We can think of Hooke&#8217;s Law as a simplified version of Young\u2019s Modulus, and it is classically applied to spring systems. However, it can also, to some extent, describe the stretch patterns observed for rubber bands.<\/p>\n<p>$F=k \\Delta L \\tag{2}$<\/p>\n<ul>\n<li>$F$ = Force applied to elastic material [N]<\/li>\n<li>$k$ = spring constant [N\/m]<\/li>\n<li>$\u0394L$ = change in length of the elastic material [m]<\/li>\n<\/ul>\n<p>If you compare the two equations, you will find (try this as an exercise) that the spring constant $k$ contains Young&#8217;s modulus $Y$ (which describes the material), the length $L_0$, and the cross-sectional area $A$ of the material, can be related as in Eqn.3.<\/p>\n<p>$k=Y\\dfrac{A}{L_0} \\tag{3}$<\/p>\n<p>This allows us now to make predictions before we do an experiment. For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. In this experiment you can check this prediction and investigate the way in which Hooke&#8217;s Law applies to rubber bands. You can also think about what happens if you use two rubber bands at the same time, either to hang an object from both bands in parallel or to create a longer band by knotting one band to the end of the other band. Write down your hypothesis and test it with an experiment.<\/p>\n<p><strong>The Challenge:<\/strong><\/p>\n<p>Design an experiment to measure the constant $k$ for rubber bands. Use items of known mass to provide the applied force. Measure the change in length and the original length for each rubber band; also record the physical properties of each band.<\/p>\n<p><strong>Key Concepts:<\/strong><br \/>\n\u2022 Young&#8217;s modulus is a measure of stress over strain.<br \/>\n\u2022 Hooke&#8217;s Law takes only applied force and change in length into account.<br \/>\n\u2022 Different rubber bands will have different constants for both laws.<\/p>\n<p><strong>Skills:<\/strong><br \/>\n\u2022 Applying Hooke&#8217;s Law<br \/>\n\u2022 Relating graphs of experimental data to given equations<br \/>\n\u2022 Understanding relationship between Hooke&#8217;s Law and Young&#8217;s modulus<br \/>\n\u2022 Simple graphical analysis<br \/>\n\u2022 Assigning errors and understanding error calculations<\/p>\n<p><strong>Materials\/Equipment:<\/strong><br \/>\n\u2022 Three rubber bands of different sizes and thicknesses<br \/>\n\u2022 Objects of given weight (granola bars, packaged foods, etc.)<br \/>\n\u2022 Small metal hanger<br \/>\n\u2022 Pushpin<br \/>\n\u2022 Ruler (30cm) or flexible tape measure<\/p>\n<p><strong>Suggested assigned time:<\/strong> 2 weeks<\/p>\n<p><strong>Question to think about:<\/strong><br \/>\n\u2022 Why does Hooke&#8217;s law not apply for greater forces?<br \/>\n\u2022 Why is Young&#8217;s modulus a more general descriptor of rubber band action than Hooke&#8217;s law?<\/p>\n<p><strong>Variations:<\/strong><br \/>\n\u2022 Try the experiment with something other than a rubber band.<br \/>\n\u2022 Compare rubber band action with spring action. How do the graphs for Hooke\u2019s law compare?<br \/>\n\u2022 Combine multiple rubbers bands and analyze stretching action.<\/p>\n<p><strong>See also<\/strong><\/p>\n<p>&#8220;<span class=\"logo-bar__title logo-bar__title--sm\" aria-label=\"Article Title\">Do Rubber Bands Act Like Springs?<\/span>&#8221; article in Wired Magazine[note] <span class=\"logo-bar__title logo-bar__title--sm\" aria-label=\"Article Title\">Do Rubber Bands Act Like Springs?<\/span> <a href=\"https:\/\/www.wired.com\/2012\/08\/do-rubber-bands-act-like-springs\">https:\/\/www.wired.com\/2012\/08\/do-rubber-bands-act-like-springs<\/a>\/[2019-10-16].[\/note] goes further and investigates the elastic hysteresis[note] Elastic Hysteresis, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Hysteresis#Elastic_hysteresis\">https:\/\/en.wikipedia.org\/wiki\/Hysteresis#Elastic_hysteresis<\/a> [2019-10-16].[\/note] of rubber bands.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Revised 2019-10-16<\/strong><\/p>\n","protected":false},"author":14,"featured_media":1420,"template":"","tags":[235,236,237,238],"date_post_made_public":"2013-03-04","post_authored_by":"Naomi Kasteel","hook":"We can use common household objects to measure properties that match physical laws. This experiment takes a very common household item, the rubber band, and applies physical laws (Hooke's Law and the Young's Modulus) to them in a hands-on way.","big_ideas":"<ul>\r\n \t<li>Young's modulus is a measure of stress over strain.<\/li>\r\n \t<li>Hooke's Law takes only applied force and change in length into account.<\/li>\r\n \t<li>Different rubber bands will have different constants for both laws.<\/li>\r\n<\/ul>","thumbnail_for_post":"<img class=\"alignnone size-large wp-image-1420\" src=\"https:\/\/c21-wp.phas.ubc.ca\/wp-content\/uploads\/2013\/03\/fig4-768x1024.jpg\" alt=\"\" width=\"620\" height=\"827\" \/>","series":false,"number_in_series":"0","supporting_classroom_materials":false,"supporting_experiment":false,"related_articles":false,"related_experiments":false,"related_classroom_materials":false,"_links":{"self":[{"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/article\/834"}],"collection":[{"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/article"}],"about":[{"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":16,"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/article\/834\/revisions"}],"predecessor-version":[{"id":2924,"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/article\/834\/revisions\/2924"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/media\/1420"}],"wp:attachment":[{"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/media?parent=834"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/c21.phas.ubc.ca\/wp-json\/wp\/v2\/tags?post=834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}