{"id":1247,"date":"2019-01-14T02:59:22","date_gmt":"2019-01-14T02:59:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/solving-physics-problems\/"},"modified":"2019-01-28T14:23:30","modified_gmt":"2019-01-28T14:23:30","slug":"solving-physics-problems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/solving-physics-problems\/","title":{"raw":"Module 1 Solving Physics Problems","rendered":"Module 1 Solving Physics Problems"},"content":{"raw":"<div class=\"boundless-concept\">\r\n<h2>Dimensional Analysis<\/h2>\r\nAny physical quantity can be expressed as a product of a combination of the basic physical dimensions.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nCalculate the conversion from one kind of dimension to another\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>Dimensional analysis is the practice of checking relations amount physical quantities by identifying their dimensions.<\/li>\r\n \t<li>It is common to be faced with a problem that uses different dimensions to express the same basic quantity. The following equation can be used to find the conversion factor between the two derived dimensions: [latex]{\\text{n}_2=\\frac{\\text{u}_2}{\\text{u}_1}*\\text{n}_1}[\/latex].<\/li>\r\n \t<li>Dimensional analysis can also be used as a simple check to computations, theories and hypotheses.<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>dimension<\/strong>: A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Dimensions<\/h3>\r\nThe dimension of a physical quantity indicates how it relates to one of the seven basic quantities. These fundamental quantities are:\r\n<ul>\r\n \t<li>[M] Mass<\/li>\r\n \t<li>[L] Length<\/li>\r\n \t<li>[T] Time<\/li>\r\n \t<li>[A] Current<\/li>\r\n \t<li>[K] Temperature<\/li>\r\n \t<li>[mol] Amount of a Substance<\/li>\r\n \t<li>[cd] Luminous Intensity<\/li>\r\n<\/ul>\r\nAs you can see, the symbol is enclosed in a pair of square brackets. This is often used to represent the dimension of individual basic quantity. An example of the use of basic dimensions is speed, which has a dimension of 1 in length and -1 in time; [latex]\\displaystyle \\frac{[\\text{L}]}{[\\text{T}]} = [\\text{LT}^{-1}][\/latex]. Any physical quantity can be expressed as a product of a combination of the basic physical dimensions.\r\n<h3>Dimensional Analysis<\/h3>\r\nDimensional analysis is the practice of checking relations between physical quantities by identifying their dimensions. The dimension of any physical quantity is the combination of the basic physical dimensions that compose it. Dimensional analysis is based on the fact that physical law must be independent of the units used to measure the physical variables. It can be used to check the plausibility of derived equations, computations and hypotheses.\r\n<h3>Derived Dimensions<\/h3>\r\nThe dimensions of derived quantities may include few or all dimensions in individual basic quantities. In order to understand the technique to write dimensions of a derived quantity, we consider the case of force. Force is defined as:\r\n\r\n[latex]\\small{\\text{F}=\\text{m}\\cdot\\text{a}\\\\\\text{F}=[\\text{M}][\\text{a}]}[\/latex]\r\n\r\nThe dimension of acceleration, represented as [a], is itself a derived quantity being the ratio of velocity and time. In turn, velocity is also a derived quantity, being ratio of length and time.\r\n\r\n[latex]\\small{\\text{F}=[\\text{M}][\\text{a}]=[\\text{M}][\\text{vT}^{-1}]\\\\\\text{F}=[\\text{M}][\\text{LT}^{-1}\\text{T}^{-1}]=[\\text{MLT}^{-2}]}[\/latex]\r\n<h3>Dimensional Conversion<\/h3>\r\nIn practice, one might need to convert from one kind of dimension to another. For common conversions, you might already know how to convert off the top of your head. But for less common ones, it is helpful to know how to find the conversion factor:\r\n\r\n[latex]\\small{\\text{Q}=\\text{n}_1\\text{u}_1=\\text{n}_2\\text{u}_2}[\/latex]\r\n\r\nwhere n represents the amount per u dimensions. You can then use ratios to figure out the conversion:\r\n\r\n[latex]\\displaystyle \\small{\\text{n}_2=\\frac{\\text{u}_2}{\\text{u}_1}\\cdot\\text{n}_1}[\/latex]\r\n\r\n<\/div>\r\n<div class=\"boundless-concept\"><\/div>\r\n<div class=\"boundless-concept\">\r\n<div class=\"wp-caption aligncenter\" style=\"width: 213px\">\r\n<div class=\"figure-cont\">\r\n<p class=\"wp-caption-text\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"boundless-concept\">\n<h2>Dimensional Analysis<\/h2>\n<p>Any physical quantity can be expressed as a product of a combination of the basic physical dimensions.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Calculate the conversion from one kind of dimension to another<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>Dimensional analysis is the practice of checking relations amount physical quantities by identifying their dimensions.<\/li>\n<li>It is common to be faced with a problem that uses different dimensions to express the same basic quantity. The following equation can be used to find the conversion factor between the two derived dimensions: [latex]{\\text{n}_2=\\frac{\\text{u}_2}{\\text{u}_1}*\\text{n}_1}[\/latex].<\/li>\n<li>Dimensional analysis can also be used as a simple check to computations, theories and hypotheses.<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>dimension<\/strong>: A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.<\/li>\n<\/ul>\n<\/div>\n<h3>Dimensions<\/h3>\n<p>The dimension of a physical quantity indicates how it relates to one of the seven basic quantities. These fundamental quantities are:<\/p>\n<ul>\n<li>[M] Mass<\/li>\n<li>[L] Length<\/li>\n<li>[T] Time<\/li>\n<li>[A] Current<\/li>\n<li>[K] Temperature<\/li>\n<li>[mol] Amount of a Substance<\/li>\n<li>[cd] Luminous Intensity<\/li>\n<\/ul>\n<p>As you can see, the symbol is enclosed in a pair of square brackets. This is often used to represent the dimension of individual basic quantity. An example of the use of basic dimensions is speed, which has a dimension of 1 in length and -1 in time; [latex]\\displaystyle \\frac{[\\text{L}]}{[\\text{T}]} = [\\text{LT}^{-1}][\/latex]. Any physical quantity can be expressed as a product of a combination of the basic physical dimensions.<\/p>\n<h3>Dimensional Analysis<\/h3>\n<p>Dimensional analysis is the practice of checking relations between physical quantities by identifying their dimensions. The dimension of any physical quantity is the combination of the basic physical dimensions that compose it. Dimensional analysis is based on the fact that physical law must be independent of the units used to measure the physical variables. It can be used to check the plausibility of derived equations, computations and hypotheses.<\/p>\n<h3>Derived Dimensions<\/h3>\n<p>The dimensions of derived quantities may include few or all dimensions in individual basic quantities. In order to understand the technique to write dimensions of a derived quantity, we consider the case of force. Force is defined as:<\/p>\n<p>[latex]\\small{\\text{F}=\\text{m}\\cdot\\text{a}\\\\\\text{F}=[\\text{M}][\\text{a}]}[\/latex]<\/p>\n<p>The dimension of acceleration, represented as [a], is itself a derived quantity being the ratio of velocity and time. In turn, velocity is also a derived quantity, being ratio of length and time.<\/p>\n<p>[latex]\\small{\\text{F}=[\\text{M}][\\text{a}]=[\\text{M}][\\text{vT}^{-1}]\\\\\\text{F}=[\\text{M}][\\text{LT}^{-1}\\text{T}^{-1}]=[\\text{MLT}^{-2}]}[\/latex]<\/p>\n<h3>Dimensional Conversion<\/h3>\n<p>In practice, one might need to convert from one kind of dimension to another. For common conversions, you might already know how to convert off the top of your head. But for less common ones, it is helpful to know how to find the conversion factor:<\/p>\n<p>[latex]\\small{\\text{Q}=\\text{n}_1\\text{u}_1=\\text{n}_2\\text{u}_2}[\/latex]<\/p>\n<p>where n represents the amount per u dimensions. You can then use ratios to figure out the conversion:<\/p>\n<p>[latex]\\displaystyle \\small{\\text{n}_2=\\frac{\\text{u}_2}{\\text{u}_1}\\cdot\\text{n}_1}[\/latex]<\/p>\n<\/div>\n<div class=\"boundless-concept\"><\/div>\n<div class=\"boundless-concept\">\n<div class=\"wp-caption aligncenter\" style=\"width: 213px\">\n<div class=\"figure-cont\">\n<p class=\"wp-caption-text\">\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1247\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Curation and Revision. <strong>Provided by<\/strong>: Boundless.com. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Dimensional analysis. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Dimensional_analysis\">http:\/\/en.wikipedia.org\/wiki\/Dimensional_analysis<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Sunil Kumar Singh, Dimensional Analysis. September 18, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m15037\/latest\/\">http:\/\/cnx.org\/content\/m15037\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>dimension. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/dimension\">http:\/\/en.wiktionary.org\/wiki\/dimension<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Sunil Kumar Singh, Free Body Diagram (Application). September 17, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m14720\/latest\/\">http:\/\/cnx.org\/content\/m14720\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>trigonometry. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/trigonometry\">http:\/\/en.wiktionary.org\/wiki\/trigonometry<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Sunil Kumar Singh, Free Body Diagram (Application). February 16, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m14720\/latest\/\">http:\/\/cnx.org\/content\/m14720\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Sunil Kumar Singh, Free Body Diagram (Application). February 16, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m14720\/latest\/\">http:\/\/cnx.org\/content\/m14720\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Free body diagram. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Free_body_diagram\">http:\/\/en.wikipedia.org\/wiki\/Free_body_diagram<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>dynamic. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/dynamic\">http:\/\/en.wiktionary.org\/wiki\/dynamic<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>static. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/static\">http:\/\/en.wiktionary.org\/wiki\/static<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Sunil Kumar Singh, Free Body Diagram (Application). February 16, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m14720\/latest\/\">http:\/\/cnx.org\/content\/m14720\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Sunil Kumar Singh, Free Body Diagram (Application). February 16, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m14720\/latest\/\">http:\/\/cnx.org\/content\/m14720\/latest\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Free Body Diagram. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/File:Free_Body_Diagram.png\">http:\/\/en.wikipedia.org\/wiki\/File:Free_Body_Diagram.png<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>How To Solve Any Physics Problem. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=YocWuzi4JhY\">http:\/\/www.youtube.com\/watch?v=YocWuzi4JhY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":18,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Dimensional analysis\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/Dimensional_analysis\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Sunil Kumar Singh, Dimensional Analysis. 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