{"id":5,"date":"2023-01-18T12:02:17","date_gmt":"2023-01-18T17:02:17","guid":{"rendered":"https:\/\/opentextbc.ca\/foundationsofphysics\/?p=5"},"modified":"2023-09-18T11:46:40","modified_gmt":"2023-09-18T15:46:40","slug":"measurement-and-solutions","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/foundationsofphysics\/chapter\/measurement-and-solutions\/","title":{"raw":"Measurement and Solutions","rendered":"Measurement and Solutions"},"content":{"raw":"<h1>1.1 Metric to English (US) Conversions<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Resources<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ul>\r\n \t<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=XtMmeAjQTXc\">Mechanical Universe - Episode 1 Introduction<\/a><\/li>\r\n \t<li>Extra Help: <a href=\"http:\/\/www.a-levelphysicstutor.com\/index.php\">A-Level Physics Tutor<\/a><\/li>\r\n \t<li>Article to Read:\u00a0<a href=\"https:\/\/blogs.scientificamerican.com\/hot-planet\/why-i-wont-debate-science\/\">Marvel, K. (2018, June 14) Why I Won\u2019t Debate Science<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h2>Distance<\/h2>\r\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\r\n \t<li>12 in = 1 ft<\/li>\r\n \t<li>3 ft = 1 yd<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">760<\/span><span style=\"margin-left: 0.25em;\">yd = 1 mi<\/span><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em;\">280<\/span> ft = 1 mi<\/li>\r\n \t<li>1 inch = 2.54 cm<\/li>\r\n \t<li>\u00a01 ft = 0.3048 m<\/li>\r\n \t<li>1 mile = 1.602 km<\/li>\r\n \t<li>1 Nautical Mile = 1<span style=\"margin-left: 0.25em;\">852<\/span> m<\/li>\r\n \t<li>10 mm = 1 cm<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span> mm = 1 m<\/li>\r\n \t<li>100 cm = 1 m<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span><span style=\"margin-left: 0.25em;\"> m = 1 km<\/span><\/li>\r\n<\/ul>\r\n<h2>Area<\/h2>\r\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\r\n \t<li>144 in<sup>2<\/sup> = 1 ft<sup>2<\/sup><\/li>\r\n \t<li>1 in<sup>2<\/sup> = 6.45 cm<sup>2<\/sup><\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em;\">000<\/span> cm<sup>2<\/sup> = 1 m<sup>2<\/sup><\/li>\r\n \t<li>43<span style=\"margin-left: 0.25em;\">560<\/span> ft<sup>2<\/sup> = 1 acre<\/li>\r\n \t<li>1 ft<sup>2<\/sup> = 0.092903 m<sup>2\u00a0\u00a0\u00a0 <\/sup><\/li>\r\n \t<li>10<span style=\"margin-left: 0.25em;\">000<\/span> m<sup>2<\/sup> = 1 hectare<\/li>\r\n \t<li>640 acres = 1 mi<sup>2 <\/sup><\/li>\r\n \t<li>1 mi<sup>2<\/sup> = 2.59 km<sup>2<\/sup><\/li>\r\n \t<li>100 hectare = 1 km<sup>2<\/sup><\/li>\r\n<\/ul>\r\n<h2>Volume<\/h2>\r\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\r\n \t<li>57.75 in<sup>3<\/sup> = 1 qt<\/li>\r\n \t<li>16.39 cm<sup>3<\/sup> = 1 in<sup>3<\/sup><\/li>\r\n \t<li>1 cm<sup>3<\/sup> = 1 ml<\/li>\r\n \t<li>4 qt = 1 gal<\/li>\r\n \t<li>1 ft<sup>3<\/sup> = 0.0283168 m<sup>3<\/sup><\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span> ml = 1 liter<\/li>\r\n \t<li>42 gal (oil) = 1 barrel<\/li>\r\n \t<li>3.79 liters = 1 gal<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span> liter = 1 m<sup>3 \u00a0<\/sup><\/li>\r\n<\/ul>\r\n<h2>Mass\/Weight<\/h2>\r\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\r\n \t<li>437.5 grains = 1 oz<\/li>\r\n \t<li>453 g = 1 lb.<\/li>\r\n \t<li>1000 mg = 1 g<\/li>\r\n \t<li>16 oz = 1 lb.<\/li>\r\n \t<li>2.2 lb. = 1 kg<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span> g = 1 kg<\/li>\r\n \t<li>2<span style=\"margin-left: 0.25em;\">000<\/span> lb. = 1 short ton<\/li>\r\n \t<li>1<span style=\"margin-left: 0.25em;\">000<\/span> kg = 1 metric ton<\/li>\r\n<\/ul>\r\n<h2>Time<\/h2>\r\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\r\n \t<li>1 h = 60 min<\/li>\r\n \t<li>1 min = 60 s<\/li>\r\n \t<li>1 yr = 365.2425 day (average)<\/li>\r\n \t<li>1 h = 3<span style=\"margin-left: 0.25em;\">600<\/span> s<\/li>\r\n \t<li>1 day = 24 h<\/li>\r\n \t<li>1 yr = 365.25 day (Astronomical)<\/li>\r\n<\/ul>\r\n<h2>Temperature<\/h2>\r\n<img class=\"aligncenter wp-image-234 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp.jpg\" alt=\"Fahrenheit to Celsius conversion table.\" width=\"624\" height=\"52\" \/>\r\n<p style=\"text-align: center;\">Fahrenheit to Celsius Conversions:\u00a0 \u00b0C = [latex]\\frac{5}{9} (\u00b0F - 32)[\/latex] and [latex]\u00b0F = \\frac{9}{5} (\u00b0C + 32)[\/latex]<\/p>\r\n\r\n<h1>Dimensional Analysis<\/h1>\r\nAs a student of physics, one of the challenges you encounter in physics deals with converting units. In converting units of measure, you can multiply several fractions together in a process known as dimensional analysis. In dimensional analysis, you create a fraction that equals one, so when it is multiplied to another fraction, it does not change the actual measure; instead, it changes to some equivalent measure.\r\n\r\nThe challenge in doing this is to decide which fractions to multiply correctly. One process in doing this is to decide which unit of measure you wish to replace and to substitute the equivalent measure in the form you desire. This is done so that the undesired unit is cancelled out when multiplied by this equivalent fraction, which leaves the desired unit to take its place.\r\n<div>\r\n\r\nYou can see this process used in the following examples.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div>\r\n\r\nIf 1 pound (lb) = 16 ounces (oz), how many pounds are in 435 ounces?\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=435\\text{ oz}\\times\\dfrac{1\\text{ lb}}{16\\text{ oz}}[\/latex]<\/td>\r\n<td style=\"width: 26.8797%;\">This operation cancels the oz and leaves the units of the lb.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=\\dfrac{435\\text{ lb}}{16}[\/latex]<\/td>\r\n<td style=\"width: 26.8797%;\">Which then reduces to<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=27\\frac{3}{16}\\text{ lb}[\/latex]<\/td>\r\n<td style=\"width: 26.8797%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<span style=\"text-align: initial; font-size: 14pt;\">The same process can be used to convert problems with several units in them.\u00a0 Consider the following example.<\/span>\r\n<div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA student averaged 45 miles\/hour (mi\/h) on a trip. What was the student\u2019s speed in feet\/second (ft\/s)?\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 72.3684%;\">[latex]\\dfrac{45 \\text{ mi}}{\\text{hr}} = 45 \\text{ mi} \\times \\dfrac{5280 \\text{ ft}}{1 \\text{ mi}} \\times \\dfrac{1 \\text{ hr}}{3600 \\text{ s}}[\/latex]<\/td>\r\n<td style=\"width: 27.6316%;\">This will cancel the units of mi &amp; hr, and leave ft &amp; s<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3684%;\">[latex]\\dfrac{45 \\text{ mi}}{\\text{hr}} = 45 \\times \\dfrac{5280}{} \\times \\dfrac{1}{1} \\dfrac{\\text{ft}}{3600 \\text{ s}}[\/latex]<\/td>\r\n<td style=\"width: 27.6316%;\">This then reduces to<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 72.3684%;\">[latex]45 \\text{ mi\/hr} = 66 \\text{ ft\/s}[\/latex]<\/td>\r\n<td style=\"width: 27.6316%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 1.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nConvert 8 cubic feet (ft<sup>3<\/sup>) to cubic yards (yd<sup>3<\/sup>).\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 130px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 49px;\">\r\n<td style=\"width: 71.4286%; height: 49px;\">[latex]8 \\text{ ft}^{3} = 8 \\text{ ft}^{3} \\times \\dfrac{(1 \\text{ yd})^{3}}{(3 \\text{ ft})^{3}}[\/latex]<\/td>\r\n<td style=\"width: 28.5714%; height: 49px;\">This will cancel the units ft<sup>3<\/sup> and replace them with yd<sup>3<\/sup><\/td>\r\n<\/tr>\r\n<tr style=\"height: 49px;\">\r\n<td style=\"width: 71.4286%; height: 49px;\">[latex]8 \\text{ ft}^{3} = 8 \\text{ ft}^{3} \\times \\dfrac{1 \\text{ yd}^{3}}{27 \\text{ ft}^{3}}.[\/latex]<\/td>\r\n<td style=\"width: 28.5714%; height: 49px;\">Cube the parenthesis<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 71.4286%; height: 16px;\">[latex]8 \\text{ ft}^3 = 8 \\times \\dfrac{1 \\text{ yd}^3}{27}[\/latex]<\/td>\r\n<td style=\"width: 28.5714%; height: 16px;\">Which then reduces to<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px;\">\r\n<td style=\"width: 71.4286%; height: 16px;\">[latex]8 \\text{ ft}^3 = \\dfrac{8}{27} \\text{ yd}^{3}[\/latex], (\u2248 0.3 yd<sup>3<\/sup>)<\/td>\r\n<td style=\"width: 28.5714%; height: 16px;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 1.4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA room is 10 ft by 12 ft.\u00a0 How many square yards are in the room? The area of the room is 120 square feet (ft<sup>2<\/sup>). ([latex]Area = Length \\times Width[\/latex]).\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ ft}^2 = 120 \\text{ ft}^2 \\times \\dfrac{(1 \\text{ yd})^3}{(3 \\text{ ft})^2}[\/latex]<\/td>\r\n<td style=\"width: 35.1504%;\">Convert the area. Cancel ft<sup>2<\/sup> and replace with yd<sup>2<\/sup><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ft}^2 = \\dfrac{120 \\text{yd}^2}{9}[\/latex]<\/td>\r\n<td style=\"width: 35.1504%;\">This then reduces to<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ft}^2 = 13 \\dfrac{1}{3} \\text{ yd}^2[\/latex]<\/td>\r\n<td style=\"width: 35.1504%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n<div>\r\n\r\nThe process of dimensional analysis can be used to convert other types of units as well.\u00a0 If we can identify relationships that represent the same value we can make them into a conversion factor.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example 1.5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA child is prescribed a dosage of 12 mg of a certain drug per day and is allowed to refill his prescription twice.\u00a0 If there are 60 tablets in a prescription, and each tablet has 4 mg, how many doses are in the 3 prescriptions (original + 2 refills)?\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 68.0451%;\">[latex]\\begin{array}{l}3 \\text{ Prescriptions} = \\\\ 3 \\text{ Prescriptions} \\times \\dfrac{60 \\text{ tablets}}{1 \\text{ prescription}}\\times \\dfrac{4 \\text{ mg}}{1 \\text{ tablet}}\\times \\dfrac{1 \\text{ dosage}}{12\\text{ mg}}\\end{array}[\/latex]<\/td>\r\n<td style=\"width: 31.9549%;\">This cancels all unwanted units<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 68.0451%;\">[latex]3 \\text{ Prescriptions} = \\dfrac{3 \\times 60 \\times 4 \\times 1}{1 \\times 1 \\times 12} \\text{ or } \\dfrac{720}{12} \\text{ dosages}[\/latex]<\/td>\r\n<td style=\"width: 31.9549%;\">Which then reduces to<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 68.0451%;\">[latex]3 \\text{ Prescriptions} = 60 \\text{ daily dosages}[\/latex]<\/td>\r\n<td style=\"width: 31.9549%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nWrite the corresponding names behind the given unit.\r\n\r\nOne Dimensional Measures:\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>mi <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>oz <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>mg <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>km <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>mm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>ft <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>yd <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>t <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>g <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>cm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>\u03bcm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>in <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n<\/ul>\r\nTwo Dimensional Measures:\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>ft<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>m<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>km<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>in<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>yd<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>cm<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>mm<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li><em>\u03bc<\/em>m<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n<\/ul>\r\nThree Dimensional Measures:\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>ft<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>m<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>km<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>in<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>yd<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>cm<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li>mm<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n \t<li><em>\u03bc<\/em>m<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nConvert the following measures.\r\n<ol>\r\n \t<li>7 miles (mi) to yards (yd)<\/li>\r\n \t<li>234 ounces (oz) to short tons (t)<\/li>\r\n \t<li>11.2 milligrams (mg) to grams (g)<\/li>\r\n \t<li>1.35 kilometres (km) to centimetres (cm)<\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em;\">800<\/span><span style=\"margin-left: 0.25em;\">000<\/span> millimetres (mm) to miles (mi)<\/li>\r\n \t<li>4.5 square feet (ft<sup>2<\/sup>) to square yards (yd<sup>2<\/sup>)<\/li>\r\n \t<li>435<span style=\"margin-left: 0.25em;\">000<\/span> square metres (m<sup>2<\/sup>) to square kilometres (km<sup>2<\/sup>)<\/li>\r\n \t<li>8.0 square kilometres (km<sup>2<\/sup>) to square feet (ft<sup>2<\/sup>)<\/li>\r\n \t<li>0.0065 cubic kilometres (km<sup>3<\/sup>) to cubic metres (m<sup>3<\/sup>)<\/li>\r\n \t<li>14.62 square inches (in<sup>2<\/sup>) to square centimetres (cm<sup>2<\/sup>)<\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em;\">500<\/span> cubic centimetres (cm<sup>3<\/sup>) to cubic yards (yd<sup>3<\/sup>)<\/li>\r\n \t<li>3.5 miles per hour (mi\/h or mph) to feet\/second (ft\/s)<\/li>\r\n \t<li>185 yards per minute (yd\/min) to miles per hour (mi\/h or mph)<\/li>\r\n \t<li>153 feet per second (ft\/s) to miles per hour (mi\/h or mph)<\/li>\r\n \t<li>248 miles per hour (mi\/h or mph) to metres\/second (m\/s)<\/li>\r\n \t<li>186<span style=\"margin-left: 0.25em;\">000<\/span> miles per hour (mi\/h or mph) to kilometres per year (km\/a or km\/yr)<\/li>\r\n \t<li>7.50 tons per square yards (t\/yd<sup>2<\/sup>) to tons per square inches (t\/in<sup>2<\/sup>)<\/li>\r\n \t<li>16 feet per second squared (ft\/s<sup>2<\/sup>) to kilometres per hour squared (km\/h<sup>2<\/sup>)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1.3: Measures of Length and Weight, Time Zones<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol>\r\n \t<li>How many palms are in one league?<\/li>\r\n \t<li>How many points are equal to a poppyseed?<img class=\"aligncenter size-full wp-image-791\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1.png\" alt=\"\" width=\"320\" height=\"758\" \/><\/li>\r\n \t<li>Convert your weight in stones. For this you need to research the internet to find which stone conversion to use.\r\n<img class=\"aligncenter size-full wp-image-790\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai.png\" alt=\"\" width=\"320\" height=\"572\" \/><\/li>\r\n \t<li>Using the <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:STANDARD_TIME_ZONES_WORLD.png\">Standard Time Zones of the World<\/a>, what are the most time zones you can find for the same latitude?[footnote]<a href=\"https:\/\/www.calculator.net\/time-zone-calculator.html\">Online Time Zone Calculator<\/a>[\/footnote]<img class=\"aligncenter wp-image-792 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925.png\" alt=\"\" width=\"2476\" height=\"1305\" \/><\/li>\r\n<\/ol>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n<ul>\r\n \t<li>Article to Read: <a href=\"http:\/\/www.geologyin.com\/2016\/12\/10-interesting-facts-about-geological.html\">The Geologists Time Scale<\/a><\/li>\r\n \t<li>Article to Read: <a href=\"https:\/\/blogs.scientificamerican.com\/observations\/time-on-the-brain-how-you-are-always-living-in-the-past-and-other-quirks-of-perception\/\">Time on the Brain: How You Are Always Living In the Past, and Other Quirks of Perception<\/a><\/li>\r\n \t<li>Article to Read: <a href=\"https:\/\/llis.nasa.gov\/llis_lib\/pdf\/1009464main1_0641-mr.pdf\">NASA's MCO Mishap Investigation Report<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>SS Warrimoo Position and Date Oddity<\/h2>\r\n<img class=\"alignleft wp-image-240 \" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand.jpeg\" alt=\"\" width=\"260\" height=\"195\" \/>The passenger steamer SS Warrimoo was quietly knifing its way through the waters of the mid-Pacific on its way from Vancouver to Australia. The navigator had just finished working out a star fix and brought the master, Captain John Phillips, the result. The Warrimoo\u2019s position was latitude 0\u00b0 31\u2019 North and longitude 179\u00b0 30\u2019 West. The date was 30 December 1899 and it was quickly known that they were only a few miles from the intersection of the Equator and the International Date Line.\r\n\r\nCaptain Phillips was prankish enough to take full advantage of the opportunity for achieving the navigational freak of a lifetime. He called his navigators to the bridge to check and double check the position of the ship. He changed course slightly to bear directly on his mark. Then he adjusted the engine speed. The calm weather and clear night worked in his favour. At midnight the Warrimoo lay on the Equator at exactly the point where it crossed the International Date Line!\r\n\r\n<strong>The consequences:\u00a0 <\/strong>The forward part of the ship was in the Southern Hemisphere, and the middle of summer and the stern was in the Northern Hemisphere and the middle of winter. The date in the aft part of the ship was December 31, 1899, while in the forward, it was January 1, 1900. This ship was, therefore, not only in two different days, two different months, two different seasons and two different years but in two different centuries, all at the same time.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise 1.4: Exponential Growth<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nOne sometimes runs into the challenge of how many times can one fold a piece of paper. The result seems to work out to a maximum of 7 or 8 times with the wad of paper growing increasingly thicker. Every fold doubles the thickness of the paper being folded. This ends up being an exponential problem where the thickness of the paper being folded can be found from the following equation:\r\n<p style=\"text-align: center;\">[latex]\\text{Thickness}=(\\text{thickness of a single sheet of paper})\\times2^{\\text{number of folds}}[\/latex]<\/p>\r\nor simply:\r\n<p style=\"text-align: center;\">[latex]\\text{Thickness}=(0.0001\\text{ m})\\times2^{\\text{n}}[\/latex]<\/p>\r\nThis means...\r\n<ul>\r\n \t<li>For n = 1 (1 fold), the thickness is [latex](0.0001 \\text{ m}) \\times 21[\/latex] which equals 0.0002 m.<\/li>\r\n \t<li>For n = 2 (2 folds), the thickness is [latex](0.0001 \\text{ m}) \\times 22[\/latex] which equals 0.0004 m.<\/li>\r\n \t<li>For n = 3 (3 folds), the thickness is [latex](0.0001 \\text{ m}) \\times 23[\/latex] which equals 0.0008 m.<\/li>\r\n<\/ul>\r\nImagine that someone is able to fold the paper once every week for a year (52 folds). The thickness of this folded paper is surprising.\r\n\r\n<strong>Question<\/strong>:\r\n<ol>\r\n \t<li>How thick would a piece of paper be if it could be folded 52 times?<\/li>\r\n \t<li>How does this compare to the distance from the Earth to the Sun?\r\n([latex]d = 1.496 \\times 1011 \\text{ m}[\/latex])<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n\r\nArticle to Read:\u00a0<a href=\"https:\/\/sploid.gizmodo.com\/if-you-fold-a-paper-in-half-103-times-it-will-be-as-thi-1607632639\">If you fold a paper in half 103 times it\u2019ll get as thick as the universe<\/a>\r\n\r\n<\/div>\r\n<h1>Exercise Answers<\/h1>\r\n<h2>1.1 Names &amp; Measurement Terms:<\/h2>\r\n<\/div>\r\n<\/div>\r\n<h3 style=\"text-align: left;\">One Dimensional Measures:<\/h3>\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>mi: mile<\/li>\r\n \t<li>oz: ounce<\/li>\r\n \t<li>mg: milligram<\/li>\r\n \t<li>km: kilometre<\/li>\r\n \t<li>mm: millimetre<\/li>\r\n \t<li>ft: feet<\/li>\r\n \t<li>yd: yard<\/li>\r\n \t<li>t: ton<\/li>\r\n \t<li>g: gram<\/li>\r\n \t<li>cm: centimetre<\/li>\r\n \t<li><em>\u03bc<\/em>m: micrometre<\/li>\r\n \t<li>in: inch<\/li>\r\n<\/ul>\r\n<h3 style=\"text-align: left;\">Two Dimensional Measures:<\/h3>\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>ft<sup>2<\/sup>: square feet<\/li>\r\n \t<li>m<sup>2<\/sup>: square metre<\/li>\r\n \t<li>km<sup>2<\/sup>: square metre<\/li>\r\n \t<li>in<sup>2<\/sup>: square inch<\/li>\r\n \t<li>yd<sup>2<\/sup>: square yard<\/li>\r\n \t<li>cm<sup>2<\/sup>: square centimetre<\/li>\r\n \t<li>mm<sup>2<\/sup>: square millimetre<\/li>\r\n \t<li>\u03bcm<sup>2<\/sup>: square micrometre<\/li>\r\n<\/ul>\r\n&nbsp;\r\n<h3 style=\"text-align: left;\">Three Dimensional Measures:<\/h3>\r\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\r\n \t<li>ft<sup>3<\/sup>: cubic feet<\/li>\r\n \t<li>m<sup>3<\/sup>: cubic metre<\/li>\r\n \t<li>km<sup>3<\/sup>: cubic kilometre<\/li>\r\n \t<li>in<sup>3<\/sup>: cubic inch<\/li>\r\n \t<li>yd<sup>3<\/sup>: cubic yard<\/li>\r\n \t<li>cm<sup>3<\/sup>: cubic centimetre<\/li>\r\n \t<li>mm<sup>3<\/sup>: cubic millimetre<\/li>\r\n \t<li><em>\u03bc<\/em>m<sup>3<\/sup>: cubic micrometre<\/li>\r\n<\/ul>\r\n<h2>1.2 Convert the Following:<\/h2>\r\n<ol class=\"twocolumn\">\r\n \t<li>7 mi = 12<span style=\"margin-left: 0.25em;\">320<\/span> yd<\/li>\r\n \t<li>234 oz = 000731 ton<\/li>\r\n \t<li>11.2 mg = 0.0112 g<\/li>\r\n \t<li>1.35 km = 135<span style=\"margin-left: 0.25em;\">000<\/span> cm<\/li>\r\n \t<li>9<span style=\"margin-left: 0.25em;\">800<\/span><span style=\"margin-left: 0.25em;\">000<\/span> mm \u2248 6.12 mi<\/li>\r\n \t<li>4.5 ft<sup>2<\/sup> = 0.50 yd<sup>2<\/sup><\/li>\r\n \t<li>435<span style=\"margin-left: 0.25em;\">000 m<sup>2<\/sup> = 0.435 km<sup>2<\/sup><\/span><\/li>\r\n \t<li>8 km<sup>2<\/sup> \u2248 87<span style=\"margin-left: 0.25em;\">000<\/span><span style=\"margin-left: 0.25em;\">000<\/span> ft<sup>2<\/sup><\/li>\r\n \t<li>0.0065 km<sup>3<\/sup> = 6<span style=\"margin-left: 0.25em;\">500<\/span><span style=\"margin-left: 0.25em;\">000<\/span> m<sup>3<\/sup><\/li>\r\n \t<li>14.62 in<sup>2<\/sup> \u2248 94.3 cm<sup>2<\/sup><\/li>\r\n \t<li>5<span style=\"margin-left: 0.25em;\">500<\/span> cm<sup>3<\/sup> \u2248 0.0072 yd<sup>3<\/sup><\/li>\r\n \t<li>3.5 mi\/h \u2248 5.1 ft\/s<\/li>\r\n \t<li>185 yd\/min \u22486.31 mi\/h<\/li>\r\n \t<li>153 ft\/s \u2248104 mi\/h<\/li>\r\n \t<li>248 mi\/h \u2248 110 m\/s<\/li>\r\n \t<li>186<span style=\"margin-left: 0.25em;\">000<\/span> mi\/h \u2248 2.61 \u00d7 10<sup>2<\/sup> km\/y<\/li>\r\n \t<li>7.50 ton\/yd<sup>2<\/sup> \u2248 0.00579 ton\/in<sup>2<\/sup><\/li>\r\n \t<li>16 ft\/s<sup>2<\/sup> \u2248 63<span style=\"margin-left: 0.25em;\">000<\/span> km\/h<sup>2<\/sup><\/li>\r\n<\/ol>\r\n<h2>1.3 Measures of Length and Weight, Time Zones:<\/h2>\r\n<ol>\r\n \t<li>1 league = 63<span style=\"margin-left: 0.25em;\">360<\/span> palms<\/li>\r\n \t<li>1 poppyseed = 6 points<\/li>\r\n \t<li>1 stone = 14 pounds (use this to convert your weight)<\/li>\r\n \t<li>180\u00b0 Longitude has 5 different time zones<\/li>\r\n<\/ol>\r\n<h2>1.4 Exponential Growth<\/h2>\r\n<ol>\r\n \t<li>Thickness is 4.50 \u00d710<sup>11<\/sup> m<\/li>\r\n \t<li>Approximately 3 times the distance from the Earth to the Sun<\/li>\r\n<\/ol>\r\n<h3>Media Attributions<\/h3>\r\n<ul>\r\n \t<li>\"<a href=\"https:\/\/en.wikipedia.org\/wiki\/SS_Warrimoo#\/media\/File:SS_Warrimoo_-_New_Zealand.jpg\">New Zealand passenger ship SS Warrimoo<\/a>\" by Allan C. Green (1878-1954) is in the <a href=\"https:\/\/creativecommons.org\/share-your-work\/public-domain\/pdm\/\">public domain<\/a>.<\/li>\r\n \t<li>\"<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:STANDARD_TIME_ZONES_WORLD.png\">STANDARD TIME ZONES WORLD<\/a>\" by United States Central Intelligence Agency is in the <a href=\"https:\/\/creativecommons.org\/share-your-work\/public-domain\/pdm\/\">public domain<\/a>.<\/li>\r\n<\/ul>","rendered":"<h1>1.1 Metric to English (US) Conversions<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Resources<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ul>\n<li>Video to Watch: <a href=\"https:\/\/www.youtube.com\/watch?v=XtMmeAjQTXc\">Mechanical Universe &#8211; Episode 1 Introduction<\/a><\/li>\n<li>Extra Help: <a href=\"http:\/\/www.a-levelphysicstutor.com\/index.php\">A-Level Physics Tutor<\/a><\/li>\n<li>Article to Read:\u00a0<a href=\"https:\/\/blogs.scientificamerican.com\/hot-planet\/why-i-wont-debate-science\/\">Marvel, K. (2018, June 14) Why I Won\u2019t Debate Science<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h2>Distance<\/h2>\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\n<li>12 in = 1 ft<\/li>\n<li>3 ft = 1 yd<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">760<\/span><span style=\"margin-left: 0.25em;\">yd = 1 mi<\/span><\/li>\n<li>5<span style=\"margin-left: 0.25em;\">280<\/span> ft = 1 mi<\/li>\n<li>1 inch = 2.54 cm<\/li>\n<li>\u00a01 ft = 0.3048 m<\/li>\n<li>1 mile = 1.602 km<\/li>\n<li>1 Nautical Mile = 1<span style=\"margin-left: 0.25em;\">852<\/span> m<\/li>\n<li>10 mm = 1 cm<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span> mm = 1 m<\/li>\n<li>100 cm = 1 m<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span><span style=\"margin-left: 0.25em;\"> m = 1 km<\/span><\/li>\n<\/ul>\n<h2>Area<\/h2>\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\n<li>144 in<sup>2<\/sup> = 1 ft<sup>2<\/sup><\/li>\n<li>1 in<sup>2<\/sup> = 6.45 cm<sup>2<\/sup><\/li>\n<li>10<span style=\"margin-left: 0.25em;\">000<\/span> cm<sup>2<\/sup> = 1 m<sup>2<\/sup><\/li>\n<li>43<span style=\"margin-left: 0.25em;\">560<\/span> ft<sup>2<\/sup> = 1 acre<\/li>\n<li>1 ft<sup>2<\/sup> = 0.092903 m<sup>2\u00a0\u00a0\u00a0 <\/sup><\/li>\n<li>10<span style=\"margin-left: 0.25em;\">000<\/span> m<sup>2<\/sup> = 1 hectare<\/li>\n<li>640 acres = 1 mi<sup>2 <\/sup><\/li>\n<li>1 mi<sup>2<\/sup> = 2.59 km<sup>2<\/sup><\/li>\n<li>100 hectare = 1 km<sup>2<\/sup><\/li>\n<\/ul>\n<h2>Volume<\/h2>\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\n<li>57.75 in<sup>3<\/sup> = 1 qt<\/li>\n<li>16.39 cm<sup>3<\/sup> = 1 in<sup>3<\/sup><\/li>\n<li>1 cm<sup>3<\/sup> = 1 ml<\/li>\n<li>4 qt = 1 gal<\/li>\n<li>1 ft<sup>3<\/sup> = 0.0283168 m<sup>3<\/sup><\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span> ml = 1 liter<\/li>\n<li>42 gal (oil) = 1 barrel<\/li>\n<li>3.79 liters = 1 gal<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span> liter = 1 m<sup>3 \u00a0<\/sup><\/li>\n<\/ul>\n<h2>Mass\/Weight<\/h2>\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\n<li>437.5 grains = 1 oz<\/li>\n<li>453 g = 1 lb.<\/li>\n<li>1000 mg = 1 g<\/li>\n<li>16 oz = 1 lb.<\/li>\n<li>2.2 lb. = 1 kg<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span> g = 1 kg<\/li>\n<li>2<span style=\"margin-left: 0.25em;\">000<\/span> lb. = 1 short ton<\/li>\n<li>1<span style=\"margin-left: 0.25em;\">000<\/span> kg = 1 metric ton<\/li>\n<\/ul>\n<h2>Time<\/h2>\n<ul class=\"threecolumn\" style=\"list-style-type: none;\">\n<li>1 h = 60 min<\/li>\n<li>1 min = 60 s<\/li>\n<li>1 yr = 365.2425 day (average)<\/li>\n<li>1 h = 3<span style=\"margin-left: 0.25em;\">600<\/span> s<\/li>\n<li>1 day = 24 h<\/li>\n<li>1 yr = 365.25 day (Astronomical)<\/li>\n<\/ul>\n<h2>Temperature<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-234 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp.jpg\" alt=\"Fahrenheit to Celsius conversion table.\" width=\"624\" height=\"52\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp.jpg 624w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp-300x25.jpg 300w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp-65x5.jpg 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp-225x19.jpg 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/temp-350x29.jpg 350w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/p>\n<p style=\"text-align: center;\">Fahrenheit to Celsius Conversions:\u00a0 \u00b0C = [latex]\\frac{5}{9} (\u00b0F - 32)[\/latex] and [latex]\u00b0F = \\frac{9}{5} (\u00b0C + 32)[\/latex]<\/p>\n<h1>Dimensional Analysis<\/h1>\n<p>As a student of physics, one of the challenges you encounter in physics deals with converting units. In converting units of measure, you can multiply several fractions together in a process known as dimensional analysis. In dimensional analysis, you create a fraction that equals one, so when it is multiplied to another fraction, it does not change the actual measure; instead, it changes to some equivalent measure.<\/p>\n<p>The challenge in doing this is to decide which fractions to multiply correctly. One process in doing this is to decide which unit of measure you wish to replace and to substitute the equivalent measure in the form you desire. This is done so that the undesired unit is cancelled out when multiplied by this equivalent fraction, which leaves the desired unit to take its place.<\/p>\n<div>\n<p>You can see this process used in the following examples.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div>\n<p>If 1 pound (lb) = 16 ounces (oz), how many pounds are in 435 ounces?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=435\\text{ oz}\\times\\dfrac{1\\text{ lb}}{16\\text{ oz}}[\/latex]<\/td>\n<td style=\"width: 26.8797%;\">This operation cancels the oz and leaves the units of the lb.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=\\dfrac{435\\text{ lb}}{16}[\/latex]<\/td>\n<td style=\"width: 26.8797%;\">Which then reduces to<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.1203%;\">[latex]435\\text{ oz}=27\\frac{3}{16}\\text{ lb}[\/latex]<\/td>\n<td style=\"width: 26.8797%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"text-align: initial; font-size: 14pt;\">The same process can be used to convert problems with several units in them.\u00a0 Consider the following example.<\/span><\/p>\n<div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A student averaged 45 miles\/hour (mi\/h) on a trip. What was the student\u2019s speed in feet\/second (ft\/s)?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 72.3684%;\">[latex]\\dfrac{45 \\text{ mi}}{\\text{hr}} = 45 \\text{ mi} \\times \\dfrac{5280 \\text{ ft}}{1 \\text{ mi}} \\times \\dfrac{1 \\text{ hr}}{3600 \\text{ s}}[\/latex]<\/td>\n<td style=\"width: 27.6316%;\">This will cancel the units of mi &amp; hr, and leave ft &amp; s<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3684%;\">[latex]\\dfrac{45 \\text{ mi}}{\\text{hr}} = 45 \\times \\dfrac{5280}{} \\times \\dfrac{1}{1} \\dfrac{\\text{ft}}{3600 \\text{ s}}[\/latex]<\/td>\n<td style=\"width: 27.6316%;\">This then reduces to<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 72.3684%;\">[latex]45 \\text{ mi\/hr} = 66 \\text{ ft\/s}[\/latex]<\/td>\n<td style=\"width: 27.6316%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 1.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Convert 8 cubic feet (ft<sup>3<\/sup>) to cubic yards (yd<sup>3<\/sup>).<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 130px;\">\n<tbody>\n<tr style=\"height: 49px;\">\n<td style=\"width: 71.4286%; height: 49px;\">[latex]8 \\text{ ft}^{3} = 8 \\text{ ft}^{3} \\times \\dfrac{(1 \\text{ yd})^{3}}{(3 \\text{ ft})^{3}}[\/latex]<\/td>\n<td style=\"width: 28.5714%; height: 49px;\">This will cancel the units ft<sup>3<\/sup> and replace them with yd<sup>3<\/sup><\/td>\n<\/tr>\n<tr style=\"height: 49px;\">\n<td style=\"width: 71.4286%; height: 49px;\">[latex]8 \\text{ ft}^{3} = 8 \\text{ ft}^{3} \\times \\dfrac{1 \\text{ yd}^{3}}{27 \\text{ ft}^{3}}.[\/latex]<\/td>\n<td style=\"width: 28.5714%; height: 49px;\">Cube the parenthesis<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 71.4286%; height: 16px;\">[latex]8 \\text{ ft}^3 = 8 \\times \\dfrac{1 \\text{ yd}^3}{27}[\/latex]<\/td>\n<td style=\"width: 28.5714%; height: 16px;\">Which then reduces to<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 71.4286%; height: 16px;\">[latex]8 \\text{ ft}^3 = \\dfrac{8}{27} \\text{ yd}^{3}[\/latex], (\u2248 0.3 yd<sup>3<\/sup>)<\/td>\n<td style=\"width: 28.5714%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 1.4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A room is 10 ft by 12 ft.\u00a0 How many square yards are in the room? The area of the room is 120 square feet (ft<sup>2<\/sup>). ([latex]Area = Length \\times Width[\/latex]).<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ ft}^2 = 120 \\text{ ft}^2 \\times \\dfrac{(1 \\text{ yd})^3}{(3 \\text{ ft})^2}[\/latex]<\/td>\n<td style=\"width: 35.1504%;\">Convert the area. Cancel ft<sup>2<\/sup> and replace with yd<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ft}^2 = \\dfrac{120 \\text{yd}^2}{9}[\/latex]<\/td>\n<td style=\"width: 35.1504%;\">This then reduces to<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 64.8496%;\">[latex]120 \\text{ft}^2 = 13 \\dfrac{1}{3} \\text{ yd}^2[\/latex]<\/td>\n<td style=\"width: 35.1504%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div>\n<div>\n<p>The process of dimensional analysis can be used to convert other types of units as well.\u00a0 If we can identify relationships that represent the same value we can make them into a conversion factor.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example 1.5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A child is prescribed a dosage of 12 mg of a certain drug per day and is allowed to refill his prescription twice.\u00a0 If there are 60 tablets in a prescription, and each tablet has 4 mg, how many doses are in the 3 prescriptions (original + 2 refills)?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 68.0451%;\">[latex]\\begin{array}{l}3 \\text{ Prescriptions} = \\\\ 3 \\text{ Prescriptions} \\times \\dfrac{60 \\text{ tablets}}{1 \\text{ prescription}}\\times \\dfrac{4 \\text{ mg}}{1 \\text{ tablet}}\\times \\dfrac{1 \\text{ dosage}}{12\\text{ mg}}\\end{array}[\/latex]<\/td>\n<td style=\"width: 31.9549%;\">This cancels all unwanted units<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 68.0451%;\">[latex]3 \\text{ Prescriptions} = \\dfrac{3 \\times 60 \\times 4 \\times 1}{1 \\times 1 \\times 12} \\text{ or } \\dfrac{720}{12} \\text{ dosages}[\/latex]<\/td>\n<td style=\"width: 31.9549%;\">Which then reduces to<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 68.0451%;\">[latex]3 \\text{ Prescriptions} = 60 \\text{ daily dosages}[\/latex]<\/td>\n<td style=\"width: 31.9549%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Write the corresponding names behind the given unit.<\/p>\n<p>One Dimensional Measures:<\/p>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>mi <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>oz <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>mg <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>km <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>mm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>ft <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>yd <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>t <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>g <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>cm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>\u03bcm <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>in <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n<p>Two Dimensional Measures:<\/p>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>ft<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>m<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>km<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>in<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>yd<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>cm<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>mm<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li><em>\u03bc<\/em>m<sup>2<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n<p>Three Dimensional Measures:<\/p>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>ft<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>m<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>km<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>in<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>yd<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>cm<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li>mm<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<li><em>\u03bc<\/em>m<sup>3<\/sup> <span style=\"text-decoration: underline;\" aria-label=\"blank\"> \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0<\/span><\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Convert the following measures.<\/p>\n<ol>\n<li>7 miles (mi) to yards (yd)<\/li>\n<li>234 ounces (oz) to short tons (t)<\/li>\n<li>11.2 milligrams (mg) to grams (g)<\/li>\n<li>1.35 kilometres (km) to centimetres (cm)<\/li>\n<li>9<span style=\"margin-left: 0.25em;\">800<\/span><span style=\"margin-left: 0.25em;\">000<\/span> millimetres (mm) to miles (mi)<\/li>\n<li>4.5 square feet (ft<sup>2<\/sup>) to square yards (yd<sup>2<\/sup>)<\/li>\n<li>435<span style=\"margin-left: 0.25em;\">000<\/span> square metres (m<sup>2<\/sup>) to square kilometres (km<sup>2<\/sup>)<\/li>\n<li>8.0 square kilometres (km<sup>2<\/sup>) to square feet (ft<sup>2<\/sup>)<\/li>\n<li>0.0065 cubic kilometres (km<sup>3<\/sup>) to cubic metres (m<sup>3<\/sup>)<\/li>\n<li>14.62 square inches (in<sup>2<\/sup>) to square centimetres (cm<sup>2<\/sup>)<\/li>\n<li>5<span style=\"margin-left: 0.25em;\">500<\/span> cubic centimetres (cm<sup>3<\/sup>) to cubic yards (yd<sup>3<\/sup>)<\/li>\n<li>3.5 miles per hour (mi\/h or mph) to feet\/second (ft\/s)<\/li>\n<li>185 yards per minute (yd\/min) to miles per hour (mi\/h or mph)<\/li>\n<li>153 feet per second (ft\/s) to miles per hour (mi\/h or mph)<\/li>\n<li>248 miles per hour (mi\/h or mph) to metres\/second (m\/s)<\/li>\n<li>186<span style=\"margin-left: 0.25em;\">000<\/span> miles per hour (mi\/h or mph) to kilometres per year (km\/a or km\/yr)<\/li>\n<li>7.50 tons per square yards (t\/yd<sup>2<\/sup>) to tons per square inches (t\/in<sup>2<\/sup>)<\/li>\n<li>16 feet per second squared (ft\/s<sup>2<\/sup>) to kilometres per hour squared (km\/h<sup>2<\/sup>)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1.3: Measures of Length and Weight, Time Zones<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol>\n<li>How many palms are in one league?<\/li>\n<li>How many points are equal to a poppyseed?<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-791\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1.png\" alt=\"\" width=\"320\" height=\"758\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1.png 320w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1-127x300.png 127w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1-65x154.png 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/320px-English_length_units_graph-1-225x533.png 225w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/li>\n<li>Convert your weight in stones. For this you need to research the internet to find which stone conversion to use.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-790\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai.png\" alt=\"\" width=\"320\" height=\"572\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai.png 320w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai-168x300.png 168w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai-65x116.png 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/English_mass_units_graph-Ai-225x402.png 225w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/li>\n<li>Using the <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:STANDARD_TIME_ZONES_WORLD.png\">Standard Time Zones of the World<\/a>, what are the most time zones you can find for the same latitude?<a class=\"footnote\" title=\"Online Time Zone Calculator\" id=\"return-footnote-5-1\" href=\"#footnote-5-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-792 size-full\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925.png\" alt=\"\" width=\"2476\" height=\"1305\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925.png 2476w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-300x158.png 300w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-1024x540.png 1024w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-768x405.png 768w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-1536x810.png 1536w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-2048x1079.png 2048w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-65x34.png 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-225x119.png 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/STANDARD_TIME_ZONES_WORLD-e1680198669925-350x184.png 350w\" sizes=\"auto, (max-width: 2476px) 100vw, 2476px\" \/><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<ul>\n<li>Article to Read: <a href=\"http:\/\/www.geologyin.com\/2016\/12\/10-interesting-facts-about-geological.html\">The Geologists Time Scale<\/a><\/li>\n<li>Article to Read: <a href=\"https:\/\/blogs.scientificamerican.com\/observations\/time-on-the-brain-how-you-are-always-living-in-the-past-and-other-quirks-of-perception\/\">Time on the Brain: How You Are Always Living In the Past, and Other Quirks of Perception<\/a><\/li>\n<li>Article to Read: <a href=\"https:\/\/llis.nasa.gov\/llis_lib\/pdf\/1009464main1_0641-mr.pdf\">NASA&#8217;s MCO Mishap Investigation Report<\/a><\/li>\n<\/ul>\n<\/div>\n<h2>SS Warrimoo Position and Date Oddity<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-240\" src=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand.jpeg\" alt=\"\" width=\"260\" height=\"195\" srcset=\"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand.jpeg 1600w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-300x225.jpeg 300w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-1024x768.jpeg 1024w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-768x576.jpeg 768w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-1536x1152.jpeg 1536w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-65x49.jpeg 65w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-225x169.jpeg 225w, https:\/\/opentextbc.ca\/foundationsofphysics\/wp-content\/uploads\/sites\/427\/2023\/01\/SS_Warrimoo_-_New_Zealand-350x263.jpeg 350w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/>The passenger steamer SS Warrimoo was quietly knifing its way through the waters of the mid-Pacific on its way from Vancouver to Australia. The navigator had just finished working out a star fix and brought the master, Captain John Phillips, the result. The Warrimoo\u2019s position was latitude 0\u00b0 31\u2019 North and longitude 179\u00b0 30\u2019 West. The date was 30 December 1899 and it was quickly known that they were only a few miles from the intersection of the Equator and the International Date Line.<\/p>\n<p>Captain Phillips was prankish enough to take full advantage of the opportunity for achieving the navigational freak of a lifetime. He called his navigators to the bridge to check and double check the position of the ship. He changed course slightly to bear directly on his mark. Then he adjusted the engine speed. The calm weather and clear night worked in his favour. At midnight the Warrimoo lay on the Equator at exactly the point where it crossed the International Date Line!<\/p>\n<p><strong>The consequences:\u00a0 <\/strong>The forward part of the ship was in the Southern Hemisphere, and the middle of summer and the stern was in the Northern Hemisphere and the middle of winter. The date in the aft part of the ship was December 31, 1899, while in the forward, it was January 1, 1900. This ship was, therefore, not only in two different days, two different months, two different seasons and two different years but in two different centuries, all at the same time.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise 1.4: Exponential Growth<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>One sometimes runs into the challenge of how many times can one fold a piece of paper. The result seems to work out to a maximum of 7 or 8 times with the wad of paper growing increasingly thicker. Every fold doubles the thickness of the paper being folded. This ends up being an exponential problem where the thickness of the paper being folded can be found from the following equation:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Thickness}=(\\text{thickness of a single sheet of paper})\\times2^{\\text{number of folds}}[\/latex]<\/p>\n<p>or simply:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Thickness}=(0.0001\\text{ m})\\times2^{\\text{n}}[\/latex]<\/p>\n<p>This means&#8230;<\/p>\n<ul>\n<li>For n = 1 (1 fold), the thickness is [latex](0.0001 \\text{ m}) \\times 21[\/latex] which equals 0.0002 m.<\/li>\n<li>For n = 2 (2 folds), the thickness is [latex](0.0001 \\text{ m}) \\times 22[\/latex] which equals 0.0004 m.<\/li>\n<li>For n = 3 (3 folds), the thickness is [latex](0.0001 \\text{ m}) \\times 23[\/latex] which equals 0.0008 m.<\/li>\n<\/ul>\n<p>Imagine that someone is able to fold the paper once every week for a year (52 folds). The thickness of this folded paper is surprising.<\/p>\n<p><strong>Question<\/strong>:<\/p>\n<ol>\n<li>How thick would a piece of paper be if it could be folded 52 times?<\/li>\n<li>How does this compare to the distance from the Earth to the Sun?<br \/>\n([latex]d = 1.496 \\times 1011 \\text{ m}[\/latex])<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<p>Article to Read:\u00a0<a href=\"https:\/\/sploid.gizmodo.com\/if-you-fold-a-paper-in-half-103-times-it-will-be-as-thi-1607632639\">If you fold a paper in half 103 times it\u2019ll get as thick as the universe<\/a><\/p>\n<\/div>\n<h1>Exercise Answers<\/h1>\n<h2>1.1 Names &amp; Measurement Terms:<\/h2>\n<\/div>\n<\/div>\n<h3 style=\"text-align: left;\">One Dimensional Measures:<\/h3>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>mi: mile<\/li>\n<li>oz: ounce<\/li>\n<li>mg: milligram<\/li>\n<li>km: kilometre<\/li>\n<li>mm: millimetre<\/li>\n<li>ft: feet<\/li>\n<li>yd: yard<\/li>\n<li>t: ton<\/li>\n<li>g: gram<\/li>\n<li>cm: centimetre<\/li>\n<li><em>\u03bc<\/em>m: micrometre<\/li>\n<li>in: inch<\/li>\n<\/ul>\n<h3 style=\"text-align: left;\">Two Dimensional Measures:<\/h3>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>ft<sup>2<\/sup>: square feet<\/li>\n<li>m<sup>2<\/sup>: square metre<\/li>\n<li>km<sup>2<\/sup>: square metre<\/li>\n<li>in<sup>2<\/sup>: square inch<\/li>\n<li>yd<sup>2<\/sup>: square yard<\/li>\n<li>cm<sup>2<\/sup>: square centimetre<\/li>\n<li>mm<sup>2<\/sup>: square millimetre<\/li>\n<li>\u03bcm<sup>2<\/sup>: square micrometre<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: left;\">Three Dimensional Measures:<\/h3>\n<ul class=\"twocolumn\" style=\"list-style-type: none;\">\n<li>ft<sup>3<\/sup>: cubic feet<\/li>\n<li>m<sup>3<\/sup>: cubic metre<\/li>\n<li>km<sup>3<\/sup>: cubic kilometre<\/li>\n<li>in<sup>3<\/sup>: cubic inch<\/li>\n<li>yd<sup>3<\/sup>: cubic yard<\/li>\n<li>cm<sup>3<\/sup>: cubic centimetre<\/li>\n<li>mm<sup>3<\/sup>: cubic millimetre<\/li>\n<li><em>\u03bc<\/em>m<sup>3<\/sup>: cubic micrometre<\/li>\n<\/ul>\n<h2>1.2 Convert the Following:<\/h2>\n<ol class=\"twocolumn\">\n<li>7 mi = 12<span style=\"margin-left: 0.25em;\">320<\/span> yd<\/li>\n<li>234 oz = 000731 ton<\/li>\n<li>11.2 mg = 0.0112 g<\/li>\n<li>1.35 km = 135<span style=\"margin-left: 0.25em;\">000<\/span> cm<\/li>\n<li>9<span style=\"margin-left: 0.25em;\">800<\/span><span style=\"margin-left: 0.25em;\">000<\/span> mm \u2248 6.12 mi<\/li>\n<li>4.5 ft<sup>2<\/sup> = 0.50 yd<sup>2<\/sup><\/li>\n<li>435<span style=\"margin-left: 0.25em;\">000 m<sup>2<\/sup> = 0.435 km<sup>2<\/sup><\/span><\/li>\n<li>8 km<sup>2<\/sup> \u2248 87<span style=\"margin-left: 0.25em;\">000<\/span><span style=\"margin-left: 0.25em;\">000<\/span> ft<sup>2<\/sup><\/li>\n<li>0.0065 km<sup>3<\/sup> = 6<span style=\"margin-left: 0.25em;\">500<\/span><span style=\"margin-left: 0.25em;\">000<\/span> m<sup>3<\/sup><\/li>\n<li>14.62 in<sup>2<\/sup> \u2248 94.3 cm<sup>2<\/sup><\/li>\n<li>5<span style=\"margin-left: 0.25em;\">500<\/span> cm<sup>3<\/sup> \u2248 0.0072 yd<sup>3<\/sup><\/li>\n<li>3.5 mi\/h \u2248 5.1 ft\/s<\/li>\n<li>185 yd\/min \u22486.31 mi\/h<\/li>\n<li>153 ft\/s \u2248104 mi\/h<\/li>\n<li>248 mi\/h \u2248 110 m\/s<\/li>\n<li>186<span style=\"margin-left: 0.25em;\">000<\/span> mi\/h \u2248 2.61 \u00d7 10<sup>2<\/sup> km\/y<\/li>\n<li>7.50 ton\/yd<sup>2<\/sup> \u2248 0.00579 ton\/in<sup>2<\/sup><\/li>\n<li>16 ft\/s<sup>2<\/sup> \u2248 63<span style=\"margin-left: 0.25em;\">000<\/span> km\/h<sup>2<\/sup><\/li>\n<\/ol>\n<h2>1.3 Measures of Length and Weight, Time Zones:<\/h2>\n<ol>\n<li>1 league = 63<span style=\"margin-left: 0.25em;\">360<\/span> palms<\/li>\n<li>1 poppyseed = 6 points<\/li>\n<li>1 stone = 14 pounds (use this to convert your weight)<\/li>\n<li>180\u00b0 Longitude has 5 different time zones<\/li>\n<\/ol>\n<h2>1.4 Exponential Growth<\/h2>\n<ol>\n<li>Thickness is 4.50 \u00d710<sup>11<\/sup> m<\/li>\n<li>Approximately 3 times the distance from the Earth to the Sun<\/li>\n<\/ol>\n<h3>Media Attributions<\/h3>\n<ul>\n<li>&#8220;<a href=\"https:\/\/en.wikipedia.org\/wiki\/SS_Warrimoo#\/media\/File:SS_Warrimoo_-_New_Zealand.jpg\">New Zealand passenger ship SS Warrimoo<\/a>&#8221; by Allan C. Green (1878-1954) is in the <a href=\"https:\/\/creativecommons.org\/share-your-work\/public-domain\/pdm\/\">public domain<\/a>.<\/li>\n<li>&#8220;<a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:STANDARD_TIME_ZONES_WORLD.png\">STANDARD TIME ZONES WORLD<\/a>&#8221; by United States Central Intelligence Agency is in the <a href=\"https:\/\/creativecommons.org\/share-your-work\/public-domain\/pdm\/\">public domain<\/a>.<\/li>\n<\/ul>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-5-1\"><a href=\"https:\/\/www.calculator.net\/time-zone-calculator.html\">Online Time Zone Calculator<\/a> <a href=\"#return-footnote-5-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":90,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-5","chapter","type-chapter","status-publish","hentry","chapter-type-standard"],"part":3,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/5","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":26,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/5\/revisions"}],"predecessor-version":[{"id":1222,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/5\/revisions\/1222"}],"part":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapters\/5\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/media?parent=5"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/pressbooks\/v2\/chapter-type?post=5"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/contributor?post=5"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/foundationsofphysics\/wp-json\/wp\/v2\/license?post=5"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}