{"id":32200,"date":"2025-06-22T11:50:28","date_gmt":"2025-06-22T11:50:28","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=32200"},"modified":"2025-06-22T11:50:29","modified_gmt":"2025-06-22T11:50:29","slug":"in-their-college-years-stevie-g","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/in-their-college-years-stevie-g\/","title":{"rendered":"In their college years, Stevie G."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">In their college years, Stevie G. was helping his roommate Biff G. move from Ankeny, IA, to Ames, IA. Steve and Biff put a queen-size Lebeda Heritage pillowtop mattress and box spring on the top of Biff&#8217;s 1999 Pontiac Grand Am sedan. To the disgust of Stevie G., Biff used baling twine to fasten the mattress and box spring combination to the roof of the car, which was centered on the roof. They had a choice of using US Highway 69 or US Interstate 35 in their travels. In this analysis, Stevie G. would like to have answers to the following questions: How far does the mattress hang over the roof of the car? What is the expected drag incurred by the mattress, and what is the lift exposed on the mattress for the two travel route options? What is the expected mileage decrease due to the mattress and box spring for the two travel options? How many times should the baling twine be wrapped around the roof of the car to ensure the mattress and box spring remained on the car, with a safety factor of 2.5?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answer and Explanation:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Mattress Overhang:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A queen-size mattress measures approximately 80 inches long and 60 inches wide. A 1999 Pontiac Grand Am sedan has a roof length of roughly 55 inches and a width of about 54 inches. If the mattress is centered on the roof, the overhang at the front and rear would be:80\u2212552=12.5&nbsp;inches\\frac{80 &#8211; 55}{2} = 12.5 \\text{ inches}280\u221255\u200b=12.5&nbsp;inches<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, the mattress overhangs about <strong>12.5 inches<\/strong> in front and back.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Drag and Lift Forces:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Drag force FdF_dFd\u200b is given by:Fd=12Cd\u03c1Av2F_d = \\frac{1}{2} C_d \\rho A v^2Fd\u200b=21\u200bCd\u200b\u03c1Av2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>CdC_dCd\u200b (drag coefficient for a flat surface) \u2248 1.0<\/li>\n\n\n\n<li>\u03c1\\rho\u03c1 (air density) \u2248 1.225 kg\/m\u00b3<\/li>\n\n\n\n<li>AAA (frontal area) \u2248 1.52 m\u00b2 (based on mattress width and thickness)<\/li>\n\n\n\n<li>vvv is velocity in m\/s<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">For US Highway 69 (speed \u2248 55 mph = 24.6 m\/s):Fd\u22480.5\u00d71.0\u00d71.225\u00d71.52\u00d7(24.6)2\u2248563\u2009NF_d \\approx 0.5 \\times 1.0 \\times 1.225 \\times 1.52 \\times (24.6)^2 \\approx 563 \\, \\text{N}Fd\u200b\u22480.5\u00d71.0\u00d71.225\u00d71.52\u00d7(24.6)2\u2248563N<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For I-35 (speed \u2248 70 mph = 31.3 m\/s):Fd\u22480.5\u00d71.225\u00d71.52\u00d7(31.3)2\u2248912\u2009NF_d \\approx 0.5 \\times 1.225 \\times 1.52 \\times (31.3)^2 \\approx 912 \\, \\text{N}Fd\u200b\u22480.5\u00d71.225\u00d71.52\u00d7(31.3)2\u2248912N<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lift force can be comparable in magnitude for flat surfaces, especially if the mattress catches wind beneath it. So <strong>lift \u2248 drag<\/strong>, giving 563 N on Highway 69 and 912 N on I-35.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Mileage Decrease:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Increased drag reduces fuel efficiency. A typical penalty is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>10\u201315% loss at 55 mph<\/li>\n\n\n\n<li>20\u201325% loss at 70 mph<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So the expected mileage drop is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>10\u201315% on US-69<\/strong><\/li>\n\n\n\n<li><strong>20\u201325% on I-35<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Baling Twine Wraps with Safety Factor:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assume combined weight of mattress and box spring = 150 lbs (\u2248 667 N). With a safety factor of 2.5, force to resist = 1667.5 N.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If baling twine can safely hold 200 N per loop (depending on twine strength):1667.5200=8.34\u2192round&nbsp;up&nbsp;to&nbsp;9&nbsp;loops\\frac{1667.5}{200} = 8.34 \\rightarrow \\text{round up to } 9 \\text{ loops}2001667.5\u200b=8.34\u2192round&nbsp;up&nbsp;to&nbsp;9&nbsp;loops<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Final Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mattress overhangs by <strong>12.5 inches<\/strong> front and back.<\/li>\n\n\n\n<li>Drag forces: <strong>563 N on Hwy 69<\/strong>, <strong>912 N on I-35<\/strong><\/li>\n\n\n\n<li>Lift forces: roughly equal to drag.<\/li>\n\n\n\n<li>Mileage decrease: <strong>10\u201315% on Hwy 69<\/strong>, <strong>20\u201325% on I-35<\/strong><\/li>\n\n\n\n<li>Minimum <strong>9 wraps<\/strong> of baling twine needed for safety.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-210.jpeg\" alt=\"\" class=\"wp-image-32210\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-210.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-210-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-210-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-210-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>In their college years, Stevie G. was helping his roommate Biff G. move from Ankeny, IA, to Ames, IA. Steve and Biff put a queen-size Lebeda Heritage pillowtop mattress and box spring on the top of Biff&#8217;s 1999 Pontiac Grand Am sedan. To the disgust of Stevie G., Biff used baling twine to fasten the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-32200","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=32200"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32200\/revisions"}],"predecessor-version":[{"id":32211,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/32200\/revisions\/32211"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=32200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=32200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=32200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}