{"id":3842,"date":"2020-11-11T05:21:43","date_gmt":"2020-11-11T05:21:43","guid":{"rendered":"http:\/\/onlineclassesguru.com\/?p=3842"},"modified":"2020-11-11T05:21:43","modified_gmt":"2020-11-11T05:21:43","slug":"the-book-weighs","status":"publish","type":"post","link":"https:\/\/onlineclassesguru.com\/index.php\/2020\/11\/11\/the-book-weighs\/","title":{"rendered":"The book weighs"},"content":{"rendered":"<style type=\"text\/css\"><\/style><p>1. Find the work done in lifting a book as described:<\/p>\n<p>a) The book weighs 4 lbs and is lifted through 5 ft.<\/p>\n<p>b) The book has mass 4 kg and is lifted through 5 m.<\/p>\n<p>2. An object located x units from a fixed starting position is moved along a straight path by a force of 10\/(1 + x)2 pounds. How much work is done in moving the object through 9 feet?<\/p>\n<p>3. The graph of a force function (in newtons) is shown. How much work is done by the force in moving an object through a distance of 8 meters?<\/p>\n<p>x<\/p>\n<p>F<\/p>\n<p>1 2 3 4 5 6 7 8<\/p>\n<p>10<\/p>\n<p>20<\/p>\n<p>30<\/p>\n<p>4. A force of 10 lbs is required to hold a spring stretched 4 in beyond its natural length. How much work is done in stretching the spring from its natural length to 8 in beyond its natural length?<\/p>\n<p>5. A spring has a natural length of 30 cm. If a 25 N force is required to keep it stretched to a length of 40 cm, how much work is required to stretch it from 30 cm to 40 cm?<\/p>\n<p>? 6\u00969 For the given cable problem, do the following:<\/p>\n<p>a) Draw a picture, and set up the Riemann Sum ?<\/p>\n<p>Wi that approximates the work.<\/p>\n<p>b) Express the work as an integral and evaluate it.<\/p>\n<p>6. A heavy rope, 50 ft long and weighing 30 lbs hangs over the edge of a building. How much work is required to pull the rope to the top of the building?<\/p>\n<p>7. For the rope in Problem (6), how much work is required to pull half the rope to the top of the building?<\/p>\n<p>Hint: Consider the top and bottom halves separately.<\/p>\n<p>8. A cable weighing 2 lbs\/ft is used to lift 800 lbs of coal up a mineshaft 500 ft deep. Find the work done.<\/p>\n<p>Hint: Consider the cable and coal independently.<\/p>\n<p>1 of 2<\/p>\n<p>9. A 10 m long cable with a mass of 25 kg hangs from a hook. Find the work done in lifting the lower end of the chain (straight up) to hang from the same hook, as shown.<\/p>\n<p>Hint: Be careful with the distance di.<\/p>\n<p>y = 10<\/p>\n<p>y = 0<\/p>\n<p>Solutions to Selected Problems<\/p>\n<p>1. a) 20 ft-lbs<\/p>\n<p>b) 196 J<\/p>\n<p>2. 9 ft-sbs<\/p>\n<p>3. 180 J<\/p>\n<p>4. 20<\/p>\n<p>3 ft-lbs<\/p>\n<p>5. 1.25 J<\/p>\n<p>6. a) Wi = 3 5y<\/p>\n<p>? i ?y<\/p>\n<p>b) 750 ft-lbs<\/p>\n<p>7. a) Top half: Wi = 3 5y<\/p>\n<p>? i ?y<\/p>\n<p>Bottom half: 15(25)<\/p>\n<p>b) 562.5 ft-lbs<\/p>\n<p>8. a) Cable: Wi = 2y ? i ?y<\/p>\n<p>Coal: 800(500)<\/p>\n<p>b) 650,000 ft-lbs<\/p>\n<p>9. a) Wi = 24.5(10 ? 2y?i )?y<\/p>\n<p>b) 612.5 J<\/p>\n<p>2 of 2<\/p>\n<p><center><a href=\"http:\/\/onlineclassesguru.com\/orders\/ordernow\"><img decoding=\"async\" src=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcTyj99p60XCLyLk1htB7-1neRt8-2QdnenNlQ&usqp=CAU\"target=\"_http:\/\/onlineclassesguru.com\/orders\/ordernow\"\/><\/center><p>","protected":false},"excerpt":{"rendered":"<p>1. Find the work done in lifting a book as described: a) The book weighs 4 lbs and is lifted through 5 ft. b) The book has mass 4 kg and is lifted through 5 m. 2. An object located x units from a fixed starting position is moved along a straight path by a&#8230;<\/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-3842","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The book weighs - onlineclassesguru<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/onlineclassesguru.com\/index.php\/2020\/11\/11\/the-book-weighs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The book weighs - onlineclassesguru\" \/>\n<meta property=\"og:description\" content=\"1. 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