A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27 m\/s. What was the average force of air resistance?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To find the average force of air resistance<\/strong>, we compare the actual energy change (including air resistance) to the ideal case (free fall without air resistance). Here’s how to approach it:<\/p>\n\n\n\n If there were no air resistance, all the potential energy would convert into kinetic energy: Potential Energy=mgh=2.0\u00d79.8\u00d755=1078\u2009J\\text{Potential Energy} = mgh = 2.0 \\times 9.8 \\times 55 = 1078 \\, \\text{J} Kinetic Energy (actual)=12mv2=12\u00d72.0\u00d7272=729\u2009J\\text{Kinetic Energy (actual)} = \\frac{1}{2}mv^2 = \\frac{1}{2} \\times 2.0 \\times 27^2 = 729 \\, \\text{J}<\/p>\n\n\n\n The difference in energy is due to air resistance<\/strong>: Energy lost to air resistance=1078\u2212729=349\u2009J\\text{Energy lost to air resistance} = 1078 – 729 = 349 \\, \\text{J}<\/p>\n\n\n\n Work done by air resistance = Force \u00d7 Distance \u00d7 cos(\u03b8)<\/p>\n\n\n\n Here, air resistance is opposite to motion<\/strong>, so cos\u2061(180\u2218)=\u22121\\cos(180^\\circ) = -1: W=\u2212Fair\u22c5d\u21d2Fair=\u2212Wd=\u2212\u221234955\u22486.35\u2009NW = -F_{\\text{air}} \\cdot d \\Rightarrow F_{\\text{air}} = -\\frac{W}{d} = -\\frac{-349}{55} \\approx 6.35 \\, \\text{N}<\/p>\n\n\n\n So, the magnitude<\/strong> of the average force of air resistance is: 6.35\u2009N\\boxed{6.35 \\, \\text{N}}<\/p>\n\n\n\n To calculate the average force of air resistance acting on a 2.0-kg purse dropped from the Leaning Tower of Pisa, we use energy principles. In an ideal vacuum, gravity is the only force acting on a falling object, and thus all potential energy converts to kinetic energy. However, since the purse fell through air and reached a speed of 27 m\/s rather than the higher speed expected in vacuum, energy was lost\u2014specifically, it was dissipated due to air resistance.<\/p>\n\n\n\n First, we calculate the gravitational potential energy (PE) at the start: PE=mgh=2.0\u00d79.8\u00d755=1078\u2009JPE = mgh = 2.0 \\times 9.8 \\times 55 = 1078 \\, \\text{J}. Then, we calculate the actual kinetic energy (KE) the purse had just before hitting the ground: KE=12mv2=12\u00d72.0\u00d7272=729\u2009JKE = \\frac{1}{2}mv^2 = \\frac{1}{2} \\times 2.0 \\times 27^2 = 729 \\, \\text{J}. The difference between these two energies\u2014349 J\u2014represents the energy lost to air resistance.<\/p>\n\n\n\n This energy loss is due to the work done by air resistance<\/strong> as it opposes the motion. Using the work-energy principle, we calculate the average force by dividing the energy lost by the distance fallen: F=34955\u22486.35\u2009NF = \\frac{349}{55} \\approx 6.35 \\, \\text{N}. This force acts opposite the direction of motion, so the purse ends with less speed than it would have had in a vacuum.<\/p>\n\n\n\n Therefore, the average force of air resistance<\/strong> is 6.35 newtons<\/strong> acting upward against the motion.<\/p>\n","protected":false},"excerpt":{"rendered":" A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 27 m\/s. What was the average force of air resistance? The correct answer and explanation is: To find the average force of air resistance, we compare the actual energy […]<\/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-16848","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16848","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=16848"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16848\/revisions"}],"predecessor-version":[{"id":16849,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16848\/revisions\/16849"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16848"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16848"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16848"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Known Values<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 2: Energy Without Air Resistance<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 3: Work Done by Air Resistance<\/strong><\/h3>\n\n\n\n
\n\n\n\n300-word Explanation<\/strong><\/h3>\n\n\n\n