Sheet8 - Math 21B Kouba Challenge Sheet 8 1 An object of...

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Unformatted text preview: Math 21B Kouba Challenge Sheet 8 1.) An object of mass 2 kg. travels with a linear velocity of 5 m./sec. Compute its kinetic energy. 2.) A thin, straight rod of mass 2 kg. and length 3 meters rotates around one of its ends at the rate of 5 revolutions per second SET UP BUT DO NOT EVALUATE integral(s) which represent the kinetic energy of the rod. 3.) A thin, flat, square plate of mass 2 kg. and side length 3 meters rotates around one of its edges at the rate of 5 revolutions per second. SET UP BUT DO NOT EVALUATE integral(s) which represent the kinetic energy of the rod. 4.) A circular cylinder of mass 2 kg., height 3 meters, and diameter 3 meters rotates around an axis at the rate of 5 revolutions per second. SET UP BUT DO NOT EVALUATE integral(s) which represent the kinetic energy of the rod if the axis is a.) a line throught the centers of the circular ends of the cylinder. b.) a line parallel to the axis in part a.) and touching the outer edge of the cylinder. 5.) Determine the centroid (:2, 3]) of the region bounded by the graphs of a.) y 2 In an, m = 2, and y = 0. Does the centroid lie inside the region ? b.) y = :64 and y : 935. Does the centroid lie inside the region ‘? 6.) A tiny volcanic island has formed in the Pacific Ocean. The depth of the ocean :6 miles from the island is 331:2 miles. Compute the volume of ocean water within a 2-mile radius of the island. 7.) The region in the first quadrant bounded by the graphs of y = 302, y 2 8 — 21:2, and :1: = 0 is rotated around the y-axis to form a “flying saucer.” Sketch a graph of the saucer and compute its volume....
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