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 2mile 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 yaxis to form a “flying saucer.” Sketch a
graph of the saucer and compute its volume. ...
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 Winter '09
 Kouba
 Calculus

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