311ps6 - PROBLEM SET 6 ECE 311 Autumn Quarter 2011...

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Unformatted text preview: PROBLEM SET 6 ECE 311 Autumn Quarter 2011 Assigned: Wednesday, Nov. 2nd Due: Monday, Nov. 7th in class Instructor: Joel T. Johnson Problem 1 Point P is located at coordinates (R=3, =45, =210) in a spherical coordinate system. Point Q is located at (r=3, =45, z=1) in a cylindrical coordinate system. Find (a) a position vector written in terms of cylindrical unit vectors from the origin to point P (b) the coordinates of points P and Q in a Cartesian coordinate system (c) , a vector written in terms of Cartesian unit vectors from point P to point Q (d) , the distance between points P and Q (e) the coordinates of point Q in a spherical coordinate system Problem 2 This problem involves performing the integral of a scalar over a volume. A mountain takes the shape of a hemisphere (on top of the surrounding flat Earth) with radius 3 km. Note that the intersection of the hemisphere with the surrounding flat Earth is a circle; the center of this circle is defined as the origin in what follows. The mass density of the mountain in kg per circle is defined as the origin in what follows....
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311ps6 - PROBLEM SET 6 ECE 311 Autumn Quarter 2011...

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