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# hw4 - 2.016 HW#4 Out October 4 2005 Due 1 A sphere of...

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2.016 HW #4 Out: October 4, 2005 Due: October 18, 2005 1) A sphere of volume V in a fluid of density ρ is located at a point (0, L , 0) with respect to a certain coordinate system. In terms of this coordinate system , identify whether each of the 6x6 added mass coefficients are zero (0), or non-zero (x) (do not work out ). x y z ( ) any values 0, L, 0 2) A positively buoyant cone with length L, and maximum radius R o is placed with the apex at the origin of a coordinate system as shown below. z y a) Calculate the center of buoyancy for the cone.

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b) Determine which added mass coefficients are zero or non-zero. You can fill out a 6x6 matrix with X for non-zero and 0 for zero. c) Use Strip Theory to calculate M 55 , M 11 , M 44 , M 66 , M 51 , and M 22 . Hint: first consider any symmetry that might make these calculations easier. d) Write the equation of motion of the cone in roll, and calculate the natural frequency. 3) A new class of submarine can be modeled by a cylinder of length L and radius R , with a vertical sail and horizontal elliptical wings of major and minor axis radii a and b and length h , as shown. Assuming that these main members are slender so that their longitudinal added mass may
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hw4 - 2.016 HW#4 Out October 4 2005 Due 1 A sphere of...

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