Ch 7. Centroid/Distributed Loads/Inertia st Multimedia Engineering Statics Centroid: Line Area Vol Centroid: Composite Distributed Loads Area Moment of Inertia
 Chapter 1. Basics 2. Vectors 3. Forces 4. Moments 5. Rigid Bodies 6. Structures 7. Centroids/Inertia 8. Internal Loads 9. Friction 10. Work & Energy Appendix Basic Math Units Sections Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Kurt Gramoll ©Kurt Gramoll

 STATICS - CASE STUDY Introduction Geometry Diagram In order to determine a submarine's buoyancy characteristics, designers must accurately determine the centroid, center of mass, and center of gravity for various parts of the sub. What is known: The radius of the nose cone is given by r(x) = B - CxD. The length of the nose cone is 100 ft. The base of the nose cone has a radius 20 ft. The shape exponent D is 4, but as a first approximation, the designers use D = 1 in order to simplify the mathematics. The density of the nose cone varies linearly from 1 slug/ft3 at the base to 2 slug/ft3 at the tip. Question Submarine Path Animation Click to view movie (746k) As a first approximation, assume the nose code is a simple cone shape (D = 1 in the above equation). Where is the centroid, center of mass, and center of gravity? Approach Use symmetry to determine the y and z locations of the centroid, center of mass, and center of gravity. Solve for the x location by integrating the appropriate quantities from the base to the tip of the nose cone.