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Analytical Mech Homework Solutions 104

Analytical Mech Homework Solutions 104 - 2 b zcm = 0 z bzdz...

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2 2 0 0 0 0 b b cm b b z bzdz z dz z bzdz zdz ρ π ρπ = = 2 3 cm z b = (e) The center of mass is on the z-axis. α is the half-angle of the apex of the cone. is the radius of the base at z = 0 and is radius of a circle at some arbitrary z in a plane parallel to the base. r D r tan r r b b z α = = D , a constant ( ) 2 2 2 tan dv r dz b z dz π π α = = 2 3 1 1 tan 3 3 b b 2 m r ρ π πρ = = D α ( ) ( ) 2 2 2 2 3 0 3 0 3 2 tan 3 2 1 tan 3 b b cm z b z dz z b b b ρ π α πρ α = = z bz z dz + 4 cm b z = 8.2 2 0 0 b cm b cx dx xdx x dx cxdx ρ ρ = = 2 3 cm b x = 8.3 The center of mass is on the z-axis. Consider the sphere with the cavity to be made of a (i) solid sphere of radius and mass a s M , with its center of mass at , and (ii) a solid sphere the size of the cavity, with
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