Analytical Mech Homework Solutions 98

Analytical Mech Homework Solutions 98 - At t = 0 , z = 0 ,...

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At 0 t = , z , and 0 = ± zb = 2 2 3 ag b =+ D 0 b 3 2 3 =− D b 3 2 2 22 33 b zgg z + ± z At za , = () 3 23 bg zg a a b aa  = −   ± 3 1 2 2 2 3 g b a    ± 7.25 Initially, the upward buoyancy force balances the weight of the balloon and sand. ( 1 ) 0 B FMm g −+ = D Let mm the mass of sand at time t where 0 t tt ≤≤ D 1 t t D D ( 2 ) The velocity of sand relative to the balloon is zero upon release so V in equation 7.7.5 … there is no upward “rocket-thrust.” 0 = As sand is released, the net upward force is the difference between the initial buoyancy force, F B , and the weight of the balloon and remaining sand. Let be the subsequent displacement of the balloon, so equation 7.7.5 reduces to
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