At 0t=, z, and 0=±zb=223agb=+D0b323=−Db3222233bzggz+±zAt za, =()323bgzgaabaa= −±312223gba±7.25Initially, the upward buoyancy force balances the weight of the balloon and sand. (1)0BFMmg−+=DLet mmthe mass of sand at time twhere 0ttt≤≤D1ttDD(2)The velocity of sand relative to the balloon is zero upon release so Vin 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, FB, 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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