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 “rocketthrust.”
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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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
 Buoyancy, Force, Work

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