Problem 3.104
[Difficulty: 2]
(
L + c
)/2
L
c
F
BR
W
R
L
/2
a
θ
Given:
Geometry of rod
Find:
How much of rod is submerged; force to lift rod out of water
Solution:
Basic equations
Σ
M
Hinge
0
=
F
B
ρ
g
⋅
V
⋅
=
(Buoyancy)
The free body diagram is as shown.
F
BR
is the buoyancy of the rod; c is
the (unknown) exposed length of the rod
Taking moments about the hinge
F
BR
−
Lc
+
()
2
⋅
cos
θ
⋅
W
R
L
2
⋅
cos
θ
⋅
+
0
=
with
F
BR
ρ
g
⋅
−
⋅
A
⋅
=
W
R
M
R
g
⋅
=
Hence
ρ
−
A
⋅
−
⋅
+
2
⋅
M
R
L
2
⋅
+
0
=
We can solve for c
ρ
A
⋅
L
2
c
2
−
⋅
M
R
L
⋅
=
cL
2
LM
R
⋅
ρ
A
⋅
−
=
c5
m
⋅
2
5m
⋅
m
3
1000 kg
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 Fall '07
 Lear
 Fluid Mechanics

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