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Problem 4.3
[Difficulty: 2]
θ
F
n
M
V
Given:
Data on ball and pipe
Find:
Speed and location at which contact is lost
Solution:
The given data is
r1
m
m
⋅
=
R5
0
m
m
⋅
=
F
n
∑
F
n
mg
⋅
cos
θ
()
⋅
−
=
ma
n
⋅
=
a
n
V
2
Rr
+
−
=
Contact is lost when
F
n
0
=
or
m
−
g
⋅
cos
θ
⋅
m
−
V
2
+
⋅
=
V
2
gR r
+
⋅
cos
θ
⋅
=
(1)
For no resistance energy is conserved, so
Em
g
⋅
z
⋅
m
V
2
2
⋅
+
=
⋅
+
⋅
cos
θ
⋅
m
V
2
2
⋅
+
=
E
0
=
⋅
+
⋅
=
Hence from energy considerations
V
2
2g
⋅
+
⋅
1
cos
θ
−
⋅
=
(2)
Combining 1 and 2,
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 Fall '07
 Lear
 Fluid Mechanics

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