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Problem 1.52
[Difficulty: 4]
Given:
American golf ball, m = 1.62 ± 0.01 oz, D = 1.68 in.
Find:
Precision to which D must be measured to estimate density within uncertainty of ± 1percent.
Solution:
Apply uncertainty concepts
Definition: Density,
3
3
D
m4
36
R
π
ρπ
∀
≡∀
=
=
Computing equation:
1
2
1
2
1
Rx
1
R
uu
x
⎡
⎤
⎛⎞
∂
⎢
⎥
=±
+
⎜⎟
∂
⎢
⎥
⎝⎠
⎣
⎦
L
From the definition,
3/6
3
6m
m
DD
(m, D)
ππ
ρρ
==
=
Thus
m
m
1
ρ
∂
∂
=
and
D
D
3
∂
∂
=
, so
1
2
22
mD
222
u[
(
1
u
)
(
3
u
)
]
9
u
+
=+
Solving,
1
2
1
Dm
3
u
u
]
−
From the data given,
1
2
m
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics

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