Rodriguez, Brandon – Homework 27 – Due: Nov 28 2006, 11:00 am – Inst: Andrew J Rader
1
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printout
should
have
11
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
Please notice that for your homework to be
considered towards your grade, it needs to be
submitted one hour before the corresponding
recitation starts.
Work submitted after this
time, but before the DUE DATE on top of
this page, will be accepted but not graded.
PLEASE
REMEMBER
THAT
YOU
MUST CARRY OUT YOUR CALCULA
TIONS TO AT LEAST THREE SIGNIFI
CANT FIGURES. YOUR ANSWER MUST
BE
WITHIN
ONE
PERCENT
OF
THE
CORRECT RESULT TO BE MARKED AS
CORRECT BY THE SERVER.
001
(part 1 of 2) 5 points
An air bubble originating from a underwater
diver has a radius of 7 mm at some depth
h
.
When the bubble reaches the surface of the
water, it has a radius of 8
.
8 mm.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Assuming the temperature of the air in the
bubble remains constant, determine the depth
h
of the diver.
Correct answer: 10
.
1701 m.
Explanation:
Given :
ρ
= 1000 kg
/
m
3
,
g
= 9
.
8 m
/
s
2
,
P
atm
= 101000 Pa
,
R
1
= 8
.
8 mm = 0
.
0088 m
,
and
R
2
= 7 mm = 0
.
007 m
.
From the ideal gas law
P V
=
n R T
= constant
,
so
P
1
V
1
=
P
2
V
2
P
1
P
2
=
V
2
V
1
P
atm
P
atm
+
ρ g h
=
4
3
π R
3
2
4
3
π R
3
1
=
R
3
2
R
3
1
R
3
1
P
atm
=
R
3
2
(
P
atm
+
ρ g h
)
.
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 Spring '08
 pedon
 Work, Correct Answer, Andrew J Rader

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