Nguyen, Don – Final 1 – Due: Dec 8 2004, 5:00 pm – Inst: Charles Chiu
1
This printout should have 21 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
be±ore answering.
The due time is Central
time.
001
(part 1 o± 1) 10 points
The velocity,
v
, o± a sound wave traveling in
the air depends on
B
, the bulk modulus, and
ρ
, the density o± the air.
The bulk mod
ulus is defned by the variation o± pressure
Δ
P
=

B
Δ
V/V
, where Δ
V/V
is the ±rac
tional change o± the volume.
Assume
v
=
B
x
ρ
y
.
The powers o±
x
and
y
may be determined
based on a dimensional analysis.
Through
equating the powers o± M, o± L and o± T,
one arrives at correspondingly a set o± three
equations.
Choose the correct set.
1.
0 =
x
+
y
, 1 =
x
+ 3
y
and 1 =

2
x
2.
0 =
x
+
y
, 1 =

x
+ 3
y
and

1 =

2
x
3.
0 =
x

y
, 1 =
x

3
y
and 1 =

2
x
4.
1 =
x
+
y
, 0 =
x

3
y
and 1 =

2
x
5.
0 =
x
+
y
, 1 =

x

3
y
and

1 =

2
x
correct
6.
0 =
x

y
,

1 =
x

3
y
and

1 =

2
x
7.
0 =
x

y
, 1 =
x
+ 3
y
and 1 =

2
x
8.
0 =
x

y
, 2 =
x
+ 3
y
and

1 =

2
x
9.
0 =
x
+
y
, 1 =
x

3
y
and 1 =

2
x
10.
0 =
x
+
y
, 0 =
x

3
y
and 1 =

2
x
Explanation:
Denote the dimension o± a quantity by
a square bracket.
[
v
]=L/T, [
B
]=[
F/A
],
[
ρ
]=M/L
3
.
The last two equations lead
to [
B
x
ρ
y
] =(ML/(TL)
2
)
x
(M/L
3
)
y
. Now we
write [
v
]=[
B
x
ρ
y
]. Equating the power o± M
gives 0 =
x
+
y
. Equating power o± L gives
1 =

x

3
y
, and powers o± T gives

1 =

2
x
.
002
(part 1 o± 1) 10 points
The graph shows position as a ±unction o± time
±or two trains running on parallel tracks. At
time
t
=0 (origin) the position o± both trains
is 0. Which is true:
position
time
t
B
B
A
1.
Both trains speed up all the time
2.
In the time interval ±rom
t
=0 to
t
=
t
B
,
train B covers more distance than train A
3.
At time
t
B
, both trains have the same
velocity
4.
Somewhere be±ore time
t
B
, both trains
have the same acceleration
5.
Both trains have the same velocity at
some time be±ore
t
B
correct
Explanation:
The slope o± the curve B is parallel to line
A at some point
t < t
B
.
003
(part 1 o± 1) 10 points
Consider a man standing on a scale which is
placed in an elevator. When the elevator is
stationary, the scale reading is
S
s
.