Nguyen, Phan – Homework 1 – Due: Jan 27 2004, 4:00 am – Inst: V Kaplunovsky
1
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The due time is Central time.
001
(part 1 of 1) 10 points
One cubic meter (1.0 m
3
) of aluminum has a
mass of 2700 kg, and a cubic meter of iron has
a mass of 7860 kg.
Find the radius of a solid aluminum sphere
that has the same mass as a solid iron sphere
of radius 2
.
2 cm. Answer in units of cm.
002
(part 1 of 1) 10 points
Consider the following set of equations, where
s
,
s
0
,
x
and
r
have units of length,
t
has units
of time,
v
has units of velocity,
g
and
a
have
units of acceleration, and
k
is dimensionless.
Which one is dimensionally
incorrect
?
1.
a
=
g
+
kv
t
+
v
2
s
0
2.
t
=
v
a
+
x
v
3.
s
=
s
0
+
vt
+
v
2
a
4.
t
=
k
r
s
g
+
a
v
5.
v
2
= 2
as
+
ksv
t
003
(part 1 of 2) 10 points
Stokes law says
F
= 6
πrηv.
F
is a force,
r
the radius and
v
the velocity.
The parameter
η
has the dimension of
1.
[
η
] =
M
T L
2.
[
η
] =
T
2
L
2
M
3.
[
η
] =
M
T L
2
4.
[
η
] =
T
M
5.
[
η
] =
T
2
L
M
6.
[
η
] =
M
T
7.
[
η
] =
M
T
2
L
2
8.
[
η
] =
M
T
2
L
9.
[
η
] =
T L
M
10.
[
η
] =
T L
2
M
004
(part 2 of 2) 10 points
Consider a simple pendulum which consists of
a string with a bob attached to its end.
Its
period, (
i.e.
, the time interval taken for the
bob to complete one cycle of motion), may be
written in the form
T
=
k m
x
g
y
b
z
,
where
k
is a dimensionless constant,
g
the
magnitude of the gravitational acceleration,
m
the mass of the bob, and
b
the length of the
string.
The appropriate
x
,
y
, and
z
values are given
respectively by
1.
(
x, y, z
) =
1
,
1
2
,

1
2
¶
2.
(
x, y, z
) =
0
,

1
2
,

1
2
¶
3.
(
x, y, z
) =
1
,

1
2
,
1
2
¶
4.
(
x, y, z
) =
0
,

1
2
,
1
2
¶
5.
(
x, y, z
) =
0
,
1
2
,

1
2
¶
6.
(
x, y, z
) =
1
,

1
2
,

1
2
¶
7.
(
x, y, z
) = (1
,

1
,
1)
8.
(
x, y, z
) =
0
,
1
2
,
1
2
¶
9.
(
x, y, z
) = (0
,

1
,
1)
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Nguyen, Phan – Homework 1 – Due: Jan 27 2004, 4:00 am – Inst: V Kaplunovsky
2
10.
(
x, y, z
) =
1
,
1
2
,
1
2
¶
005
(part 1 of 1) 10 points
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