alexander (jra2623) – homework 02 – Turner – (92510)
1
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8
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001
10.0 points
A rope has a cross section
A
= 11
.
4 m
2
and
density
ρ
= 1680 kg
/
m
3
. The linear density
of the rope
μ
, defined to be the mass per unit
length, can be written in the form
μ
=
ρ
x
A
y
.
Based on dimensional analysis, determine
the powers
x
and
y
by choosing an expression
below.
1.
μ
=
ρ A
correct
2.
μ
=
A
ρ
2
3.
μ
=
A
2
ρ
2
4.
μ
=
ρ
A
5.
μ
=
ρ
A
2
6.
μ
=
A
ρ
7.
μ
=
A
2
ρ
8.
μ
=
1
ρ A
9.
μ
=
ρ A
2
10.
μ
=
1
ρ A
2
Explanation:
[
x
] means ”the units of
x
”.
[
μ
] = [
ρ
x
A
y
]
[M]
[L]
=
parenleftbigg
M
L
3
parenrightbigg
x
(
L
2
)
y
[M]
+1
[L]
−
1
= M
x
L
−
3
x
L
2
y
= M
x
L
2
y
−
3
x
Equating the exponents,
x
= 1
2
y

3
x
=

1
2
y

3 =

1
y
= 1
.
Thus
μ
=
ρ
1
A
1
=
ρ A .
002
10.0 points
An angle of 249
◦
is equivalent to how many
radians?
Correct answer: 4
.
34587 rad.
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 Summer '08
 Kaplunovsky
 Cartesian Coordinate System, Work, Correct Answer, Polar coordinate system, tan θ

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