Hood, Charles – Homework 1 – Due: Sep 14 2006, 11:00 pm – Inst: Jan Opyrchal
1
This
printout
should
have
10
questions.
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beFore answering.
The due time is Central
time.
001
(part 1 oF 1) 10 points
This problem shows how dimensional analysis
helps us check our work and sometimes even
help us fnd a Formula.
A rope has a cross section
A
= 9
.
5 m
2
and
density
ρ
= 2150 kg
/
m
3
. The “linear” density
oF the rope
μ
, is defned to be the mass per
unit length, in the Form
μ
=
ρ
x
A
y
.
Based on dimensional analysis, fnd the
powers
x
and
y
.
1.
x
=

2
, y
= 2
2.
x
=

1
, y
= 2
3.
x
= 1
, y
= 2
4.
x
= 1
, y
= 1
correct
5.
x
= 1
, y
=

1
6.
x
=

2
, y
=

1
7.
x
=

1
, y
= 1
8.
x
=

2
, y
= 1
9.
x
=

1
, y
=

1
Explanation:
Kilogram (kg): a unit oF mass (M).
Meter (m): a unit oF length (L).
[
x
] means “the units oF
x
”.
The units oF both sides oF any equation must
be the same For the equation to make sense.
The units oF the leFt hand side (LHS) are given
as
[
μ
] =
M
L
=
M L

1
and the right hand side has
[
ρ
x
A
y
] =
µ
M
L
3
¶
x
×
(
L
2
)
y
=
M
x
L

3
x
L
2
y
=
M
x
L
2
y

3
x
The powers on the units oF mass and length
need to be the same as For the LHS above, so
x
= 1
2
y

3
x
=

1
2
y
=

1 + 3 = 2
y
= 1
Thus the answer is (
x, y
) = (1
,
1).
keywords:
002
(part 1 oF 1) 10 points
A 19
th
century British naturalist with a pen
chant For archaic units oF measurement de
scribed a species oF snail crawling at an
average speed oF one Furlong per Fortnight.
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 Fall '08
 KEN
 Work, Orders of magnitude, Inch, Acre, Jan Opyrchal

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