Homework set 1
Solutions
Chapter 1:
2
•
In doing a calculation, you end up with m/s in the numerator and m/s
2
in the
denominator. What are your final units? (
a
) m
2
/s
3
, (
b
) 1/s, (
c
) s
3
/m
2
, (
d
) s, (
e
) m/s.
Picture the Problem
We can express and simplify the ratio of m/s to m/s
2
to determine
the final units.
Express and simplify the ratio of m/s to
m/s
2
:
s
s
m
s
m
s
m
s
m
2
2
=
⋅
⋅
=
and
)
(
d
is correct.
4
•
The prefix mega means (
a
) 10
–9
, (
b
) 10
–6
, (
c
) 10
–3
, (
d
) 10
6
, (
e
) 10
9
.
Determine the Concept
Consulting Table 1
‐
1 we note that the prefix mega
means 10
6
.
)
(
d
is correct.
17
••
There is an environmental debate over the use of cloth versus disposable diapers. (
a
) If
we assume that between birth and 2.5 y of age, a child uses 3 diapers per day, estimate the total
number of disposable diapers used in the United States per year. (
b
) Estimate the total landfill volume
due to these diapers, assuming that 1000 kg of waste fills about 1 m
3
of landfill volume. (
c
) How many
square miles of landfill area at an average height of 10 m is needed for the disposal of diapers each
year?
Picture the Problem
We’ll assume a population of 300 million (fairly accurate as of
September, 2002) and a life expectancy of 76 y. We’ll also assume that a diaper has a
volume of about half a liter. In (
c
) we’ll assume the disposal site is a rectangular hole in
the ground and use the formula for the volume of such an opening to estimate the
surface area required.
(
a
) Express the total number
N
of
disposable diapers used in the United
States per year in terms of the number of
children
n
in diapers and the number of
diapers
D
used by each child in 2.5 y:
nD
N
=
Use the daily consumption, the number of
days in a year, and the estimated length of
time a child is in diapers to estimate the
number of diapers
D
required per child:
ild
diapers/ch
10
3
y
5
.
2
y
d
24
.
365
d
diapers
3
3
×
≈
×
×
=
D
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View Full DocumentUse the assumed life expectancy to
estimate the number of children
n
in
diapers:
()
children
10
children
10
300
y
76
y
5
.
2
7
6
≈
×
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
n
Substitute to obtain:
( )
diapers
10
3
ild
diapers/ch
10
3
children
10
10
3
7
×
≈
×
×
=
N
(
b
) Express the required landfill volume
V
in terms of the volume of diapers to be
buried:
diaper
one
NV
V
=
Substitute numerical values and evaluate
V
:
3
7
3
3
10
m
10
2
L
m
10
diaper
L
5
.
0
diapers
10
3
×
≈
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
×
×
=
−
V
(
c
) Express the required volume in terms
of the volume of a rectangular
parallelepiped:
Ah
V
=
⇒
h
V
A
=
Substitute numerical values evaluate
A
:
2
6
3
7
m
10
2
m
10
m
10
2
×
=
×
=
A
Use a conversion factor to express this
area in square miles:
2
2
2
6
2
2
2
6
mi
8
.
0
m
km
10
km
2.590
mi
1
m
10
2
≈
×
×
×
=
−
A
36
•
What are the dimensions of the constants in each part of Problem 23?
Picture the Problem
We can use the facts that each term in an equation must have the
same dimensions and that the arguments of a trigonometric or exponential function
must be dimensionless to determine the dimensions of the constants.
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 Fall '09
 BUCK
 Physics, Work, Velocity, m/s, Δx, ΔT, numerical values

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