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Muraj, Hamza – Homework 3 – Due: Jan 27 2006, 4:00 am – Inst: Florin
1
This
printout
should
have
12
questions.
Multiplechoice questions may continue on
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be±ore answering.
The due time is Central
time.
001
(part 1 o± 1) 10 points
A structural
I
beam is made o± iron. A view o±
its crosssection and its dimensions is shown
in the fgure, where
d
= 3 cm,
w
= 27 cm,
h
= 29 cm and the length (not shown) o± the
beam is
‘
= 1
.
44 m.
The density o± iron is 7560 kg
/
m
3
.
The
atomic weight o± iron is 55.85 g/mol and Avo
gadro number is
N
A
= 6
.
02214
×
10
23
/
mol.
27 cm
29 cm
3 cm
3 cm
How many atoms are there in this section?
Correct answer: 2
.
71159
×
10
27
atoms.
Explanation:
Let :
d
= 3 cm
,
w
= 27 cm
,
h
= 29 cm
,
and
‘
= 1
.
44 m
.
w
h
d
d
The crosssectional area o± the beam is
A
= 2
·
(27 cm) (3 cm)
+ (29 cm

2
·
3 cm) (1 cm)
= 231 cm
2
= 0
.
0231 m
2
.
The volume o± a piece
‘
= 1
.
44 m long is then
V
=
A ‘
= 0
.
033264 m
3
.
The mass is then given by
m
=
ρ V
= 251
.
476 kg
.
Let :
m
= 251
.
476 kg = 251476 g
and
N
A
= 6
.
02214
×
10
23
/
mol
.
Presuming that the atoms are iron, we look to
the periodic table and fnd the molar mass to
be
M
= 55
.
85 g
/
mol
.
The number o± moles is
then
n
=
m
M
=
251476 g
55
.
85 g
/
mol
= 4502
.
7 mol
and the number o± atoms is
N
=
n N
A
= (4502
.
7 mol) (6
.
02214
×
10
23
/
mol)
=
2
.
71159
×
10
27
atoms
.
002
(part 1 o± 1) 10 points
Identi±y the equation below which is dimen
sionally
incorrect
.
A, x, y
and
r
have units o± length.
k
here
has units o± inverse length.
v
0
and
v
have units
o± velocity.
a
and
g
have units o± acceleration.
ω
has units o± inverse time.
t
is time,
m
is
mass,
V
is volume,
ρ
is density, and
F
is ±orce.
1.
v
0
=
p
v
2

2
a x
2.
t
=

v
0
+
q
v
2
0
+ 2
a x
a
+
v
2
a
2
t
3.
v
=
p
2
g y
+
r
r F
m
4.
F
=
m ω
2
r
5.
v
=
±
ω
p
A
2

x
2
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View Full DocumentMuraj, Hamza – Homework 3 – Due: Jan 27 2006, 4:00 am – Inst: Florin
2
6.
g
=
F
m
+
ρ
m
g V
7.
y
=
A
cos(
kx

ωt
)
8.
F
=
m g
•
1 +
v
r g
‚
correct
Explanation:
Check
y
=
A
cos(
kx

ωt
):
Since
k
is an inverse length,
kx
is dimension
less, and similarly,
ωt
is also dimensionless,
so
kx

ωt
is dimensionless, as an argument
of a trigonometry function must always be.
The value of a trigonometry function (
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