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muir (cem2577) – HW1 – Niu – (58205)
1
This printout should have 26 questions.
Multiplechoice questions may continue on
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beFore answering.
001
(part 1 oF 2) 10.0 points
The rectangular and polar coordinates oF a
point are (
x, y
) and (
r, θ
), where
x
= 6 and
θ
= 16
◦
.
Determine the value oF r.
Correct answer: 6
.
2418.
Explanation:
The relation between rectangular and polar
coordinates is:
x
=
r
cos
θ
y
=
r
sin
θ
solving For r,
r
=
x
cos
θ
=
6
cos(16
◦
)
= 6
.
2418
002
(part 2 oF 2) 10.0 points
Determine the value oF y.
Correct answer: 1
.
72047.
Explanation:
y
=
r
sin
θ
= (6
.
2418) sin(16
◦
) = 1
.
72047
003
10.0 points
A human hair is approximately 54
μ
m in di
ameter.
Express this diameter in meters.
Correct answer: 5
.
4
×
10
−
5
m.
Explanation:
Basic Concept:
1
μ
m = 1
×
10
−
6
m
Let:
diameter = 54
μ
m
Solution:
diameter = 54
μ
m
=
(
5
.
4
×
10
1
μ
m
)
·
1
×
10
−
6
m
1
μ
m
= 5
.
4
×
10
−
5
m
keywords:
/* IF you use any oF these, fx the comment
symbols.
004
10.0 points
The modern standard oF length is 1 m
and the speed oF light is approximately
2
.
99792
×
10
8
m
/
s
.
±ind the time Δ
t
For light to cover 1 m at
the given speed.
1.
Δ
t
≈
3
.
3
×
10
−
8
s
2.
Δ
t
≈
3
.
3
×
10
−
7
s
3.
Δ
t
≈
3
×
10
−
6
s
4.
Δ
t
≈
3
×
10
−
8
s
5.
Δ
t
≈
3
.
3
×
10
−
6
s
6.
Δ
t
≈
3
.
3
×
10
−
9
s
correct
7.
Δ
t
≈
3
×
10
−
10
s
8.
Δ
t
≈
3
×
10
−
7
s
9.
Δ
t
≈
3
×
10
−
9
s
10.
Δ
t
≈
3
.
3
×
10
−
10
s
Explanation:
Since distance is speed times velocity, we
have
speed =
distance
time
.
±rom the relationship oF speed to distance and
time, we get
Δ
t
=
distance
speed
=
d
c
=
1 m
2
.
99792
×
10
8
m
/
s
=
3
.
33564
×
10
−
9
s
.
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2
005
10.0 points
The standard of time is based on
1.
a precision pendulum clock.
2.
the frequency of light emitted by
86
Kr.
3.
the daily rotation of the earth.
4.
the yearly revolution of the earth about
the sun.
5.
None of these
correct
Explanation:
The second is deFned from oscillations of
cesium133 atoms.
006
10.0 points
A gram is
1.
10
6
kg
2.
1 kg
3.
10
3
kg
4.
10
−
6
kg
5.
10
−
3
kg
correct
Explanation:
A kg is the notation for a kilogram, and kilo
refers to 1000, or 10
3
, hence 1 g = 10
−
3
kg.
007
10.0 points
You can obtain a rough estimate of the size
of a molecule by the following simple exper
iment. Let a droplet of oil spread out on a
smooth water surface. The resulting oil slick
will be approximately one molecule thick.
Given an oil droplet of mass of 8
.
67
×
10
−
7
kg and density of 930 kg
/
m
3
that spreads
out into a circle of radius 36
.
7 cm on the
water surface, estimate of magnitude of the
diameter of an oil molecule.
Correct answer: 2
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 Spring '09
 NIU

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