tang (nmt352) – oldhomework 02 – Turner – (56705)
1
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printout
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have
10
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001
10.0 points
You have 1
.
8 kg of water. One mole of water
has a mass of 18
.
1 g
/
mol and each molecule
of water contains 10 electrons since water is
H
2
O.
What is the total electron charge contained
in this volume of water?
Correct answer:
−
9
.
58218
×
10
7
C.
Explanation:
Let :
N
A
= 6
.
02214
×
10
23
molec
/
mol
,
q
e
=
−
1
.
6
×
10
−
19
C
/
electron
,
m
= 1
.
8 kg
,
M
= 18
.
1 g
/
mol = 0
.
0181 kg
/
mol
,
and
Z
= 10 electrons
/
molec
.
The mass is proportional to the number of
molecules, so for
m
grams in
n
molecules and
M
grams in
N
A
molecules,
m
M
=
n
N
A
n
=
m
M
N
A
Since 10 electrons are in each molecule of
water, then the total number of electrons
n
e
in the coin is
n
e
=
Z n
=
Z
m
M
N
A
and the
total charge
q
for the
n
e
electrons is
q
=
n
e
q
e
=
Z
m N
A
q
e
M
= (10 electrons
/
molec)
1
.
8 kg
0
.
0181 kg
/
mol
×
(
6
.
02214
×
10
23
molec
/
mol
)
×
(
−
1
.
6
×
10
−
19
C
/
electron
)
=
−
9
.
58218
×
10
7
C
.
002
10.0 points
Two identical small charged spheres hang in
equilibrium with equal masses as shown in
the figure. The length of the strings are equal
and the angle (shown in the figure) with the
vertical is identical.
0
.
25 m
3
◦
0
.
04 kg
0
.
04 kg
Find
the
magnitude
of
the
charge
on
each sphere.
The acceleration of gravity is
9
.
8 m
/
s
2
and the value of Coulomb’s constant
is 8
.
98755
×
10
9
N m
2
/
C
2
.
Correct answer: 3
.
95631
×
10
−
8
C.
Explanation:
Let :
L
= 0
.
25 m
,
m
= 0
.
04 kg
,
and
θ
= 3
◦
.
L
a
θ
m
m
q
q
From the right triangle in the figure above,
we see that
sin
θ
=
a
L
.
Therefore
a
=
L
sin
θ
= (0
.
25 m) sin(3
◦
)
= 0
.
013084 m
.
The separation of the spheres is
r
= 2
a
=
0
.
026168 m
.
The forces acting on one of the
spheres are shown in the figure below.
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tang (nmt352) – oldhomework 02 – Turner – (56705)
2
θ
θ
m
g
F
T
e
T
sin
θ
T
cos
θ
Because the sphere is in equilibrium, the
resultant of the forces in the horizontal and
vertical directions must separately add up to
zero:
summationdisplay
F
x
=
T
sin
θ
−
F
e
= 0
summationdisplay
F
y
=
T
cos
θ
−
m g
= 0
.
F
sin
θ
F
cos
θ
=
F
e
m g
F
e
=
m g
tan
θ
= (0
.
04 kg)
(
9
.
8 m
/
s
2
)
tan(3
◦
)
= 0
.
0205439 N
,
for the electric force.
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 Spring '10
 Lam
 Mass, Work, Correct Answer, Electric charge

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