karna (pk4534) – HW 17 – coker – (58245)
1
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This is the last chapter covered on Quiz 4.
001
10.0 points
The four tires of an automobile are inflated
to an absolute pressure of 2
.
5
×
10
5
Pa. Each
tire has an area of 0
.
022 m
2
in contact with
the ground.
Determine the weight of the automobile.
Correct answer: 22000 N.
Explanation:
Let :
P
= 2
.
5
×
10
5
Pa
and
A
= 0
.
022 m
2
.
F
g
= 4
P A
= 4 (2
.
5
×
10
5
Pa) (0
.
022 m
2
)
=
22000 N
.
002
10.0 points
The air pressure above the liquid in figure is
1
.
52 atm
.
The depth of the air bubble in the
liquid is 45
.
3 cm and the liquid’s density is
795 kg
/
m
3
.
45
.
3 cm
air
air
Determine the air pressure in the bubble
suspended in the liquid. The acceleration of
gravity is 9
.
8 m
/
s
2
.
Correct answer: 1
.
57505
×
10
5
Pa.
Explanation:
Let :
ρ
= 795 kg
/
m
3
,
P
0
= 1
.
52 atm
,
g
= 9
.
8 m
/
s
2
,
and
h
= 45
.
3 cm = 0
.
453 m
.
P
=
P
0
+
ρ g h
= (1
.
52 atm)
·
1
.
013
×
10
5
Pa
atm
+ (795 kg
/
m
3
) (9
.
8 m
/
s
2
) (0
.
453 m)
=
1
.
57505
×
10
5
Pa
.
003
10.0 points
A simple Utube that is open at both ends is
partially filled with a heavy liquid of density
1000 kg
/
m
3
.
A liquid of density 286 kg
/
m
3
is
then poured into one arm of the tube, forming
a column 13 cm in height, as shown.
h
13 cm
light liquid
286 kg
/
m
3
heavy liquid
1000 kg
/
m
3
What is the difference in the heights of the
two liquid surfaces?
Correct answer: 9
.
282 cm.
Explanation:
Let :
ℓ
= 13 cm
,
ρ
ℓ
= 286 kg
/
m
3
,
and
ρ
h
= 1000 kg
/
m
3
.
Because the liquid in the Utube is static,
the pressure exerted by the heavy liquid col
umn of height
ℓ

h
in the left branch of the
tube must balance the pressure exerted by
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karna (pk4534) – HW 17 – coker – (58245)
2
the liquid of height
h
poured into the right
branch, so
P
0
+ (
ℓ

h
)
ρ
h
g
=
P
0
+
ℓ ρ
ℓ
g .
h
=
ℓ
parenleftbigg
1

ρ
ℓ
ρ
h
parenrightbigg
= (13 cm)
parenleftbigg
1

286 kg
/
m
3
1000 kg
/
m
3
parenrightbigg
=
9
.
282 cm
.
004
10.0 points
The small piston of a hydraulic lift has a
crosssectional area of 8
.
1 cm
2
and the large
piston has an area of 63 cm
2
, as in the figure
below.
F
8
.
1 cm
2
area
63 cm
2
What force
F
must be applied to the small
piston to maintain the load of 89 kN at a
constant elevation?
Correct answer: 11442
.
9 N.
Explanation:
Let :
A
1
= 8
.
1 cm
2
,
A
2
= 63 cm
2
,
and
W
= 89 kN
.
According to Pascal’s law, the pressure ex
erted on
A
1
must be equal to the one exerted
on
A
2
.
The pressure
P
1
=
F
A
1
must be equal
to the pressure
P
2
=
W
A
2
due to the load.
F
A
1
=
W
A
2
,
so
F
=
A
1
A
2
W
=
(8
.
1 cm
2
)
(63 cm
2
)
(89000 N)
=
11442
.
9 N
.
005
10.0 points
Compared to an empty ship, would a ship
loaded with a cargo of Styrofoam sink deeper
or rise in the water?
1.
The ship will float at the same level be
cause its density hasn’t changed.
2.
Since Styrofoam is less dense than water,
the ship rises.
3.
Since Styrofoam pushes down on the ship
with its weight, the ship sinks deeper.
cor
rect
4.
It depends on the weight of the Styro
foam.
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 Spring '08
 Turner
 Physics, Correct Answer, Karna

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