Chapter 14 – Student Solutions Manual
1. The pressure increase is the applied force divided by the area:
Δ
p
=
F
/
A
=
F
/
π
r
2
, where
r
is the radius of the piston. Thus
Δ
p
= (42 N)/
π
(0.011 m)
2
= 1.1
×
10
5
Pa.
This is equivalent to 1.1 atm.
3. The air inside pushes outward with a force given by
p
i
A
, where
p
i
is the pressure inside
the room and
A
is the area of the window. Similarly, the air on the outside pushes inward
with a force given by
p
o
A
, where
p
o
is the pressure outside. The magnitude of the net
force is
F
= (
p
i
–
p
o
)
A
. Since 1 atm = 1.013
×
10
5
Pa,
54
(1.0 atm
0.96 atm)(1.013 10 Pa/atm)(3.4 m)(2.1 m) = 2.9
10 N.
F
=−
×
×
19. When the levels are the same the height of the liquid is
h
= (
h
1
+
h
2
)/2, where
h
1
and
h
2
are the original heights. Suppose
h
1
is greater than
h
2
. The final situation can then be
achieved by taking liquid with volume
A
(
h
1
–
h
) and mass
ρ
A
(
h
1
–
h
), in the first vessel,
and lowering it a distance
h
–
h
2
. The work done by the force of gravity is
W
=
A
(
h
1
–
h
)
g
(
h
–
h
2
).
We substitute
h
= (
h
1
+
h
2
)/2 to obtain
()
2
33
2
4
2
12
11
(1.30 10 kg/m )(9.80 m/s )(4.00 10 m )(1.56 m
0.854 m)
44
0.635 J
Wg
A
h
h
−
=
×
×
−
=
2
.
27. (a) We use the expression for the variation of pressure with height in an
incompressible fluid:
p
2
=
p
1
–
g
(
y
2
–
y
1
). We take
y
1
to be at the surface of Earth, where
the pressure is
p
1
= 1.01
×
10
5
Pa, and
y
2
to be at the top of the atmosphere, where the
pressure is
p
2
= 0. For this calculation, we take the density to be uniformly 1.3 kg/m
3
.
Then,
5
3
1
21
32
1.01
10 Pa
7.9
10 m = 7.9 km.
(1.3 kg/m )(9.8m/s )
p
yy
g
×
−=
=
=×
(b) Let
h
be the height of the atmosphere. Now, since the density varies with altitude, we
integrate
0
.
h
p
pg
∫
d
y
Assuming
=
0
(1 
y
/
h
), where
0
is the density at Earth’s surface and
g
= 9.8 m/s
2
for
0
≤
y
≤
h
, the integral becomes
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document21
0
1
0
0
1
1.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 drty
 mechanics, Buoyancy, Force, H1

Click to edit the document details