# College Physics, 6 Edition

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1

Wilson,
College Physics, 6
th

Edition

Chapter 9

Exercises

MC

=
Multiple
Choice Question,
CQ

=
Conceptual
Question, and
IE

=
Integrated

Exercise. Throughout the text,
many exercise sections will include “paired” exercises. These exercise pairs, identified wi
th
red numbers
, are
intended to assist you in problem solving and learning. In a pair, the first exercise (even numbered) is worked out in
the Study Guide so that you can consult it should you need assistance in solving it. The second exercise (odd
numbere
d) is similar in nature, and its answer is given at the back of the book.

9.1 Solids and Elastic Moduli

Use as many significant figures as you need to show small changes.

1.

MC

The pressure on an elastic body is described by (a) a modulus, (b) work, (c) st
ress, (d) strain.

(c)

2.

MC

Shear moduli are not zero for (a) solids, (b) liquids, (c) gases, (d) all of these.

(a)

3.

MC

A relative measure of deformation is (a) a modulus, (b) work, (c) stress, (d) strain.

(d)

4.

MC

The volume stress for the bulk modu
lus is (a)
,
p

(b)
,
V

(c)
o
,
V

(d)
o
/.
V V

(a)

5.

CQ

Which has a greater Young’s modulus, a steel wire or a rubber band? Explain.

steel wire

6.

CQ

Why are scissor
s sometimes called shears? Is this a descriptive name in the physical sense?

see ISM

7.

CQ

Ancient stonemasons sometimes split huge blocks of rock by inserting wooden pegs into holes drilled in
the rock and then pouring water on the pegs. Can you explain
the physics that underlies this technique? [
Hint
:
Think about sponges and paper towels.]

see ISM

8.

A tennis racket has nylon strings. If one of the strings with a diameter of 1.0 mm is under a tension of 15 N,
how much is it lengthened from its origina
l length of 40 cm?

0.0015 m

9.

Suppose you use the tip of one finger to support a 1.0
-
kg object. If your finger has a diameter of 2.0 cm,
what is the stress on your finger?

4 2
3.1 10 N/m

10.

A 5.0
-
m
-

0.020

11.

A 250
-

s楤攮 Wh慴a 慲攠 (愩 瑨攠 捯mpr敳e楯n慬a s瑲敳e and (b) 瑨攠 sh敡r s瑲敳s on th攠 b慲?

(愩
4 2
9.4 10 N/m

(b)
5 2
1.2 10 N/m

2

12.

A 4.0
-
kg object is supported by an aluminum wire of length 2.0 m and diameter 2.0 mm. How much will
the wire stretch?

0.36 mm

13.

A copper wire has a length of 5.0 m and a diam
eter of 3.0 mm. Under what load will its length increase by
0.3 mm?

47 N

14.

A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6.0
-
kg object suspended from it.
If the wire stretches 1.4 mm under the tension, what is the value of Yo
ung’s modulus for the
metal?

11 2
1.1 10 N/m

15.

IE

When railroad tracks are installed, gaps are left between the rails. (a) Should a greater gap be used if
the rails are installed on (1) a cold day or (2) a hot day? Or (3) Does it make any

difference? Why? (b) Each
steel rail is 8.0 m long and has a cross
-
sectional area of
2
0.0025 m.

On a hot day, each rail thermally expands
as much as
3
3.0 10 m.

If there were no gaps between the rails, what would be the fo
rce on the ends of each
rail?

(a) (1) a cold day (b)
5
1.9 10 N

16.

A rectangular steel column
(20.0 cm 15.0 cm)

supports a load of 12.0 metric tons. If the column is 2.00
m in length before being stressed, what is the decrea
se in length?

5
3.92 10 m

17.

IE

A bimetallic rod as illustrated in

Fig 9.26 is composed of brass and copper. (a) If the rod is subjected
to a compressive force, will the rod bend toward the brass or the copper? Why? (b) Justify your a
nswer
mathematically if the compressive force is
4
5.00 10 N.

(a) bends toward brass (b) see ISM

18.

IE

Two same
-
size metal posts, one aluminum and one copper, are subjected to equal shear stresses. (a)
Which post will show the larger de
formation angle, (1) the copper post or (2) the aluminum post? Or (3) Is the
angle the same for both? Why? (b) By what factor is the deformation angle of one post greater than the
other?

(a) (2) the aluminium post (b)
Al Cu
1.5
 

19.

85.0
-
kg p敲son s瑡nds on on攠汥g and 90┠of th攠睥楧h琠楳 suppor瑥t by th攠upp敲 汥l 捯nn散瑩ng 瑨e
kn敥 and h楰 jo楮t

the femur. Assuming the femur is 0.650 m long and has a radius of 2.00 cm, by how much
is the bone compressed?

7
4.2 10 m

20.

Two m整慬ep污瑥s 慲攠h敬e 瑯g整e敲 by two s瑥敬triv整猬ee慣h of d楡m整敲 0.20 捭 and l敮gth 1.0 cm. 䡯w
much for捥 mus琠t攠慰p汩敤 p慲慬汥氠瑯 瑨攠p污瑥猠瑯 sh敡r off bo瑨 r楶整s?

5
1.0 10 N

3

21.

IE

(a) Which of the liquids i
n Table 9.1 has the greatest compressibility? Why? (b) For equal volumes of
ethyl alcohol and water, which would require more pressure to be compressed by 0.10%, and how many times
more?

(a) ethyl alcohol (b)
w ea
/2.2
p p
  

22.

A brass cu
be 6.0 cm on each side is placed in a pressure chamber and subjected to a pressure of
7 2
1.2 10 N/m

on all of its surfaces. By how much will each side be compressed under this
pressure?

6
3.2 10 m

23.

A cylindrical erase
r of negligible mass is dragged across a paper at a constant velocity to the right by its
pencil. The coefficient of kinetic friction between eraser and paper is 0.650. The pencil pushes down with 4.20
N. The height of the eraser is 1.10 cm and its diamete
r is 0.760 cm. Its top surface is displaced horizontally
0.910 mm relative to the bottom. Determine the shear modulus of the eraser material.

5 2
7.28 10 N/m

24.

A 45
-
kg traffic light is suspended from two steel cables of equal length and
radii 0.50 cm. If each cable
makes a 15° angle with the horizontal, what is the fractional increase in their length due to the weight of the
light?

5
5.4 10

9.2 Fluids: Pressure and Pascal’s Principle

25.

MC

For a liquid in an open cont
ainer, the total pressure at any depth depends on (a) atmospheric pressure, (b)
liquid density, (c) acceleration due to gravity, (d) all of the preceding.

(d)

26.

MC

For the pressure

depth relationship for a fluid
( ),
p gh

it is assumed

that (a) the pressure decreases
with depth, (b) a pressure difference depends on the reference point, (c) the fluid density is constant, (d) the
relationship applies only to liquids.

(c)

27.

MC

When measuring automobile tire pressure, what type of pressu
re is this: (a) gauge, (b) absolute, (c)
relative, or (d) all of the preceding?

(a)

28.

CQ

Figure 9.27 shows a famous “bed of nails” trick. The woman lies on a bed of nails with a cinder block
on her chest. A person hits the anvil with a sledgehammer. Th
e nails do not pierce the woman’s skin. Explain
why.

see ISM

29.

CQ

Automobile tires are inflated to about
2
30 lb/in.,

whereas thin bicycle tires are inflated to 90 to
2
115 lb/in.

at least three times as much pressure! Why?

see ISM

4

30.

CQ

(a) Why is blood pressure usually measured at the arm? (b) Suppose the pressure reading were taken on
the calf of the leg of a standing person. Would there be a difference, in principle? Explain.

see ISM

31.

CQ

(a) Two dams form artifici
al lakes of equal depth. However, one lake backs up 15 km behind the dam, and
the other backs up 50 km behind. What effect does the difference in length have on the pressures on the dams?
(b) Dams are usually thicker at the bottom. Why?

see ISM

32.

CQ

Wat
er towers (storage tanks) are generally bulb shaped as shown in

Fig. 9.28. Wouldn’t it be better to
have a cylindrical storage tank of the same height? Explain.

see ISM

33.

CQ

(a) Liquid storage cans, such as gasoline cans, generally have capped vents. W
hat is the purpose of the
vents, and what happens if you forget to remove the cap before you pour the liquid? (b) Explain how a
medicine dropper works. (c) Explain how we breathe (inhalation and exhalation).

see ISM

34.

CQ

A water dispenser for pets has a
n inverted plastic bottle, as shown in

Fig. 9.29. (The water is dyed blue
for contrast.) When a certain amount of water is drunk from the bowl, more water flows automatically from
the bottle into the bowl. The bowl never overflows. Explain the operation o
f the dispenser. Does the height of
the water in the bottle depend on the surface area of the water in the bowl?

see ISM

35.

IE

In his original barometer, Pascal used water instead of mercury. (a) Water is less dense than mercury, so
the water barometer

would have (1) a higher height than, (2) a lower height than, or (3) the same height as the
mercury barometer. Why? (b) How high would the water column have been?

(a) (1) a higher height than (b)
10 m

36.

If you dive to 10 m below the surface of a lake
, (a) what is the pressure due to the water alone? (b) What is
the total or absolute pressure at that depth?

(a)
4
9.8 10 Pa

(b)
5
2.0 10 Pa

37.

IE

In an open U
-
tube, the pressure of a water column on one side is balanced

by the pressure of a column of
gasoline on the other side. (a) Compared to the height of the water column, the gasoline column will have (1) a
higher, (2) a lower, or (3) the same height. Why? (b) If the height of the water column is 15 cm, what is the
he
ight of the gasoline column?

(a) (1) a higher (b) 22 cm

38.

A 75
-
kg athlete does a single
-
hand handstand. If the area of the hand in contact with the floor is
2
125 cm,

what pressure is exerted on the floor?

4
5.9 10 Pa

5

39.

The gauge pressure in both tires of a bicycle is 690 kPa. If the bicycle and the rider have a combined mass
of 90.0 kg, what is the area of contact of
each

tire with the ground? (Assume that each tire supports half the
total weight of the bicycle.
)

4 2
6.39 10 m

40.

In a sample of seawater taken from an oil spill, an oil layer 4.0 cm thick floats on 55 cm of water. If the
density of the oil is
3 3
0.75 10 kg/m,

what is the absolute pressure on the bottom of the
container
?

5
1.07 10 Pa

41.

IE

In a lecture demonstration, an empty can is used to demonstrate the force exerted by air pressure
(

Fig. 9.30). A small quantity of water is poured into the can, and the water is brought to a boil. Then the can
is s
ealed with a rubber stopper. As you watch, the can is slowly crushed with sounds of metal bending. (Why
is a rubber stopper used as a safety precaution?) (a) This is because of (1) thermal expansion and contraction,
(2) a higher steam pressure inside the c
an, or (3) a lower pressure inside the can as steam condenses. Why? (b)
Assuming the dimensions of the can are
0.24 m 0.16 m 0.10 m
 

and the inside of the can is in a perfect
vacuum, what is the total force exerted on the can by the air pressure?

(a
) (3) a lower pressure inside the can
as steam condenses (b)
4
1.6 10 N 3600 lb
 

42.

What is the fractional decrease in pressure when a barometer is raised 40.0 m to the top of a building?
(Assume that the density of air is constant over that di
stance.)

0.50%

43.

A student decides to compute the standard barometric reading on top of Mt. Everest
(29 028 ft)

by
assuming that the density of air has the same constant density as at sea level. Try this yourself. What does the
result

tell you?

air density decreases rapidly with altitude; see ISM

44.

To drink a soda (assume same density as water) through a straw requires you to lower the pressure at the
top of the straw. What does the pressure need to be at the top of a straw that
is 15.0 cm above the surface of
the soda in order to get soda to your lips?

4
9.98 10 Pa

45.

During a plane flight, a passenger experiences ear pain due to a head cold that has clogged his Eustachian
tubes. Assuming the pressure in his t
ubes remained at 1.00 atm (from sea level) and the cabin pressure is
maintained at 0.900 atm, determine the air pressure force (including its direction) on one eardrum, assuming it
has a diameter of 0.800 cm.

0.51 N

6

46.

Here is a demonstration Pascal
used to show the importance of a fluid’s pressure on the fluid’s depth
(

Fig. 9.31): An oak barrel with a lid of area
2
0.20 m

is filled with water. A long, thin tube of cross
-
sectional
area
5 2
5.0 10 m

is inserted into a

hole at the center of the lid, and water is poured into the tube. When the
water reaches 12 m high, the barrel bursts. (a) What was the weight of the water in the tube? (b) What was the
pressure of the water on the lid of the barrel? (c) What was the net
force on the lid due to the water
pressure?

(a) 5.9 N (b)
5
1.2 10 Pa

(c)
4
2.4 10 N

47.

The door and the seals on an aircraft are subject to a tremendous amount of force during flight. At an
altitude of
10 000 m

33 000 ft
), the air pressure outside the airplane is only
4 2
2.7 10 Nm,

while the
inside is still at normal atmospheric pressure, due to pressurization of the cabin. Calculate the net force due to
the air

pressure on a door of area
2
3.0 m.

5
2.2 10 N

50 000 lb
)

48.

The pressure exerted by a person’s lungs can be measured by having the person blow as hard as possible
into one side of a manome
ter. If a person blowing into one side of an open
-
tube manometer produces an 80
-
cm difference between the heights of the columns of water in the manometer arms, what is the gauge pressure
of the lungs?

3
7.8 10 Pa

49.

-
on auto
collision, the driver had his air bags disconnected and his head hits the windshield,
fracturing his skull. Assuming the driver’s head has a mass of 4.0 kg, the area of the head to hit the windshield
to be
2
25 cm,

and an impact time of
3.0 ms, with what speed does the head hit the windshield? (Take the
compressive fracture strength of the cranial bone to be
8
1.0 10 Pa.

)

2
1.9 10 m/s

50.

A cylinder has a diameter of 15 cm (

Fig. 9.32). The water level in

the cylinder is maintained at a
constant height of 0.45 m. If the diameter of the spout pipe is 0.50 cm, how high is
h
, the vertical stream of
water? (Assume the water to be an ideal fluid.)

0.45 m

51.

In 1960, the U.S. Navy’s bathyscaphe
Trieste

(a s
ubmersible) descended to a depth of
10 912 m

35 000 ft
) into the Mariana Trench in the Pacific Ocean. (a) What was the pressure at that depth? (Assume
that seawater is incompressible.) (b) What was the force on a

circular observation window with a diameter of
15 cm?

(a)
8
1.1 10 Pa

(b)
6
1.9 10 N

7

52.

The output piston of a hydraulic press has a cross
-
sectional area of
2
0.25 m.

(a) How much pressure on
the in
put piston is required for the press to generate a force of
6
1.5 10 N?

(b) What force is applied to the
input piston if it has a diameter of 5.0 cm?

(a)
6
6.0 10 Pa

(b)
4
1.2 10 N

53.

A hydraulic lift i
n a garage has two pistons: a small one of cross
-
sectional area
2
4.00 cm

and a large one
of cross
-
sectional area
2
250 cm.

(a) If this lift is designed to raise a 3500
-
kg car, what minimum force must
be applied to the s
mall piston? (b) If the force is applied through compressed air, what must be the minimum
air pressure applied to the small piston?

(a) 549 N (b)
6
1.37 10 Pa

54.

A hypodermic syringe has a plunger of area
2
2.5 cm

an
d a
3 2
5.0 10 -cm

needle. (a) If a 1.0
-
N force is
applied to the plunger, what is the gauge pressure in the syringe’s chamber? (b) If a small obstruction is at the
end of the needle, what force does the fluid exert on it? (c) If the blood pre
ssure in a vein is 50 mm Hg, what
force must be applied on the plunger so that fluid can be injected into the vein?

(a)
3 2
4.0 10 N/m

(b)
3
2.0 10 N

(c) 1.7 N

55.

A funnel has a cork blocking its drain tube. The cork has

a diameter of 1.50 cm and is held in place by
static friction with the sides of the drain tube. When water is filled to 10.0 cm above the cork, it comes flying
out. Determine the maximum force of static friction between the cork and drain tube. Neglect th
e weight of the
cork.

0.173 N

56.

A hydraulic balance used to detect small changes in mass is shown in

Fig. 9.33. If a mass
m

of 0.25 g
is placed on the balance platform, by how much will the height of the water in the smaller, 1.0
-
cm
-
diameter
cylind
er have changed when the balance comes to equilibrium?

2.6 mm

9.3 Buoyancy and Archimedes’ Principle

57.

MC

A wood block floats in a swimming pool. The buoyant force exerted on the block by water depends on (a)
the volume of water in the pool, (b) the vol
ume of the wood block, (c) the volume of the wood block under
water, (d) all of the preceding.

(c)

58.

MC

If a submerged object displaces an amount of liquid of greater weight than its own and is then released,
the object will (a) rise to the surface and
float, (b) sink, (c) remain in equilibrium at its submerged
position.

(a)

8

59.

MC

Comparing an object’s density
o
( )

to that of a fluid
f
( ),

what is the condition for the object to float:
(a)
o f
,
 

or (b)
f o
?
 

(a)

60.

CQ

(a) What is the most important factor in constructing a life jacket that will keep a person afloat? (b) Why
is it so easy to float in Utah’s Great Salt Lake?

see ISM

61.

CQ

An ice cube floats in a
glass of water. As the ice melts, how does the level of the water in the glass
change? Would it make any difference if the ice cube were hollow? Explain.

see ISM

62.

CQ

Oceangoing ships in port are loaded to the so
-
called
Plimsoll mark
, which is a line in
dicating the
maximum safe loading depth. However, in New Orleans, located at the mouth of the Mississippi River, where
the water is brackish (partly salty and partly fresh), ships are loaded until the Plimsoll mark is somewhat
below the water line. Why?

p
ort water (partly fresh) is less dense than seawater

63.

CQ

Two blocks of equal volume, one iron and one aluminum, are dropped into a body of water. Which block
will experience the greater buoyant force? Why?

same

64.

CQ

An inventor comes up with an idea
for a perpetual motion machine, as illustrated in

Fig. 9.34. It
contains a sealed chamber with mercury (Hg) in one half and water
2
(H O)

in the other. A cylinder is mounted
in the center and is free to rotate. He reasons that since me
rcury is much denser than water (
3
13.6 g/cm

to
3
1.00 g/cm
), the weight of the mercury displaced by half the cylinder is much greater than the water displaced
by the other half. Then, the buoyant force on the mercury side i
s greater than that on the water side

more
than thirteen times greater. The difference in forces and torques should cause the cylinder to rotate

perpetually. Would you invest any money in this invention? Why or why not?

see ISM

65.

IE

(a) If the density

of an object is exactly equal to the density of a fluid, the object will (1) float, (2) sink,
(3) stay at any height in the fluid, as long as it is totally immersed. (b) A cube 8.5 cm on each side has a mass
of 0.65 kg. Will the cube float or sink in wate

(a) (3) stay at any height (b) sink; see
ISM

66.

Suppose that Archimedes found that the king’s crown had a mass of 0.750 kg and a volume of
5 3
3.980 10 m.

(a) What simple approach did Archimedes use to determine the cr
own’s volume? (b) Was the
crown pure gold?

(a) water displacement (b) no; see ISM

9

67.

A rectangular boat, as illustrated in

Fig. 9.35, is overloaded such that the water level is just 1.0 cm below
the top of the boat. What is the combined mass of the p
eople and the boat?

3
2.6 10 kg

68.

An object has a weight of 8.0 N in air. However, it apparently weighs only 4.0 N when it is completely
submerged in water. What is the density of the object?

3 3
2.0 10 kg/m

69.

When a

0.80
-
kg crown is submerged in water, its apparent weight is measured to be 7.3 N. Is the crown
pure gold?

no; see ISM

70.

A steel cube 0.30 m on each side is suspended from a scale and immersed in water. What will the scale

3
1.8 10 N

71.

A wood cube 0.30 m on each side has a density of
3
700 kg/m

and floats levelly in water. (a) What is the
distance from the top of the wood to the water surface? (b) What mass has to be placed on top of the wood so
that its t
op is just at the water level?

(a) 0.09 m (b) 8.1 kg

72.

(a) Given a piece of metal with a light string attached, a scale, and a container of water in which the piece
of metal can be submersed, how could you find the volume of the piece without using t
he variation in the
water level? (b) An object has a weight of 0.882 N. It is suspended from a scale, which reads 0.735 N when
the piece is submerged in water. What are the volume and density of the piece of metal?

(a) see ISM (b)
5 3 3 3
1.50 10 m, 6.00 10 kg/m

 

73.

An aquarium is filled with a liquid. A cork cube, 10.0 cm on a side, is pushed and held at rest completely
submerged in the liquid. It takes a force of 7.84 N to hold it under the liquid. If the density of cork is
3
200 kg/m,

fin
d the density of the liquid.

3 3
1.00 10 kg/m

(probably
2
H O
)

74.

A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.0 m on
each side is made into sheets. To make these
sheets into a hollow cube that will not sink, what should be the
minimum length of the sides of the sheets?

2.0 m

75.

Plans are being made to bring back the zeppelin, a lighter
-
than
-
air airship like the Goodyear blimp that
carries passengers and cargo,

but is filled with helium, not flammable hydrogen as was used in the ill
-
fated
Hindenburg
. (See opening Physics Facts.) One design calls for the ship to be 110 m long and to have a total
mass (without helium) of 30.0 metric tons. Assuming the ship’s “enve
lope” to be cylindrical, what would its
diameter have to be so as to lift the total weight of the ship and the helium?

17.7 m

10

76.

A girl floats in a lake with 97% of her body beneath the water. What are (a) her mass density and (b) her
weight density?

(a)
2 3
9.7 10 kg/m

(b)
3 3
9.5 10 N/m

77.

A spherical navigation buoy is tethered to the lake floor by a vertical cable (

Fig. 9.36). The outside
diameter of the buoy is 1.00 m. The interior of the buoy consists of an alumin
um shell 1.0 cm thick and the
rest is solid plastic. The density of aluminum is
3
2700 kg/m

and the density of the plastic is
3
200 kg/m.

The
buoy is set to float exactly halfway out of the water. Determine the tension in th
e cable.

2
8.1 10 N

78.

Figure 9.37 shows a simple laboratory experiment. Calculate (a) the volume and (b) the density of the
suspended sphere. (Assume that the density of the sphere is uniform and that the liquid in the beaker is wa
ter.)
(c) Would you be able to make the same determinations if the liquid in the beaker were mercury? (See Table
9.2.) Explain.

(a)
4 3
9.8 10 m

(b)
3 3
1.5 10 kg/m

(c) see ISM

9.4 Fluid Dynamics and Bernoulli’s Equation

79.

MC

If the speed at some point in a fluid changes with time, the fluid flow is
not

incompressible, (d) nonviscous.

(a)

80.

MC

An ideal fluid is not (a) steady, (b) compressible, (c) irrotational, or (d) nonviscous.
(b)

81.

MC

Bernoulli’s equation is based primarily on (a) Newton’s laws, (b) conservation of momentum, (c) a
nonideal fluid, (d) conservation of energy.

(d)

82.

MC

According to Bernoulli’s equation, if the pressure on the liquid in Fig. 9.19 is increased, (a) the f
low
speed always increases, (b) the height of the liquid always increases, (c) both the flow speed and the height of
the liquid may increase, (d) none of the preceding.

(c)

83.

CQ

The speed of blood flow is greater in arteries than in capillaries. However
, the flow rate equation
( constant)
Av

seems to predict that the speed should be greater in the smaller capillaries. Can you resolve
this apparent inconsistency?

there are many capillaries

84.

CQ

(a) Explain why water shoots out farther from

a hose if you put your finger over the tip of the hose. (b)
Give a human analogy of constricted flow and greater speed.

(a) smaller area, greater speed (b) arteries to
capillaries

11

85.

CQ

(a) If an Indy racer had a flat bottom, it would be highly unstabl
e (like an airplane wing) due to the lift it
gets when it moves at a high speed. To increase friction and stability, the bottom has a concave section called
the
Venturi tunnel

(

Fig. 9.38). (a) In terms of Bernoulli’s equation, explain how this concavity s
upplies
extra downward force to the car in addition to that supplied by the front and rear wings. (b) What is the
purpose of the “spoiler” on the back of the racer?

see ISM

86.

CQ

Here are two common demonstrations of Bernoulli effects: (a) If you hold a
narrow strip of paper in front
of your mouth and blow over the top surface, the strip will rise (

Fig. 9.39a). (Try it.) Why? (b) A plastic egg
is supported vertically by a stream of air from a tube (Fig. 9.39b). The egg will not move away from the
midstre
am position. Why not?

see ISM

87.

An ideal fluid is moving at
3.0 m/s

in a section of a pipe of radius 0.20 m. If the radius in another section
is 0.35 m, what is the flow speed there?

0.98 m/s

88.

IE

(a) If the

radius of a pipe narrows to half of its original size, will the flow speed in the narrow section (1)
increase by a factor of 2, (2) increase by a factor of 4, (3) decrease by a factor of 2, or (4) decrease by a factor
of 4? Why? (b) If the radius widens t
o three times its original size, what is the ratio of the flow speed in the
wider section to that in the narrow section?

(a) (2) increase by a factor of 4 (b) decrease by a factor of 9

89.

The speed of blood in a major artery of diameter 1.0 cm is
4.5 cm/s.

(a) What is the flow rate in the
artery? (b) If the capillary system has a total cross
-
sectional area of
2
2500 cm,

the average speed of blood
through the capillaries is what percentage of that through the major art
ery? (c) Why must blood flow at low
speed through the capillaries?

(a)
3
3.5 cm/s

(b) 0.031% (c) see ISM

90.

The blood flow speed through an aorta with a radius of 1.00 cm is
0.265 m/s.

If hardening of the arteries
cau
ses the aorta to be constricted to a radius of 0.800 cm, by how much would the blood flow speed
increase?

0.149 m/s

91.

Using the data and result of Exercise 90, calculate the pressure difference between the two areas of the
aorta. (B
lood density:
3 3
1.06 10 kg/m.

 
)

53.6 Pa

12

92.

In a dramatic lecture demonstration, a physics professor blows hard across the top of a copper penny that
is at rest on a level desk. By doing this at the right speed, he can get the penny to acce
lerate vertically, into the
airstream, and then deflect it into a tray, as shown in

Fig. 9.40. Assuming the diameter of a penny is 1.80
cm and it has a mass of 3.50 g, what is the minimum airspeed needed to lift the penny off the tabletop?
Assume the air
under the penny remains at rest.

14.5 m/s

93.

A room measures 3.5 m by 4.5 m by 6.0 m. If the heating and air
-
conditioning ducts to and from the room
are circular with diameter 0.30 m and all the air in the room is to be exchanged ev
ery 12 min, (a) what is the
average flow rate? (b) What is the necessary flow speed in the duct? (Assume that the density of the air is
constant.)

(a)
3
0.13 m/s

(b)
1.8 m/s

94.

The spout heights in the container in

Fig. 9.41 are 10 cm, 20 cm, 30 cm, and 40 cm. The water level is
maintained at a 45
-
cm height by an outside supply. (a) What is the speed of the water out of each hole? (b)
Which water stream has the greatest range relative to the base of the container?

(a)
0.99 m/s;

1.7 m/s;

2.2 m/s;

2.6 m/s

(b) 0.45 m, from
20 cm
y

95.

Water flows at a rate of
25 L/min

through a ho
rizontal 7.0
-
cm
-
diameter pipe under a pressure of 6.0
Pa. At one point, calcium deposits reduce the cross
-
sectional area of the pipe to
2
30 cm.

What is the pressure
at this point? (Consider the water to be an ideal fluid.)

2.2 Pa

96.

As a fire
-
fighting method, a homeowner in the deep woods rigs up a water pump to bring water from a
lake that is 10.0 m below the level of the house. If the pump is capable of producing a gauge pressure of 140
kPa, at what rate (in
L/s
) can water be pumped to the house assuming the hose has a radius of 5.00
cm?

71.9 L/s

97.

A Venturi meter can be used to measure the flow speed of a liquid. A simple such device is shown in

Fig. 9.42. Show that the flow spee
d of an ideal fluid is given by

1
2 2
1 2
2
.
( ) 1
g h
v
A A

see ISM

*9.5 Surface Tension, Viscosity, and Poiseuille’s Law

98.

MC

Water droplets and soap bubbles tend to assume the shape of a sphere. This effect is due to (a) viscosity,
(b) surface tension
, (c) laminar flow, (d) none of the preceding.

(b)

13

14

99.

MC

Some insects can walk on water because (a) the density of water is greater than that of the insect, (b)
water is viscous, (c) water has surface tension, (d) none of the preceding.

(c)

100.

MC

The

viscosity of a fluid is due to (a) forces causing friction between the molecules, (b) surface tension, (c)
density, or (d) none of the above.

(a)

101.

CQ

A motor oil is labeled 10W
-
40. What do the numbers 10 and 40 measure? How about the W?

viscosity;
w
inter

102.

CQ

Why are clothes washed in hot water and a detergent added?

to reduce surface tension

103.

The pulmonary artery, which connects the heart to the lungs, is about 8.0 cm long and has an inside
diameter of 5.0 mm. If the flow rate in it is to

be
25 mL/s,

what is the required pressure difference over its
length?

2
3.5 10 Pa

104.

A hospital patient receives a quick 500
-
cc blood transfusion through a needle with a length of 5.0 cm and
an inner diameter of 1.
0 mm. If the blood bag is suspended 0.85 m above the needle, how long does the
transfusion take? (Neglect the viscosity of the blood flowing in the plastic tube between the bag and the
needle.)

2
2.0 10 s

105.

A nurse needs to draw 20.
0 cc of blood from a patient and deposit it into a small plastic container whose
interior is at atmospheric pressure. He inserts the needle end of a long tube into a vein where the average
gauge pressure is 30.0 mm Hg. This allows the internal pressure in
the vein to push the blood into the
collection container. The needle is 0.900 mm in diameter and 2.54 cm long. The long tube is wide and smooth
enough that we can assume its resistance is negligible, and that all the resistance to blood flow occurs in the
narrow needle. How long does it take him to collect the sample?

13.5 s

Comprehensive Exercises

106.

Show that specific gravity is equivalent to a ratio of densities, given that its strict definition is the ratio of the
weight of a given volume of a substa
nce to the weight of an equal volume of water.

see ISM

107.

A rock is suspended from a string in air. The tension in the string is 2.94 N. When the rock is then dunked into
a liquid, and the rope let go slack, it sinks and comes to rest on a spring whose
spring constant is
200 N/m.

The spring’s final compression is 1.00 cm. If the density of the rock is known to be
3
2500 kg/m,

what is the
density of the liquid?

2 3
8.0 10 kg/m

15

108.

An unevenly weighted baton
(cylindrical in shape) consists of two sections: a denser (lower) section and a less
dense (upper) section. When placed in water, it is upright and barely floats. The baton has a diameter of 2.00
cm; its lower part is made of steel with a density of
3
7800 kg/m,

and the upper part is made of wood with a
density of
3
810 kg/m.

The steel part has a length of 5.00 cm. Find the length of the wooden section.

1.79 m

109.

A crude shower is rigged up by a team of campers. It consists

of a large (top open) cylindrical container hung
from a tree. Its bottom area is punctured by a lot of small holes, each 1.00 mm in diameter, and the container is
30.0 cm in diameter and 75.0 cm high. (a) Initially, what is the speed the water comes out o
f the holes? (b)
How many holes are needed if you want a
1.20 L/s

total flow rate?

(a)
3.83 m/s

(b) 399

110.

What is the difference in volume (due only to pressure changes, not temperature or other factors) between
10
00 kg of water at the surface (assume 4°C) of the ocean and the same mass at the deepest known depth, 8.00
km? (Mariana trench; assume also 4°C.)

3
0.0356 m