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College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 9

Solids and Fluids - all with Video Answers

Educators


Chapter Questions

01:55

Problem 1

If the elastic limit of steel is $5.0 \times 10^{8} \mathrm{~Pa}$, determine the minimum diameter a steel wire can have if it is to support a $70-\mathrm{kg}$ circus performer without its elastic limit being exceeded.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:36

Problem 2

Comic-book superheroes are sometimes able to punch holes through steel walls. (a) If the ultimate shean strength of steel is taken to be $2.50 \times 10^{8} \mathrm{~Pa}$, what force is required to punch through a steel plate $2.00 \mathrm{~cm}$ thick? Assume the superhero's fist has cross-sectional area of $1.00 \times 10^{2} \mathrm{~cm}^{2}$ and is approximately circular. (b) Qualitatively, what would happen to the superhero on delivery of the punch? What physical law applies?

Prabhu Ramji
Prabhu Ramji
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00:49

Problem 3

A plank $2.00 \mathrm{~cm}$ thick and $15.0 \mathrm{~cm}$ wide is firmly attached to the railing of a ship by clamps so that the rest of the board extends $2.00 \mathrm{~m}$ horizontally over the sea below. $\mathrm{A}$ man of mass $80.0 \mathrm{~kg}$ is forced to stand on the very end. If the end of the board drops by $5.00 \mathrm{~cm}$ because of the man's weight, find the shear modulus of the wood.

Salamat Ali
Salamat Ali
Numerade Educator
01:31

Problem 4

When water freezes, it expands about $9.00 \%$. What would be the pressure increase inside your automobile engine block if the water in it froze? The bulk modulus of ice is $2.00 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
00:42

Problem 5

For safety in climbing, a mountaineer uses a nylon rope that is $50 \mathrm{~m}$ long and $1.0 \mathrm{~cm}$ in diameter. When supporting a $90-\mathrm{kg}$ climber, the rope elongates $1.6 \mathrm{~m}$. Find its Young's modulus.

Salamat Ali
Salamat Ali
Numerade Educator
02:32

Problem 6

A stainless-steel orthodontic wire is applied to a tooth, as in Figure $\mathrm{P} 9.6$. The wire has an unstretched length of $3.1 \mathrm{~cm}$ and a diameter of $0.22 \mathrm{~mm}$. If the wire is stretched $0.10 \mathrm{~mm}$, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Young's modulus for stainless steel is $18 \times 10^{10} \mathrm{~Pa}$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:17

Problem 7

Bone has a Young's modulus of about $18 \times 10^{9} \mathrm{~Pa}$. Under compression, it can withstand a stress of about 160 $\times 10^{6} \mathrm{~Pa}$ before breaking. Assume that a femur (thighbone) is $0.50 \mathrm{~m}$ long, and calculate the amount of compression this bone can withstand before breaking.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
05:23

Problem 8

A high-speed lifting mechanism supports an $800-\mathrm{kg}$ object with a steel cable that is $25.0 \mathrm{~m}$ long and $4.00 \mathrm{~cm}^{2}$ in cross-sectional area. (a) Determine the elongation of the cable. (b) By what additional amount does the cable increase in length if the object is accelerated upwards at a rate of $3.0 \mathrm{~m} / \mathrm{s}^{2} ?$ (c) What is the greatest mass that can be accelerated upwards at $3.0 \mathrm{~m} / \mathrm{s}^{2}$ if the stress in the cable is not to exceed the elastic limit of the cable, which is $2.2 \times 10^{8} \mathrm{~Pa} ?$

Prabhu Ramji
Prabhu Ramji
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01:16

Problem 9

A child slides across a floor in a pair of rubber-soled shoes. The friction force acting on each foot is $20 \mathrm{~N}$, the footprint area of each foot is $14 \mathrm{~cm}^{2}$, and the thickness of the soles is $5.0 \mathrm{~mm}$. Find the horizontal distance traveled by the sheared face of the sole. The shear modulus of the rubber is $3.0 \times 10^{6} \mathrm{~Pa}$.

Prabhu Ramji
Prabhu Ramji
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01:21

Problem 10

The distortion of Earth's crustal plates is an example of shear on a large scale. A particular crustal rock has a shear modulus of $1.5 \times 10^{10} \mathrm{~Pa}$. What shear stress is involved when a $10-\mathrm{km}$ layer of this rock is sheared through a distance of $5.0 \mathrm{~m}$ ?

Prabhu Ramji
Prabhu Ramji
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01:09

Problem 11

Determine the elongation of the rod in Figure $\mathrm{P} 9.11$ if it is under a tension of $5.8 \times 10^{3} \mathrm{~N}$.

Salamat Ali
Salamat Ali
Numerade Educator
02:03

Problem 12

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately $2.4 \mathrm{~cm}^{2}$. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of $80 \mathrm{~km} / \mathrm{h}$ in $5.0 \mathrm{~ms}$. If the arm has an effective mass of $3.0 \mathrm{~kg}$ and bone material can withstand a maximum compressional stress of $16 \times 10^{7} \mathrm{~Pa}$, is the arm likely to withstand the crash?

Averell Hause
Averell Hause
Carnegie Mellon University
01:59

Problem 13

Suppose two worlds, each having mass $M$ and radius $R$, coalesce into a single world. Due to gravitational contraction, the combined world has a radius of only $\frac{3}{4} R$. What is the average density of the combined world as a multiple of $\rho_{0}$, the average density of the original two worlds?

Averell Hause
Averell Hause
Carnegie Mellon University
05:00

Problem 14

The British gold sovereign coin is an alloy of gold and copper having a total mass of $7.988 \mathrm{~g}$, and is 22 -karat gold.
(a) Find the mass of gold in the sovereign in kilograms using the fact that the number of karats $=24 \times$ (mass of gold)/(total mass). (b) Calculate the volumes of gold and copper, respectively, used to manufacture the coin.
(c) Calculate the density of the British sovereign coin.

Averell Hause
Averell Hause
Carnegie Mellon University
04:17

Problem 15

Four acrobats of mass $75.0 \mathrm{~kg}, 68.0 \mathrm{~kg}, 62.0 \mathrm{~kg}$, and $55.0 \mathrm{~kg}$ form a human tower, with each acrobat standing on the shoulders of another acrobat. The $75.0-\mathrm{kg}$ acrobat is at the bottom of the tower. (a) What is the normal force acting on the 75 -kg acrobat? (b) If the area of each of the $75.0-\mathrm{kg}$ acrobat's shoes is $425 \mathrm{~cm}^{2}$, what average pressure (not including atmospheric pressure) does the column of acrobats exert on the floor? (c) Will the pressure be the same if a different acrobat is on the bottom?

Prabhu Ramji
Prabhu Ramji
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01:31

Problem 16

A large man sits on a four-legged chair with his feet off the floor. The combined mass of the man and chair is $95.0 \mathrm{~kg}$. If the chair legs are circular and have a radius of $0.500 \mathrm{~cm}$ at the bottom, what pressure does each leg exert on the floor?

Mayukh Banik
Mayukh Banik
Numerade Educator
02:33

Problem 17

The nucleus of an atom can be modeled as several protons and neutrons closely packed together. Each particle has a mass of $1.67 \times 10^{-27} \mathrm{~kg}$ and radius on the order of $10^{-15} \mathrm{~m}$. (a) Use this model and information to estimate the density of the nucleus of an atom. (b) Compare your result with the density of a material such as iron. What do your result and comparison suggest about the structure of matter?

Prabhu Ramji
Prabhu Ramji
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01:12

Problem 18

The four tires of an automobile are inflated to a gauge pressure of $2.0 \times 10^{5} \mathrm{~Pa}$. Each tire has an area of $0.024 \mathrm{~m}^{2}$ in contact with the ground. Determine the weight of the automobile.

Averell Hause
Averell Hause
Carnegie Mellon University
01:05

Problem 19

If $1.0 \mathrm{~m}^{3}$ of concrete weighs $5.0 \times 10^{4} \mathrm{~N}$, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? The compression strength of concrete (the maximum pressure that can be exerted on the base of the structure) is $1.7 \times 10^{7} \mathrm{~Pa}$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:57

Problem 20

The spring of the pressure gauge shown in Figure $9.8 \mathrm{~b}$ has a force constant of $1250 \mathrm{~N} / \mathrm{m}$, and the piston has a radius of $1.20 \mathrm{~cm}$. As the gauge is lowered into water, what change in depth causes the piston to move in by $0.750 \mathrm{~cm} ?$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:13

Problem 21

Calculate the absolute pressure at the bottom of a freshwater lake at a depth of $27.5 \mathrm{~m}$. Assume the density of the water is $1.00 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and the air above is at a pressure of $101.3$ kPa. (b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of $35.0 \mathrm{~cm} ?$

Salamat Ali
Salamat Ali
Numerade Educator
02:31

Problem 22

When you suddenly stand up after lying down for a while, your body may not compensate quickly enough for the pressure changes and you might feel dizzy for a moment. If the gauge pressure of the blood at your heart is $13.3 \mathrm{kPa}$ and your body doesn't compensate, (a) what would the pressure be at your head, $50.0 \mathrm{~cm}$ above your heart? (b) What would it be at your feet, $1.30 \times 10^{2} \mathrm{~cm}$ below your heart? Hint: The density of blood is $1060 \mathrm{~kg} / \mathrm{m}^{3}$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:20

Problem 23

A collapsible plastic bag (Figure $\mathrm{P} 9.23$ ) contains a gliucose solution. If the average gauge pressure in the vein is $1.33 \times 10^{3} \mathrm{~Pa}$, what must be the minimum height $h$ of the bag in order to infuse glucose into the vein? Assume the specific gravity of the solution is $1.02$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:40

Problem 24

The deepest point in the ocean is in the Mariana Trench, about $11 \mathrm{~km}$ deep. The pressure at the ocean floor is huge, about $1.13 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2} .$ (a) Calculate the change in volume of $1.00 \mathrm{~m}^{3}$ of water carried from the surface to the bottom of the Pacific. (b) The density of water at the surface is $1.03 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$. Find its density at the bottom. (c) Is it a good approximation to think of water as incompressible?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:05

Problem 25

A container is filled to a depth of $20.0 \mathrm{~cm}$ with water. On top of the water floats a $30.0-\mathrm{cm}$ -thick layer of oil with specific gravity $0.700$. What is the absolute pressure at the bottom of the container?

Salamat Ali
Salamat Ali
Numerade Educator
01:07

Problem 26

Blaise Pascal duplicated Torricelli's barometer using a red Bordeaux wine of density $984 \mathrm{~kg} / \mathrm{m}^{3}$ as the working liquid (Fig. P9.26). What was the height $h$ of the wine column for normal atmospheric pressure? Would you expect the vacuum above the column to be as good as for mercury?

Surjit Tewari
Surjit Tewari
Numerade Educator
02:02

Problem 27

.] Figure $\mathrm{P} 9.27$ shows the essential parts of a hydraulic brake system. The area of the piston in the master cylinder is $1.8 \mathrm{~cm}^{2}$ and that of the piston in the brake cylinder is $6.4 \mathrm{~cm}^{2}$. The coefficient of friction between shoe and wheel drum is $0.50$. If the wheel has a radius of $34 \mathrm{~cm}$, determine the frictional torque about the axle when a force of $44 \mathrm{~N}$ is exerted on the brake pedal.

Mayukh Banik
Mayukh Banik
Numerade Educator
02:07

Problem 28

Piston (1) in Figure P9.28 has a diameter of $0.25$ in.; piston (2) has a diameter of $1.5 \mathrm{in}$. In the absence of friction, determine the force $\overrightarrow{\mathbf{F}}$ necessary to support the $500 \mathrm{lb}$ weight.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:56

Problem 29

A rubber ball filled with air has a diameter of $25.0 \mathrm{~cm}$ and a mass of $0.540 \mathrm{~kg}$. What force is required to hold the ball in equilibrium immediately below the surface of water in a swimming pool?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:57

Problem 30

The average human has a density of $945 \mathrm{~kg} / \mathrm{m}^{3}$ after inhaling and $1020 \mathrm{~kg} / \mathrm{m}^{3}$ after exhaling. (a) Without making any swimming movements, what percentage of the human body would be above the surface in the Dead Sea (a lake with a water density of about $1230 \mathrm{~kg} / \mathrm{m}^{3}$ ) in each of these cases? (b) Given that bone and muscle are denser than fat, what physical characteristics differentiate "sinkers" (those who tend to sink in water) from "floaters" (those who readily float)?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
00:46

Problem 31

A small ferryboat is $4.00 \mathrm{~m}$ wide and $6.00 \mathrm{~m}$ long. When a loaded truck pulls onto it, the boat sinks an additional $4.00 \mathrm{~cm}$ into the river. What is the weight of the truck?

Salamat Ali
Salamat Ali
Numerade Educator
05:45

Problem 32

A $62.0$ -kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions $2.00 \mathrm{~m} \times 2.00 \mathrm{~m} \times 0.0900 \mathrm{~m}$. The bottom $0.024 \mathrm{~m}$ of the raft is submerged. (a) Draw a free-body diagram of the system consisting of the survivor and raft. (b) Write Newton's second law for the system in one dimension, using $B$ for buoyancy, $w$ for the weight of the survivor, and $w_{y}$ for the weight of the raft. (Set $a=0 .$ ) (c) Calculate the numeric value for the buoyancy, $B$. (Seawater has density $1025 \mathrm{~kg} / \mathrm{m}^{3}$.) (d) Using the value of $B$ and the weight $w$ of the survivor, calculate the weight $w_{r}$ of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:08

Problem 33

A wooden block of volume $5.24 \times 10^{-4} \mathrm{~m}^{3}$ floats in water, and a small steel object of mass $m$ is placed on top of the block. When $m=0.310 \mathrm{~kg}$, the system is in equilibrium and the top of the wooden block is at the level of the water. (a) What is the density of the wood? (b) What happens to the block when the steel object is replaced by a second steel object with a mass less than $0.310 \mathrm{~kg}$ ? What happens to the block when the steel object is replaced by yet another steel object with a mass greater than $0.310 \mathrm{~kg}$ ?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
07:21

Problem 34

A large balloon of mass $226 \mathrm{~kg}$ is filled with helium gas until its volume is $325 \mathrm{~m}^{3}$. Assume the density of air is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ and the density of helium is $0.179 \mathrm{~kg} / \mathrm{m}^{3}$.
(a) Draw a free-body diagram for the balloon. (b) Calculate the buoyant force acting on the balloon. (c) Find the net force on the balloon and determine whether the balloon will rise or fall after it is released. (d) What maximum additional mass can the balloon support in equilibrium? (e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)? (f) What limits the height to which the balloon can rise?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:34

Problem 35

A spherical weather balloon is filled with hydrogen until its radius is $3.00 \mathrm{~m}$. Its total mass including the instruments it carries is $15.0 \mathrm{~kg} .$ (a) Find the buoyant force acting on the balloon, assuming the density of air is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

Salamat Ali
Salamat Ali
Numerade Educator
03:36

Problem 36

A man of mass $m=70.0 \mathrm{~kg}$ and having a density of $\rho=1050 \mathrm{~kg} / \mathrm{m}^{3}$ (while holding his breath) is completely submerged in water. (a) Write Newton's second law for this situation in terms of the man's mass $m$, the density of water $\rho_{w}$, his volume $V$, and $g$. Neglect any viscous drag of the water. (b) Substitute $m=\rho V$ into Newton's second law and solve for the acceleration $a$, canceling common factors. (c) Calculate the numeric value of the man's acceleration. (d) How long does it take the man to sink $8.00 \mathrm{~m}$ to the bottom of the lake?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:34

Problem 37

On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of $3.35 \mathrm{~km}$ (11 $000 \mathrm{ft})$ powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about $0.50 \mathrm{~m}$ and an estimated mass of $0.30 \mathrm{~kg}$. (a) Estimate the total buoyant force on the 600 balloons. (b) Estimate the net upward force on all 600 balloons. (c) Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
05:37

Problem 38

A $10.0$ -kg block of metal is suspended from a scale and immersed in water, as in Figure P9.38. The dimensions of the block are $12.0 \mathrm{~cm} \times 10.0 \mathrm{~cm} \times$ $10.0 \mathrm{~cm}$. The $12.0-\mathrm{cm}$ dimension is vertical, and the top of the block is $5.00 \mathrm{~cm}$ below the surface of the water. (a) What are the forces exerted by the water on the top and bottom of the block? (Take $P_{0}=1.0130 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$.) (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:27

Problem 39

A bathysphere used for deep sea exploration has a radius of $1.50 \mathrm{~m}$ and a mass of $1.20 \times 10^{4} \mathrm{~kg} .$ In order to dive, the sphere takes on mass in the form of sea water. Determine the mass the bathysphere must take on so that it can descend at a constant speed of $1.20 \mathrm{~m} / \mathrm{s}$ when the resistive force on it is $1100 \mathrm{~N}$ upward. The density of sea water is $1.03 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:35

Problem 40

A light spring of force constant $k=160 \mathrm{~N} / \mathrm{m}$ rests vertically on the bottom of a large beaker of water (Fig. P9.40a). A $5.00-\mathrm{kg}$ block of wood (density $=650 \mathrm{~kg} / \mathrm{m}^{3}$ ) is connected to the spring, and the block-spring system is allowed to come to static equilibrium (Fig. $\mathrm{P} 9.40 \mathrm{~b}$ ). What is the elongation $\Delta L$ of the spring?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:24

Problem 41

A sample of an unknown material appears to weigh $300 \mathrm{~N}$ in air and $200 \mathrm{~N}$ when immersed in alcohol of specific gravity $0.700$. What are (a) the volume and (b) the density of the material?

Salamat Ali
Salamat Ali
Numerade Educator
03:10

Problem 42

An object weighing $300 \mathrm{~N}$ in air is immersed in water after being tied to a string connected to a balance. The scale now reads $265 \mathrm{~N}$. Immersed in oil, the object appears to weigh $275 \mathrm{~N}$. Find (a) the density of the object and (b) the density of the oil.

Averell Hause
Averell Hause
Carnegie Mellon University
02:37

Problem 43

]A $1.00-\mathrm{kg}$ beaker containing $2.00 \mathrm{~kg}$ of oil (density = $916 \mathrm{~kg} / \mathrm{m}^{3}$ ) rests on a scale. A $2.00-\mathrm{kg}$ block of iron is suspended from a spring scale and is completely submerged in the oil (Fig. P9.43). Find the equilibrium readings of both scales.

Salamat Ali
Salamat Ali
Numerade Educator
03:07

Problem 44

Water flowing through a garden hose of diameter $2.74 \mathrm{~cm}$ fills a 25.0-L bucket in $1.50$ min. (a) What is the speed of the water leaving the end of the hose? (b) A nozzle is now attached to the end of the hose. If the nozzle diameter is one-third the diameter of the hose, what is the speed of the water leaving the nozzle?

Averell Hause
Averell Hause
Carnegie Mellon University
02:04

Problem 45

(a) Calculate the mass flow rate (in grams per second) of blood $\left(\rho=1.0 \mathrm{~g} / \mathrm{cm}^{3}\right)$ in an aorta with a cross-sectional area of $2.0 \mathrm{~cm}^{2}$ if the flow speed is $40 \mathrm{~cm} / \mathrm{s}$. (b) Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of $3.0 \times$ $10^{3} \mathrm{~cm}^{2} .$ What is the flow speed in the capillaries?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:26

Problem 46

A liquid $\left(\rho=1.65 \mathrm{~g} / \mathrm{cm}^{3}\right)$ flows through two horizontal sections of tubing joined end to end. In the first section, the cross-sectional area is $10.0 \mathrm{~cm}^{2}$, the flow speed is $275 \mathrm{~cm} / \mathrm{s}$, and the pressure is $1.20 \times 10^{5} \mathrm{~Pa}$. In the second section, the cross-sectional area is $2.50 \mathrm{~cm}^{2}$. Calculate the smaller section's (a) flow speed and (b) pressure.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:55

Problem 47

A hypodermic syringe contains a medicine with the density of water (Fig. $\mathrm{P} 9.47$ ). The barrel of the syringe has a cross-sectional area of $2.50 \times 10^{-5} \mathrm{~m}^{2}$. In the absence of a force on the plunger, the pressure everywhere is $1.00 \mathrm{~atm} . \mathrm{A}$ force $\overrightarrow{\mathbf{F}}$ of magnitude $2.00 \mathrm{~N}$ is exerted on the plunger, making medicine squirt from the needle. Determine the medicine's flow speed through the needle. Assume the pressure in the needle remains equal to $1.00 \mathrm{~atm}$ and that the syringe is horizontal.

Salamat Ali
Salamat Ali
Numerade Educator
01:19

Problem 48

When a person inhales, air moves down the bronchus (windpipe) at $15 \mathrm{~cm} / \mathrm{s}$. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.

Averell Hause
Averell Hause
Carnegie Mellon University
06:58

Problem 49

A jet airplane in level flight has a mass of $8.66 \times$ $10^{4} \mathrm{~kg}$, and the two wings have an estimated total area of $90.0 \mathrm{~m}^{2}$. (a) What is the pressure difference between the lower and upper surfaces of the wings? (b) If the speed of air under the wings is $225 \mathrm{~m} / \mathrm{s}$, what is the speed of the air over the wings? Assume air has a density of $1.29 \mathrm{~kg} / \mathrm{m}^{3}$. (c) Explain why all aircraft have a "ceiling," maximum operational altitude.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:58

Problem 50

An airplane has a mass $M$, and the two wings have a total area $A$. During level flight, the pressure on the lower wing surface is $P_{1}$. Determine the pressure $P_{2}$ on the upper wing surface.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
05:33

Problem 51

In a water pistol, a piston drives water through a larger tube of radius $1.00 \mathrm{~cm}$ into a smaller tube of radius $1.00 \mathrm{~mm}$ as in Figure P9.51. (a) If the pistol is fired horizontally at a height of $1.50 \mathrm{~m}$, use ballistics to determine the time it takes water to travel from the nozzle to the ground. (Neglect air resistance and assume atmospheric pressure is $1.00$ atm.) (b) If the range of the stream is to be $8.00 \mathrm{~m}$, with what speed must the stream leave the nozzle? (c) Given the areas of the nozzle and cylinder, use the equation of continuity to calculate the speed at which the plunger must be moved. (d) What is the pressure at the nozzle? (e) Use Bernoulli's equation to find the pressure needed in the larger cylinder. Can gravity terms be neglected? (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.)

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:57

Problem 52

Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in Figure $9.29$, the pressure is $1.75 \times 10^{5} \mathrm{~Pa}$ and the pipe radius is $3.00 \mathrm{~cm}$. At another point $2.50 \mathrm{~m}$ higher, the pressure is $1.20 \times 10^{5} \mathrm{~Pa}$ and the pipe radius is $1.50 \mathrm{~cm}$. Find the speed of flow (a) in the lower section and (b) in the upper section. (c) Find the volume flow rate through the pipe.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:26

Problem 53

A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure $\mathrm{P} 9.53$. If the hole has a diameter of $3.50 \mathrm{~mm}$, what is the height $h$ of the water level in the tank?

Salamat Ali
Salamat Ali
Numerade Educator
02:48

Problem 54

A large storage tank, open to the atmosphere at the top and filled with water, develops a small hole in its side at a point $16.0 \mathrm{~m}$ below the water level. If the rate of flow from the leak is $2.50 \times 10^{-3} \mathrm{~m}^{3} / \mathrm{min}$, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

Averell Hause
Averell Hause
Carnegie Mellon University
03:55

Problem 55

The inside diameters of the larger portions of the horizontal pipe depicted in Figure $\mathrm{P} 9.55$ are $2.50 \mathrm{~cm} .$ Water flows to the right at a rate of $1.80 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}$. Determine the inside diameter of the constriction.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
05:22

Problem 56

Water is pumped through a pipe of diameter $15.0 \mathrm{~cm}$ from the Colorado River up to Grand Canyon Village, on the rim of the canyon. The river is at $564 \mathrm{~m}$ elevation and the village is at $2096 \mathrm{~m}$. (a) At what minimum pressure must the water be pumped to arrive at the village? (b) If $4500 \mathrm{~m}^{3}$ are pumped per day, what is the speed of the water in the pipe? (c) What additional pressure is necessary to deliver this flow? Note: You may assume the free-fall acceleration and the density of air are constant over the given range of elevations.

Averell Hause
Averell Hause
Carnegie Mellon University
03:35

Problem 57

]Old Faithful geyser in Yellowstone Park erupts at approximately 1-hour intervals, and the height of the fountain reaches $40.0 \mathrm{~m}$. (a) Consider the rising stream as a series of separate drops. Analyze the free-fall motion of one of the drops to determine the speed at which the water leaves the ground. (b) Treat the rising stream as an ideal fluid in streamline flow. Use Bernoulli's equation to determine the speed of the water as it leaves ground level. (c) What is the pressure (above atmospheric pressure) in the heated underground chamber $175 \mathrm{~m}$ below the vent? You may assume the chamber is large compared with the geyser
vent.

Salamat Ali
Salamat Ali
Numerade Educator
03:07

Problem 58

The Venturi tube shown in Figure $9.30$ may be used as a fluid flowmeter. Suppose the device is used at a service station to measure the flow rate of gasoline $(\rho=7.00 \times$ $10^{2} \mathrm{~kg} / \mathrm{m}^{3}$ ) through a hose having an outlet radius of $1.20 \mathrm{~cm} .$ If the difference in pressure is measured to be $P_{1}-P_{2}=1.20 \mathrm{kPa}$ and the radius of the inlet tube to the meter is $2.40 \mathrm{~cm}$, find $(\mathrm{a})$ the speed of the gasoline as it leaves the hose and (b) the fluid flow rate in cubic meters per second.

Averell Hause
Averell Hause
Carnegie Mellon University
03:15

Problem 59

A square metal sheet $3.0 \mathrm{~cm}$ on a side and of negligible thickness is attached to a balance and inserted into a container of fluid. The contact angle is found to be zero, as shown in Figure $\mathrm{P} 9.59 \mathrm{a}$, and the balance to which the metal sheet is attached reads $0.40 \mathrm{~N}$. A thin veneer of oil is then spread over the sheet, and the contact angle becomes $180^{\circ}$, as shown in Figure $\mathrm{Pg.} 59 \mathrm{~b} .$ The balance now reads $0.39 \mathrm{~N}$. What is the surface tension of the fluid?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:02

Problem 60

To lift a wire ring of radius $1.75 \mathrm{~cm}$ from the surface of a container of blood plasma, a vertical force of $1.61 \times$ $10^{-2} \mathrm{~N}$ greater than the weight of the ring is required. Calculate the surface tension of blood plasma from this information.

Averell Hause
Averell Hause
Carnegie Mellon University
00:54

Problem 61

A certain fluid has a density of $1080 \mathrm{~kg} / \mathrm{m}^{3}$ and is observed to rise to a height of $2.1 \mathrm{~cm}$ in a $1.0-\mathrm{mm}$ -diameter tube. The contact angle between the wall and the fluid is zero. Calculate the surface tension of the fluid.

Salamat Ali
Salamat Ali
Numerade Educator
01:30

Problem 62

Whole blood has a surface tension of $0.058 \mathrm{~N} / \mathrm{m}$ and a density of $1050 \mathrm{~kg} / \mathrm{m}^{3}$. To what height can whole blood rise in a capillary blood vessel that has a radius of $2.0 \times 10^{-6} \mathrm{~m}$ if the contact angle is zero?

Averell Hause
Averell Hause
Carnegie Mellon University
00:33

Problem 63

The block of ice (temperature $0^{\circ} \mathrm{C}$ ) shown in Figure P9. 63 is drawn over a level surface lubricated by a layer of water $0.10 \mathrm{~mm}$ thick. Determine the magnitude of the force $\overrightarrow{\mathbf{F}}$ needed to pull the block with a constant speed of $0.50 \mathrm{~m} / \mathrm{s}$. At $0^{\circ} \mathrm{C}$, the viscosity of water has the value $\eta=1.79 \times 10^{-3} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}$.

Salamat Ali
Salamat Ali
Numerade Educator
01:27

Problem 64

A thin $1.5-\mathrm{mm}$ coating of glycerine has been placed between two microscope slides of width $1.0 \mathrm{~cm}$ and length $4.0 \mathrm{~cm} .$ Find the force required to pull one of the microscope slides at a constant speed of $0.30 \mathrm{~m} / \mathrm{s}$ relative to the other slide.

Averell Hause
Averell Hause
Carnegie Mellon University
00:57

Problem 65

A straight horizontal pipe with a diameter of $1.0 \mathrm{~cm}$ and a length of $50 \mathrm{~m}$ carries oil with a coefficient of viscosity of $0.12 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}$. At the output of the pipe, the flow rate is $8.6 \times 10^{-5} \mathrm{~m}^{3} / \mathrm{s}$ and the pressure is $1.0 \mathrm{~atm}$. Find the gauge pressure at the pipe input.

Salamat Ali
Salamat Ali
Numerade Educator
01:50

Problem 66

The pulmonary artery, which connects the heart to the lungs, has an inner radius of $2.6 \mathrm{~mm}$ and is $8.4 \mathrm{~cm}$ long. If the pressure drop between the heart and lungs is $400 \mathrm{~Pa}$, what is the average speed of blood in the pulmonary artery?

Averell Hause
Averell Hause
Carnegie Mellon University
01:51

Problem 67

Spherical particles of a protein of density $1.8 \mathrm{~g} / \mathrm{cm}^{3}$ are shaken up in a solution of $20^{\circ} \mathrm{C}$ water. The solution is allowed to stand for $1.0 \mathrm{~h}$. If the depth of water in the tube is $5.0 \mathrm{~cm}$, find the radius of the largest particles that remain in solution at the end of the hour.

Salamat Ali
Salamat Ali
Numerade Educator
02:20

Problem 68

A hypodermic needle is $3.0 \mathrm{~cm}$ in length and $0.30 \mathrm{~mm}$ in diameter. What excess pressure is required along the needle so that the flow rate of water through it will be $1 \mathrm{~g} / \mathrm{s} ?$ (Use $1.0 \times 10^{-3} \mathrm{~Pa} \cdot \mathrm{s}$ as the viscosity of water.)

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:05

Problem 69

What diameter needle should be used to inject a volume of $500 \mathrm{~cm}^{3}$ of a solution into a patient in $30 \mathrm{~min} ?$ Assume the length of the needle is $2.5 \mathrm{~cm}$ and the solution is elevated $1.0 \mathrm{~m}$ above the point of injection. Further, assume the viscosity and density of the solution are those of pure water, and that the pressure inside the vein is atmospheric.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:27

Problem 70

Water is forced out of a fire extinguisher by air pressure, as shown in Figure P9.70. What gauge air pressure in the tank (above atmospheric pressure) is required for the water to have a jet speed of $30.0 \mathrm{~m} / \mathrm{s}$ when the water level in the tank is $0.500 \mathrm{~m}$ below the nozzle?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
00:59

Problem 71

The aorta in humans has a diameter of about $2.0 \mathrm{~cm}$, and at certain times the blood speed through it is about $55 \mathrm{~cm} / \mathrm{s}$. Is the blood flow turbulent? The density of whole blood is $1050 \mathrm{~kg} / \mathrm{m}^{3}$, and its coefficient of viscosity is $2.7 \times 10^{-3} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}$.

Averell Hause
Averell Hause
Carnegie Mellon University
01:13

Problem 72

A pipe carrying $20^{\circ} \mathrm{C}$ water has a diameter of $2.5 \mathrm{~cm}$. Estimate the maximum flow speed if the flow must be streamline.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:32

Problem 73

Sucrose is allowed to diffuse along a $10-\mathrm{cm}$ length of tubing filled with water. The tube is $6.0 \mathrm{~cm}^{2}$ in crosssectional area. The diffusion coefficient is equal to $5.0 \times 10^{-10} \mathrm{~m}^{2} / \mathrm{s}$, and $8.0 \times 10^{-14} \mathrm{~kg}$ is transported along
the tube in $15 \mathrm{~s}$. What is the difference in the concentration levels of sucrose at the two ends of the tube?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:23

Problem 74

Glycerin in water diffuses along a horizontal column that has a cross-sectional area of $2.0 \mathrm{~cm}^{2}$. The concentration gradient is $3.0 \times 10^{-2} \mathrm{~kg} / \mathrm{m}^{4}$, and the diffusion rate is found to be $5.7 \times 10^{-15} \mathrm{~kg} / \mathrm{s}$. Determine the diffusion coefficient.

Averell Hause
Averell Hause
Carnegie Mellon University
00:50

Problem 75

The viscous force on an oil drop is measured to be equal to $3.0 \times 10^{-13} \mathrm{~N}$ when the drop is falling through air with a speed of $4.5 \times 10^{-4} \mathrm{~m} / \mathrm{s}$. If the radius of the drop is $2.5 \times 10^{-6} \mathrm{~m}$, what is the viscosity of air?

Salamat Ali
Salamat Ali
Numerade Educator
02:18

Problem 76

Small spheres of diameter $1.00 \mathrm{~mm}$ fall through $20^{\circ} \mathrm{C}$ water with a terminal speed of $1.10 \mathrm{~cm} / \mathrm{s} .$ Calculate the density of the spheres.

Averell Hause
Averell Hause
Carnegie Mellon University
02:27

Problem 77

An iron block of volume $0.20 \mathrm{~m}^{3}$ is suspended from a spring scale and immersed in a flask of water. Then the iron block is removed, and an aluminum block of the same volume replaces it. (a) In which case is the buoyant force the greatest, for the iron block or the aluminum block? (b) In which case does the spring scale read the largest value? (c) Use the known densities of these materials to calculate the quantities requested in parts (a) and (b). Are your calculations consistent with your previous answers to parts (a) and (b)?

Salamat Ali
Salamat Ali
Numerade Educator
01:32

Problem 78

A steel ball is tossed into the ocean and comes to rest at a depth of $2.40 \mathrm{~km}$. Find its fractional change in volume, assuming the density of seawater is $1.025 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:53

Problem 79

As a first approximation, Earth's continents may be thought of as granite blocks floating in a denser rock (called peridotite) in the same way that ice floats in water. (a) Show that a formula describing this phenomenon is
$$
\rho_{g} t=\rho_{p} d
$$
where $\rho_{g}$ is the density of granite $\left(2.8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right), \rho_{p}$ is the density of peridotite $\left(3.3 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\right), t$ is the thickness of a continent, and $d$ is the depth to which a continent floats in the peridotite. (b) If a continent sinks $5.0 \mathrm{~km}$ into the peridotite layer (this surface may be thought of as the ocean floor), what is the thickness of the continent?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
01:50

Problem 80

Take the density of blood to be $\rho$ and the distance between the feet and the heart to be $h_{H}$. Ignore the flow of blood. (a) Show that the difference in blood pressure between the feet and the heart is given by $P_{F}-P_{H}=\rho g h_{H}$. (b) Take the density of blood to be $1.05 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and the distance between the heart and the feet to be $1.20 \mathrm{~m}$. Find the difference in blood pressure between these two points. This problem indicates that pumping blood from the extremities is very difficult for the heart. The veins in the legs have valves in them that open when blood is pumped toward the heart and close when blood flows away from the heart. Also, pumping action produced by physical activities such as walking and breathing assists the heart.

Averell Hause
Averell Hause
Carnegie Mellon University
02:05

Problem 81

The approximate inside diameter of the aorta is $0.50 \mathrm{~cm} ;$ that of a capillary is $10 \mu \mathrm{m}$. The approximate average blood flow speed is $1.0 \mathrm{~m} / \mathrm{s}$ in the aorta and $1.0 \mathrm{~cm} / \mathrm{s}$ in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:06

Problem 82

Superman attempts to drink water through a very long vertical straw. With his great strength, he achieves maximum possible suction. The walls of the straw don't collapse. (a) Find the maximum height through which he can lift the water. (b) Still thirsty, the Man of Steel repeats his attempt on the Moon, which has no atmosphere. Find the difference between the water levels inside and outside the straw.

Averell Hause
Averell Hause
Carnegie Mellon University
01:50

Problem 83

The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to $200 \mathrm{~mm}$ of $\mathrm{H}_{2} \mathrm{O}$ above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of $\mathrm{mm}$ of $\mathrm{H}_{2} \mathrm{O}$ because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed, as shown in Figure $\mathrm{P} 9.83 .$ If the fluid rises to a height of $160 \mathrm{~mm}$, we write its gauge pressure as $160 \mathrm{~mm} \mathrm{H}_{2} \mathrm{O} .$ (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions can be investigated by means of the Queckensted test. In this procedure the veins in the patient's neck are compressed, to make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?

Salamat Ali
Salamat Ali
Numerade Educator
01:56

Problem 84

Determining the density of a fluid has many important applications. A car battery contains sulfuric acid, and the battery will not function properly if the acid density is too low. Similarly, the effectiveness of antifreeze in your car's engine coolant depends on the density of the mixture (usually ethylene glycol and water). When you donate blood to a blood bank, its screening includes a determination of the density of the blood because higher density correlates with higher hemoglobin content. A hydrometer is an instrument used to determine the density of a liquid. A simple one is sketched in Figure $\mathrm{P} 9.84 .$ The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. (Assume the rod is cylindrical.) The rod, of length $L$ and average density $\rho_{0}$, floats partially immersed in the liquid of density $\rho .$ A length $h$ of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by
$$
\rho=\frac{\rho_{0} L}{L-h}
$$

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:53

Problem 85

Figure $\mathrm{P} 9.85$ shows a water tank with a valve. If the valve is opened, what is the maximum height attained by the stream of water coming out of the right side of the tank? Assume $h=10.0 \mathrm{~m}, L=2.00 \mathrm{~m}$, and $\theta=30.0^{\circ}$, and that the cross-sectional area at $A$ is very large compared with that at $B$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:47

Problem 86

A helium-filled balloon is tied to a 2.0-m-long, $0.050-\mathrm{kg}$ string. The balloon is spherical with a radius of $0.40 \mathrm{~m}$. When released, it lifis a length $h$ of the string and then remains in equilibrium, as in Figure $\mathrm{P} 9.86$. Determine the value of $h$. When deflated, the balloon has a mass of $0.25 \mathrm{~kg} .$ Hint: Only that part of the string above the floor contributes to the load being held up by the balloon.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
02:29

Problem 87

A 600 -kg weather balloon is designed to lift a $4000-\mathrm{kg}$ package. What volume should the balloon have after being inflated with helium at standard temperature and pressure (see Table $9.3$ ) so the total load can be lifted?

Prabhu Ramji
Prabhu Ramji
Numerade Educator
04:26

Problem 88

A U-tube open at both ends is partially filled with water (Fig. P9.88a). Oil $\left(\rho=750 \mathrm{~kg} / \mathrm{m}^{3}\right)$ is then poured into the right arm and forms a column $L=5.00 \mathrm{~cm}$ high (Fig. P9.88b). (a) Determine the difference $h$ in the heights of the two liquid surfaces. (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. $9.80 \mathrm{c}) .$ Determine the speed of the air being blown across the left arm. Assume the density of air is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$.

Prabhu Ramji
Prabhu Ramji
Numerade Educator
03:36

Problem 89

A $1.0-\mathrm{kg}$ hollow ball with a radius of $0.10 \mathrm{~m}$ and filled with air is released from rest at the bottom of a $2.0-\mathrm{m}$ -deep pool of water. How high above the water does the ball shoot upward? Neglect all frictional effects, and neglect changes in the ball's motion when it is only partially submerged.

Ivan Kochetkov
Ivan Kochetkov
Numerade Educator
02:57

Problem 90

Oil having a density of $930 \mathrm{~kg} / \mathrm{m}^{3}$ floats on water. A rectangular block of wood $4.00 \mathrm{~cm}$ high and with a density of $960 \mathrm{~kg} / \mathrm{m}^{3}$ floats partly in the oil and partly in the water. The oil completely covers the block. How far below the interface between the two liquids is the bottom of the block?

Averell Hause
Averell Hause
Carnegie Mellon University
06:03

Problem 91

A water tank open to the atmosphere at the top has two small holes punched in its side, one above the other. The holes are $5.00 \mathrm{~cm}$ and $12.0 \mathrm{~cm}$ above the floor. How high does water stand in the tank if the two streams of water hit the floor at the same place?

Salamat Ali
Salamat Ali
Numerade Educator
06:54

Problem 92

A walkway suspended across a hotel lobby is supported at numerous points along its edges by a vertical cable above each point and a vertical column underneath. The steel cable is $1.27 \mathrm{~cm}$ in diameter and is $5.75 \mathrm{~m}$ long before loading. The aluminum column is a hollow cylinder with an inside diameter of $16.14 \mathrm{~cm}$, an outside diameter of $16.24 \mathrm{~cm}$, and an unloaded length of $3.25 \mathrm{~m}$. When the walkway exerts a load force of $8500 \mathrm{~N}$ on one of the support points, through what distance does the point move down?

Prabhu Ramji
Prabhu Ramji
Numerade Educator