College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

Chapter 13 Static Fluids - all with Video Answers

Educators

Chapter Questions

02:59

Problem 1

Determine the average density of Earth. What data did you use? What assumptions did you make?

Surjit Tewari

Numerade Educator

02:24

Use data for the normal pressure and the density of air near Earth's surface to estimate the height of the atmosphere, assuming it has uniform density. Indicate any additional assumptions you made. Are you on the low or high side of the real number?

Samantha Baker

Numerade Educator

04:07

Problem 3

A single-level home has a floor area of $200 \mathrm{m}^{2}$ with ceilings that are $2.6 \mathrm{m}$ high. Estimate the mass of the air in the house.

Surjit Tewari

Numerade Educator

06:54

Problem 4

A diet decreases a person's mass by $5 \% .$ Exercise creates muscle and reduces fat, thus increasing the person's density by $2 \%$. Determine the
percent change in the person's volume.

Surjit Tewari

Numerade Educator

02:52

Problem 5

A pulsar, an extremely dense rotating star made of neutrons, has a density of $10^{18} \mathrm{~kg} / \mathrm{~m}^{3}$.
Determine the mass of a pulsar contained in a volume the size of your fist (about $200 \mathrm{~cm}^{3}$ ).

Surjit Tewari

Numerade Educator

05:20

Problem 6

Use the graph lines in Figure $P 13.6$ to determine the densities of the
three liquids, A, B, and C, in SI units. If you place them in one container, how will they position themselves? How does the density of each liquid change as its volume increases? As its mass decreases? Compare the masses of the three liquids when they occupy the same volume. Compare the volumes of the three liquids when they have the same mass.

Brandy Heflin

Numerade Educator

05:19

Problem 7

Imagine that you have gelatin cut into three cubes: the side of cube A is $a$ cm long, the side of cube $B$ is double the side of $A$, and the side of cube $C$ is three times the side of A. Compare the following properties of the cubes:
(a) density, (b) volume,
(c) surface area,
(d) cross-sectional area, and
(e) mass.

Surjit Tewari

Numerade Educator

03:20

Problem 8

An object made of material A has a mass of $90 \mathrm{kg}$ and a volume of $0.45 \mathrm{m}^{3}$. If you cut the object in half, what would be the density of each half? If you cut the object into three picces, what would be the density of each piece? What assumptions did you make?

Surjit Tewari

Numerade Educator

05:12

Problem 9

You have a steel ball that has a mass of $6.0 \mathrm{kg}$ and a volume of $3.0 \times 10^{-3} \mathrm{m}^{3} .$ How can this be?

Surjit Tewari

Numerade Educator

03:45

Problem 10

A material is made of molecules of mass $2.0 \times 10^{-26} \mathrm{kg} .$ There are $2.3 \times 10^{29}$ of these molecules in a $2.0-\mathrm{m}^{3}$ volume. What is the density of
the material?

Surjit Tewari

Numerade Educator

02:47

Problem 11

You compress all the molecules described in Problem 13.10 into $1.0 \mathrm{m}^{3}$. Now what is the density of the material? What type of material could possibly behave this way?

Surjit Tewari

Numerade Educator

01:23

Problem 12

Bowling balls are heavy. However, some bowling balls float in water. Use available resources to find the dimensions of a bowling ball and explain why some balls float while others do not.

Samantha Baker

Numerade Educator

10:11

Problem 13

Estimate the average density of a glass full of water and then the glass when the water is poured out (do not forget the air that now fills the glass instead of water).

Ankit Pandey

Numerade Educator

02:04

Problem 14

Anita holds her physics textbook and complains that it is too heavy. Andrew says that her hand should exert no force on the book because the atmosphere pushes up on it and balances the downward pull of Earth on the book (the book's weight). Jim disagrees. He says that the atmosphere presses down on things and that is why they feel heavy. Who is correct? Approximately how large is the force that the atmosphere exerts on the bottom of the book? Why does this force not balance the force exerted by Earth on the book?

Samantha Baker

Numerade Educator

03:15

Problem 15

The air pressure in the tires of a $980-\mathrm{kg}$ car is $3.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ Determine the average area of contact of each tire with the road. Indicate any assumptions that you made.

Surjit Tewari

Numerade Educator

05:33

Problem 16

Estimate the pressure that you exert on the floor while wearing hiking boots. Now estimate the pressure under each heel if you change into high-heeled shoes. Indicate any assumptions you made.

Ankit Pandey

Numerade Educator

04:50

Problem 17

Hydraulic car lift You are designing a hydraulic lift for a machine shop. The average mass of a car it needs to lift is about $1500 \mathrm{kg} .$ What should be the specifications on the dimension of the pistons if you wish to exert a force on a smaller piston of not more than 500 N? How far down will you need to push the piston in order to lift the car $30 \mathrm{cm} ?$

Surjit Tewari

Numerade Educator

02:23

Problem 18

Estimate the force that air exerts on your forehead. Describe the assumptions you made.

Surjit Tewari

Numerade Educator

04:25

Problem 19

A 30-cm-diameter cylindrical iron plunger is held against the ceiling, and the air is pumped from inside it. A 72 -kg person hangs by a rope from the plunger (Figure $P 13.19$ ). List the quantities that you can estimate about the situation and estimate them. Make assumptions if necessary.

Surjit Tewari

Numerade Educator

03:45

Problem 20

You have a rubber pad with a handle attached to it (Figure $P 13.20$ ). If you press the pad firmly on a smooth table, it is impossible to lift it off the table. Why? What force would you need to exert on the handle to lift it? The surface area of the pad is $0.023 \mathrm{m}^{2}$

Surjit Tewari

Numerade Educator

03:02

Problem 21

A child"s toy amow has a suction cup on one end. When the arrow hits the wall, it sticks. Draw a force diagram for the arrow stuck on the wall and estimate the magnitudes of the forces exerted on it when it is in equilibrium. The mass of the arrow is about $10 \mathrm{g}$. Why are the words "suction cup" not appropriate?

Surjit Tewari

Numerade Educator

03:44

Problem 22

The Titanic rests $4 \mathrm{km}(2.5 \mathrm{miles})$ below the surface of the ocean. What physical quantities can you determine using this information?

Surjit Tewari

Numerade Educator

05:04

Problem 23

You have three reservoirs (Figure $P 13.23$ ). Rank the pressures at the bottom of each and explain your rankings. Then rank the net force that the water exerts on the bottom of each reservoir. Explain your rankings.

Surjit Tewari

Numerade Educator

03:49

Problem 24

The pressure at the top of the water in a city"s gravity-fed reservoir is $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$. Determine the pressure at the faucet of a home $42 \mathrm{m}$ below the reservoir.

Surjit Tewari

Numerade Educator

03:58

Problem 25

An old story tells of a Dutch boy who used his fist to plug a 2.0 -cm-diameter hole in a dike that was $3.0 \mathrm{m}$ below sea level, thus preventing the flooding of part of Holland. What physical quantities can you determine from this information? Determine them.

Surjit Tewari

Numerade Educator

03:39

Problem 26

Estimate the pressure of the blood in your brain and in your feet when standing, relative to the average pressure of the blood in your heart of $1.3 \times 10^{4} \mathrm{N} / \mathrm{m}^{2}$ above atmospheric pressure.

Samantha Baker

Numerade Educator

04:14

Problem 27

A glucose solution of density $1050 \mathrm{kg} / \mathrm{m}^{3}$ is transferred from a collapsible bag through a tube and syringe into the vein of a person's arm. The blood pressure in the arm exceeds the atmospheric pressure by $1400 \mathrm{N} / \mathrm{m}^{2}$. How high above the arm must the top of the liquid in the bottle be so that the pressure in the glucose solution at the needle exceeds the pressure of the blood in the arm?

Surjit Tewari

Numerade Educator

04:20

Problem 28

Determine the change in air pressure as you climb from elevation of $1650 \mathrm{m}$ at the timberline of Mount Rainier to its $4392-\mathrm{m}$ summit, assuming an average air density of $0.82 \mathrm{kg} / \mathrm{m}^{3} .$ Will the real change be more or less than the one you calculated? Explain.

Surjit Tewari

Numerade Educator

01:27

Problem 29

Estimate the pressure change of the blood in the brain of a giraffe when it lifts its head from the grass to cat a leaf on an overhead tree. Without special valves in its circulatory system, the giraffe could easily faint when lifting its head.

Surjit Tewari

Numerade Educator

04:51

Problem 30

A truck transporting chemicals has crashed, and some dangerous liquid has spilled onto the ground and possibly entered a water well. An inspector fixes a pressure sensor to the end of a long string and lets the sensor slowly descend from the top of the well to the bottom. Using this device, he obtains the graph in Figure $P 13.30$ that shows how the pressure $P$ in the well changes with distance $d$ measured from the top of the well. (a) Explain what features of the graph support the idea that there is another liquid in the well in addition to water. (b) Determine the density of the unknown liquid. Is the liquid above the water or below the water?
(c) Determine the depth of the water, the depth of the unknown liquid, and the depth of the well.

Raushan Kumar

Numerade Educator

03:47

Problem 31

You are drinking water through a straw in an open glass. Select a small volume of water in the straw as a system and draw a force diagram for the water inside this volume that explains why the water goes up the straw.

Surjit Tewari

Numerade Educator

05:28

Problem 32

While you are drinking through the straw, the pressure in your mouth is $30 \mathrm{mm}$ Hg below atmospheric pressure. What is the maximum length of a straw in an open glass that you can use to drink a fruit drink of density $1200 \mathrm{kg} / \mathrm{m}^{3} ?$

Surjit Tewari

Numerade Educator

05:00

Problem 33

Your office has a $0.020 \mathrm{m}^{3}$ cylindrical container of drinking water. The radius of the container is about $14 \mathrm{cm} .$ When the container is full, what
is the gauge pressure that the water exerts on the sides of the container halfway down from the top? All the way down?

Surjit Tewari

Numerade Educator

02:15

Problem 34

Estimate the net force on your $0.5-\mathrm{cm}^{2}$ eardrum that air exerts on the inside and the outside after you drive from Denver, Colorado (elevation $1609 \mathrm{m}$ ) to the top of Pikes Peak (elevation $4301 \mathrm{m}$ ). Assume that the air pressure inside and out are balanced when you leave Denver and that the average density of the air is $0.80 \mathrm{kg} / \mathrm{m}^{3} .$ What other assumptions did you make?

Samantha Baker

Numerade Educator

02:31

Problem 35

You now go snorkeling. What is the net force exerted on your eardrum when you are $2.4 \mathrm{m}$ under the water, assuming the pressure was cqualized before the dive?

Surjit Tewari

Numerade Educator

04:25

Problem 36

Water and oil are poured into opposite sides of an open U-shaped tube. The oil and water meet at the exact center of the U at the bottom of the tube. If the column of oil of density $900 \mathrm{kg} / \mathrm{m}^{3}$ is $16 \mathrm{cm}$ high on one side, how high is the water on the other side?

Surjit Tewari

Numerade Educator

03:12

Problem 37

Examine the vertical cross section of the Hoover Dam shown in
Figure P13.37. Explain why the dam is thicker at the bottom than at the top.

Surjit Tewari

Numerade Educator

03:09

Problem 38

A test tube of length $L$ and cross-sectional area $A$ is submerged in water with the open end down so that the edge of the tube is a distance $h$ below the surface. The water goes up into the tube so its height inside the tube is $l$. Describe how you can use this information to decide whether the air that was initially in the tube obeys the mathematical description for an isothermal process (Boyle's law). List your assumptions.

Zulfiqar Ali

Numerade Educator

01:00

Problem 39

Half of a $20-\mathrm{cm}$ -tall beaker is filled with glycerol (density $1259 \mathrm{kg} / \mathrm{m}^{3}$ ) and the other half with olive oil (density $800 \mathrm{kg} / \mathrm{m}^{3}$ ). (a) Draw a graph that shows how the density of the liquids in the beaker changes with the distance from the surface to the bottom of beaker.
(b) Draw a graph that shows how the pressure in the liquids changes with the distance from the surface to the bottom of the beaker.

Raj Bala

Numerade Educator

01:56

Problem 40

Blaise Pascal found a seemingly paradoxical situation when he poured water into the apparatus shown in Figure $\mathbf{P} 13.40 .$ The water level was the same in all
four parts of the apparatus despite differences in the shapes of the parts and the masses of water in each part. Explain qualitatively the outcome of Pascal 's experiment.

Prabhu Ramji

Numerade Educator

05:04

Problem 41

Four containers are filled with different volumes of water as shown in Figure $P 13.41 .$ Rank the containers in order of decreasing pressure that the water exerts on the bottom of the containers.

Surjit Tewari

Numerade Educator

04:03

Problem 42

Venus pressure and underwater pressure Atmospheric pressure on Venus is $9.0 \times 10^{6} \mathrm{N} / \mathrm{m}^{2}$. How deep underwater on Earth would you have to go to feel the same pressure?

Surjit Tewari

Numerade Educator

03:56

Problem 43

The reading of a barometer in your room is $780 \mathrm{mm}$ Hg. What does this mean? What is the pressure in pascals?

Surjit Tewari

Numerade Educator

02:43

Problem 44

How long would Torricelli "s barometer have had to be if he had used oil of density $950 \mathrm{kg} / \mathrm{m}^{3}$ instead of mercury?

Surjit Tewari

Numerade Educator

02:21

Problem 45

Sometimes gas pressure is measured with a device called a liquid manometer (Figure P13.45). Explain how this instrument can be used to measure the pressure of gas in a bulb attached to one of the tubes.

Surjit Tewari

Numerade Educator

01:53

Problem 46

You use a liquid manometer with water to measure the pressure inside a
rubber bulb. Before you squeeze the bulb, the water is at the same level in both legs of the tube. After you squeeze the bulb, the water in the opposite leg rises $20 \mathrm{cm}$ with respect to the leg connected to the bulb (Figure $\mathrm{P} 13.46$ ). What is the pressure in the bulb? What assumptions did you make? How will the answer change if the assumptions are not valid?

Samantha Baker

Numerade Educator

04:41

Problem 47

In a mercury-filled manometer (Figure $\mathrm{P} 13.47$ ), the open end is inserted into a container of gas and the closed end of the tube is evacuated.
The difference in the height of the mercury is $80 \mathrm{mm}$. The radius of the connecting tube is $0.50 \mathrm{cm}$.
(a) Determine the pressure inside the container in newtons per square meter. (b) An identical manometer has a connecting tube that is twice as wide. If the difference in the height of the mercury is the same, then what is the pressure in the container?

Surjit Tewari

Numerade Educator

01:35

Problem 48

Examine the reading of the manometer that you use to measure the pressure inside car tires. What are the units? Does the manometer measure the absolute pressure of the air inside the tires or gauge pressure? How do you know?

Surjit Tewari

Numerade Educator

01:23

Problem 49

Draw a force diagram for an object that is floating at the surface of a liquid. Is the force exerted by air on the object included in your diagram? Explain.

Surjit Tewari

Numerade Educator

01:29

Problem 50

Draw a cubic object that is completely submerged in a fluid but not resting on the bottom of the container. Then draw arrows to represent the forces exerted by the fluid on the top, sides, and bottom of the object. Make the arrows the correct relative lengths. What is the direction of the total force exerted by the fluid on the object?

Samantha Baker

Numerade Educator

02:25

Problem 51

Three people are holding three identical sealed metal containers, ready to release them. Container A is filled with air at atmospheric pressure and room temperature, container $\mathrm{B}$ is filled with helium at atmospheric pressure and room temperature, and container $C$ is evacuated (all air has been pumped out). Draw force diagrams for the containers after they are released.

David Collins

Numerade Educator

03:05

Problem 52

Four cubes of the same volume are made of different materials: lead (density $11,300 \mathrm{~kg} / \mathrm{~m}^{3}$ ), aluminum (density $2700 \mathrm{~kg} / \mathrm{~m}^{3}$ ), wood (density $800 \mathrm{~kg} / \mathrm{~m}^{3}$ ), and Styrofoam (density $50 \mathrm{~kg} / \mathrm{~m}^{3}$ ). You place the cubes in a large container filled with water. Rank the buoyant forces that the water exerts on the cubes from largest to smallest.

Surjit Tewari

Numerade Educator

06:58

Problem 53

You place four identical cubes made of oak (density $900 \mathrm{kg} / \mathrm{m}^{3}$ ) in water, olive oil (density $880 \mathrm{kg} / \mathrm{m}^{3}$ ), alcohol (density $790 \mathrm{kg} / \mathrm{m}^{3}$ ), and mercury (density $13,600 \mathrm{kg} / \mathrm{m}^{3}$ ). Rank the buoyant forces that the liquids exert on the cubes from largest to smallest.

Surjit Tewari

Numerade Educator

02:07

Problem 54

You fill a 20-cm-tall container with glycerol so that the glycerol (density $1260 \mathrm{kg} / \mathrm{m}^{3}$ ) reaches the 10 -cm mark. You place an oak cube (density $900 \mathrm{kg} / \mathrm{m}^{3}$ ) into the container. Each side of the cube is $10 \mathrm{cm}$
(a) What
is the distance $x$ from the upper face of the cube to the glycerol surface assuming the cube is in an upright position? (b) Make a prediction using qualitative reasoning (without mathematics) about what will happen to the cube in (a) if you now add olive oil (density $800 \mathrm{kg} / \mathrm{m}^{3}$ ) to the container until it is completely full. Will the distance $x$ decrease, increase, or stay the same? (c) Determine the new distance $x$ using mathematics (physics laws) and compare your result with the prediction in (b).

Kudakwashe Mapiki

Numerade Educator

05:03

Problem 55

A 30 -g ball with volume $37.5 \mathrm{cm}^{3}$ is attached to the bottom of a glass beaker with a light string. When the beaker is filled with water, the ball floats fully submerged under the water surface. Draw a force diagram for
the ball and determine the force exerted on the ball by the string.

Surjit Tewari

Numerade Educator

04:29

Problem 56

You have a ball (volume $V$, average density $\rho_{\mathrm{B}}$ ) and a glass beaker. The ball is attached to the bottom of the beaker with a light spring (coefficient $k$ ).
When you fill the beaker with a liquid of density $\rho_{\mathrm{L}}$, the ball floats fully submerged under the surface with the spring extended by $x .$ Draw a force diagram for the ball and derive the expression for $x$ in terms $V, \rho_{B}, \rho_{L},$ and $k$ Evaluate the expression using unit analysis and limiting case analysis.

Surjit Tewari

Numerade Educator

05:56

Problem 57

This textbook says that the upward force that a fluid exerts on a submerged object is equal in magnitude to the product of the density of the fluid, the gravitational constant $g$, and the volume of the submerged part of the object. Where did this equation come from?

Surjit Tewari

Numerade Educator

02:22

Problem 58

This textbook says that the upward force that a fluid exerts on a submerged object is equal in magnitude to the product of the density of the fluid, the gravitational constant $g,$ and the volume of the submerged part of the object. Design an experiment to test this expression, including a predic-
tion about the outcome of the experiment.

Samantha Baker

Numerade Educator

05:32

Problem 59

You have four objects at rest, each of the same volume. Object A is partially submerged, and objects $\mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ are totally submerged in the same container of liquid, as shown in Figure $\mathrm{P} 13.59 .$ Draw a force diagram for each object. Rank the densities of the objects from least to greatest and indicate whether any objects have the same density.

Surjit Tewari

Numerade Educator

05:32

Problem 60

Does air affect what a scale reads? A $60-\mathrm{kg}$ woman with a density of $980 \mathrm{kg} / \mathrm{m}^{3}$ stands on a bathroom scalc. Determine the reduction of the scale reading due to air.

Surjit Tewari

Numerade Educator

05:15

Problem 61

When analyzing a sample of ore, a geologist finds that it weighs $2.00 \mathrm{N}$ in air and $1.13 \mathrm{N}$ when immersed in water. What is the density of the ore? What assumptions did you make to answer the question? If the assumptions are not correct, how would the answer be different?

Surjit Tewari

Numerade Educator

05:12

Problem 62

A pin through a hole in the middle supports a meter stick. Two identical blocks hang from strings at an cqual distance from the center so the stick is balanced. What happens to the stick if one block is submerged in water of density $1000 \mathrm{kg} / \mathrm{m}^{3}$ and the other block in kerosene of density $850 \mathrm{kg} / \mathrm{m}^{3} ?$

Surjit Tewari

Numerade Educator

00:53

Problem 63

A meter stick is supported by a pin through a hole in the middle. (a) Two blocks made of the same material but different sizes hang from strings at
different positions in such a way that the stick balances. What happens when the blocks hang entirely submerged in beakers of water?
(b) Next you hang two blocks of different masses but the same volume at different
positions so the stick balances. What happens when these blocks hang completely submerged in beakers of water? Support your answer for each part using force diagrams with arrows drawn with the correct relative lengths.

Samantha Baker

Numerade Educator

03:32

Problem 64

Goose on a lake A $3.6-\mathrm{kg}$ goose floats on a lake with $40 \%$ of its body below the $1000-\mathrm{kg} / \mathrm{m}^{3}$ water level. Determine the average density of the goose.

Surjit Tewari

Numerade Educator

03:50

Problem 65

Floating in seawater A person of average density $\rho_{1}$ floats in seawater of density $\rho_{2}$. What fraction of the person's body is submerged? Explain.

Surjit Tewari

Numerade Educator

03:49

Problem 66

Floating in seawater A person of average density $980 \mathrm{kg} / \mathrm{m}^{3}$ floats in seawater of density $1025 \mathrm{kg} / \mathrm{m}^{3} .$ What can you determine using this information? Determine it.

Surjit Tewari

Numerade Educator

07:49

Problem 67

(a) Determine the force that a vertical string exerts on a $0.80-\mathrm{kg}$ rock of density $3300 \mathrm{kg} / \mathrm{m}^{3}$ when it is fully submerged in water of density $1000 \mathrm{kg} / \mathrm{m}^{3} .$ (b) If the force exerted by the string supporting the rock increases by $12 \%$ when the rock is submerged in a different fluid, what is that fluid's density?
(c) If the density of another rock of the same volume is
$12 \%$ greater, what happens to the buoyant force the water excrts on it?

Surjit Tewari

Numerade Educator

03:53

Problem 68

Snorkeling A 60-kg snorkeler (including snorkel, mask, and other gear) displaces $0.058 \mathrm{m}^{3}$ of water when $1.2 \mathrm{m}$ under the surface. Determine the magnitude of the buoyant force exerted by the $1025-\mathrm{kg} / \mathrm{m}^{3}$ seawater on the person. Will the person sink or drift upward?

Surjit Tewari

Numerade Educator

04:03

Problem 69

A helium balloon of volume $0.12 \mathrm{m}^{3}$ has a total mass (the helium plus the
balloon) of $0.12 \mathrm{kg} .$ Determine the buoyant force exerted on the balloon by the air if the air has density $1.13 \mathrm{kg} / \mathrm{m}^{3}$. Determine the initial acceleration of the balloon when released.

Surjit Tewari

Numerade Educator

06:06

Problem 70

A protein molecule of mass $1.1 \times 10^{-22} \mathrm{kg}$ and density $1.3 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ is placed in a vertical tube of water of density $1000 \mathrm{kg} / \mathrm{m}^{3} .$ (a) Draw a motion diagram and a force diagram at the moment immediately after the molecule is released.
(b) Determine the initial acceleration of the protein.

Surjit Tewari

Numerade Educator

02:10

Problem 71

How can you determine if a steel ball of known radius is hollow? List the equipment that you will need for the experiment, and describe the procedure and calculations. Can you determine how big the hollow part is if prescnt in the ball?

Samantha Baker

Numerade Educator

09:26

Problem 72

Crown composition A crown is made of gold and silver. The scale reads its mass as $3.0 \mathrm{kg}$ when in air and $2.75 \mathrm{kg}$ when in water. Determine the masses of the gold and the silver in the crown. The density of gold is $19,300 \mathrm{kg} / \mathrm{m}^{3}$ and that of silver is $10,500 \mathrm{kg} / \mathrm{m}^{3}$

Surjit Tewari

Numerade Educator

04:26

Problem 73

"You place an open bottle filled with olive oil (density $880 \mathrm{kg} / \mathrm{m}^{3}$ ) in a container filled with water so that the surfaces of both liquids are at the same level. The bottle has a hole in it $10 \mathrm{cm}$ below the surface that is initially closed with adhesive tape (Figure $\mathbf{P} 13.73$ ). (a) Using Pascal "s laws, predict what will happen when you remove the tape. Indicate any assumptions that you made. (b) Draw pressure-versus-depth graphs (similar to the graphs in Conceptual Exercise 13.3 ) for the states before and after you remove the tape. (c) If you predict any changes, determine their numerical values.

Prabhu Ramji

Numerade Educator

02:16

Problem 74

You hold a ping-pong ball fully underwater (the initial state). When you release the ball, it jumps out of the water to a certain height above the surface. Let the final state be when the ball is just above the water surface, moving upward. Represent the process with cnergy bar charts (a) choosing the water, the ball, and Earth as the system, and
(b) choosing the ball and Earth as the system. Indicate any assumptions that you made.

Eric Mockensturm

Numerade Educator

02:16

Problem 75

Fou hang a steel ball on a string above a beaker that is filled to the top with water (the initial state). The beaker is sitting on a large empty tray. You slowly lower the ball until it reaches the bottom of the beaker. Some water spills over the rim of the beaker to the tray (the final state). (a) Represent the process with an energy bar chart choosing the water, the ball, and Earth as the system. (b) Repeat the analysis for a similar process with the same ball and the same amount of water, but a beaker tall enough so that no water spills over into the tray. Indicate any assumptions that you made.

Eric Mockensturm

Numerade Educator

View

Problem 76

One end of a light spring is attached to a ping-pong ball, the other end to a heavy metal block that is fixed to a thin-wire holder (see Figure $P 13.76$ ). You hold this setup so that the metal block is above the surface of water in a beaker (the initial state). You then slowly lower the setup until the metal block touches the bottom of the beaker (the final state). Represent the process with an energy bar chart, choosing the water, the ball, the spring, the block, and Earth as the system. Assume that the mass of the ball and the mass of the spring are much smaller than the mass of the block and so can be ignored. Indicate any other assumptions that you made.

Gregory Devenport

Numerade Educator

04:46

Problem 77

Wood raft Logs of density $600 \mathrm{kg} / \mathrm{m}^{3}$ are used to build a raft. What is the maximum mass of the load that can be supported by a raft built from $300 \mathrm{kg}$ of logs?

Surjit Tewari

Numerade Educator

05:51

Problem 78

A floating log is $L$ long and $d$ in diameter. What is the mass of a person who can stand on the log without getting her feet wet?

Surjit Tewari

Numerade Educator

08:01

Problem 79

Ferryboat A ferryboat is $12 \mathrm{m}$ long and $8 \mathrm{m}$ wide. Two cars, each of mass $1600 \mathrm{kg}$, ride on the boat for transport across the lake. How much farther does the boat sink into the water?

Surjit Tewari

Numerade Educator

06:12

Problem 80

Iceberg Icebergs are large pieces of freshwater ice. Estimate the percentage of the volume of an iceberg that is underwater. Indicate any assumptions that you made.

Surjit Tewari

Numerade Educator

08:04

Problem 81

Life preserver A life preserver is manufactured to support a $70-\mathrm{kg}$ person with $20 \%$ of his volume out of the water. If the density of the life preserver is $100 \mathrm{kg} / \mathrm{m}^{3}$ and it is completely submerged, what must its volume be? List your assumptions.

Surjit Tewari

Numerade Educator

01:03

Problem 82

To increase the effect of the buoyant force on a submarine, the crew replaces seawater in the ballast tanks with air. To push the seawater out of the tanks, they use compressed air from air flasks. The submarine is located $10 \mathrm{m}$ below the surface in seawater with density $1030 \mathrm{kg} / \mathrm{m}^{3}$ and temperature $6^{\circ} \mathrm{C} .$ How many kilograms of air should the crew let out from the flasks to increase the difference between the gravitational force and the buoyant force exerted on the submarine by $5 \times 10^{6}$ N? Assume the temperature of air in the flasks is the same as the seawater temperature.

Raj Bala

Numerade Educator

01:19

Problem 83

Compare the density of water at $0^{\circ} \mathrm{C}$ to the density of $\mathrm{ice}$ at $0^{\circ} \mathrm{C} .$ Suggest
possible explanations in terms of the molecular arrangements inside the liquid and solid forms of water that would account for the difference. If necessary, use extra resources to help answer the question.

Samantha Baker

Numerade Educator

05:28

Problem 84

Collapsing star The radius of a collapsing star destined to become a pulsar decreases by $10 \%$ while at the same time $12 \%$ of its mass escapes. Determine the percent change in its density.

Surjit Tewari

Numerade Educator

05:04

Problem 85

Deep dive The Trieste research submarine traveled $10.9 \mathrm{km}$ below the
ocean surface while exploring the Mariana Trench in the South Pacific, the deepest place in the ocean. Determine the force needed to prevent a $0.10-\mathrm{m}-$ diameter window on the side of the submarine from imploding. Assume that the pressure inside the submarine is 1 atm and the density of the water is $1025 \mathrm{kg} / \mathrm{m}^{3}$.

Surjit Tewari

Numerade Educator

04:53

Problem 86

Pascal placed a long 0.20-cm-radius tube in a wine barrel of radius $0.24 \mathrm{m}$. He sealed the barrel where the tube entered
it. When he added wine of density $1050 \mathrm{kg} / \mathrm{m}^{3}$ to the tube so the column of wine was $8.0 \mathrm{m}$ high, the cover of the barrel burst off the top of the barrel. Estimate the net force that caused the cover to come off.

Surjit Tewari

Numerade Educator

02:07

Problem 87

Experimentally determine the maximum distance you can suck water up a straw. Use this number to determine the pressure in your lungs above or below atmospheric pressure while you are sucking. Be sure to indicate any assumptions you made and show clearly how you reached your conclusion.

Samantha Baker

Numerade Educator

01:22

Problem 88

You can use an empty soda bottle with a cap to measure the depth to which you dive in the ocean. Dive to a certain depth, turn the closed bottle upside down (with the cap toward the sea bottom), and open the cap. A certain volume of seawater will enter the bottle, compressing the air that was trapped in it. Keep the bottle in an upside-down position and carefully close the bottle. Then swim up to the surface and measure the volume $V_{\text {water }}$ of water in the bottle and the total volume $V_{0}$ of the bottle. (a) Derive the expression for the depth to which you dived in terms of $V_{\text {waler }}, V_{0},$ and other relevant parameters. Indicate any assumptions that you made. Evaluate the expression using unit analysis and limiting case analysis.

Surendra Kumar

Numerade Educator

04:49

Problem 89

Justin is observing pearl-like strings of bubbles that move upward in his father's glass of champagne. He notices that as the bubbles rise, their volume increases (see Figure $\mathbf{P} 13.89$ ). He proposes the following explanation: "The pressure inside the bubble is equal to the pressure in the liquid surrounding the bubble. Because the pressure in the liquid decreases toward the surface of the liquid, the pressure in the ascending bubble decreases and therefore the volume of the bubble increases." Justin estimates that the size
of a bubble near the surface is approximately twice that of a bubble $10 \mathrm{cm}$ below the surface. Can Justin reject his explanation based on these data? Explain. If you answered yes, propose a different explanation that is consistent with the data and describe how you could test it. (Hint: Champagne contains dissolved carbon dioxide.)

Kudakwashe Mapiki

Numerade Educator

04:48

Problem 90

You have an empty water bottle. Predict how much mass you need to add to it to make it float half-submerged. Then add the calculated mass
and explain any discrepancy that you found. How did you make your prediction?

Prabhat Tyagi

Numerade Educator

04:37

Problem 91

A $1.0-\mathrm{kg}$ fish of density $1025 \mathrm{kg} / \mathrm{m}^{3}$ is in water of the same density. The fish's bladder contains $10 \mathrm{cm}^{3}$ of air. The bladder compresses to $4 \mathrm{cm}^{3} .$ Now what is the density of the fish? Will it sink or rise? Explain.

Surjit Tewari

Numerade Educator

05:50

Problem 92

When a $27,000-\mathrm{kg}$ fighter airplane lands on the deck of the aircraft carrier Nimitz, the carrier sinks $0.25 \mathrm{cm}$
deeper into the water. Determine the cross-sectional area of the carrier.

Surjit Tewari

Numerade Educator

04:00

Problem 93

Derive an equation for determining the unknown density of a liquid by measuring the magnitude of a force $T_{\mathrm{S}}$ on 0 that a string needs to exert on a hanging object of unknown mass $m$ and density $\rho$ to support it when the object is submerged in the liquid.

Surjit Tewari

Numerade Educator

04:20

Problem 94

Assuming Musimu weighs $670 \mathrm{N}(150 \mathrm{lb})$ and is $1.6 \mathrm{m}$ tall, $0.30 \mathrm{m}$ wide, and $0.15 \mathrm{m}$ thick, which answer below is closest to the magnitude of the force that the deep water exerted on one side of his body?
(a) 0
(b) $670 \mathrm{N}(130 \mathrm{lb})$
(c) $15,000 \mathrm{N}(3000 \mathrm{lb})$
(d) $10^{5} \mathrm{N}(20,000 \mathrm{lb})$
(e) $10^{6} \mathrm{N}(200,000 \mathrm{lb})$

Surjit Tewari

Numerade Educator

03:20

Problem 95

Musimu's training allows him to hold up to $9 \mathrm{L}=9000 \mathrm{cm}^{3}$ of air when in a 1 atm environment. Which answer below is closest to the volume of that
air if at pressure 22 atm?
(a) $100 \mathrm{cm}^{3}$
(b) $200 \mathrm{cm}^{3}$
(c) $400 \mathrm{cm}^{3}$
(d) $9000 \mathrm{cm}^{3}$
(e) $2 \times 10^{5} \mathrm{cm}^{3}$

Surjit Tewari

Numerade Educator

03:45

Problem 96

As Musimu descends, the buoyant force that the water exerts on him
(a) remains approximately constant.
(b) increases a lot because the pressure is so much greater.
(c) decreases significantly because his body is being compressed and made much smaller.
(d) is zero for the entire dive.
(c) There is not enough information to answer the question.

Surjit Tewari

Numerade Educator

03:12

Problem 97

Why don't his lungs, heart, and chest completely collapse?
(a) The return balloon helps counteract the external pressure.
(b) There is no external force pushing directly on the organs.
(c) The sled that helps him descend protects the front of his body.
(d) Blood plasma moves from his extremities to his chest and the organs in it.
(e) The air originally in the lungs is transferred to the vital organs.

Surjit Tewari

Numerade Educator

03:05

Problem 98

When is water densest?
(a) When liquid at $0^{\circ} \mathrm{C}$
(h) When solid ice at $0^{\circ} \mathrm{C}$
(c) When liquid at $4^{\circ} \mathrm{C}$
(d) Water density is always $1000.0 \mathrm{kg} / \mathrm{m}^{3}$.

Surjit Tewari

Numerade Educator

02:50

Problem 99

Why does water freeze from the top down?
(a) The denser water at $0^{\circ} \mathrm{C}$ sinks to the bottom of the lake.
(b) The less dense ice at $0^{\circ} \mathrm{C}$ rises above the liquid water at $0^{\circ} \mathrm{C}$.
(c) The denser water at $4^{\circ} \mathrm{C}$ sinks to the bottom of the lake.
(d) Because of both a and b
(e) Because of both b and c

Surjit Tewari

Numerade Educator

04:01

Problem 100

Using Newton's second law, expressions for buoyant force and other forces, and the densities of liquid and solid water at $0^{\circ} \mathrm{C}$, find the fraction of an iceberg or an ice cube that is under liquid water.
(a) 0.84
(b) 0.88
(c) 0.92
(d) 0.96
(c) 1.00

Surjit Tewari

Numerade Educator

02:36

Problem 101

A swimming pool at $0^{\circ} \mathrm{C}$ has a very large chunk of ice floating in it-like an iceberg in the ocean. When the ice melts, what happens to the level of the water at the edge of the pool?
(a) It rises.
(b) It stays the same.
(c) It drops.
(d) It depends on the size of the chunk.

Surjit Tewari

Numerade Educator

02:05

Problem 102

Which of the following is/are benefits of the temperature dependence of the density of water?
(a) Fish and plants can survive winters without being frozen.
(b) Over time, soil is formed from sedimentary rocks.
(c) Water pipes when frozen in the winter do not burst.
(d) Two of the above three
(e) All of the first three

Surjit Tewari

Numerade Educator