13 Liquids Questions & Answers

8/14/2019 13 Liquids Questions & Answers

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CHAPTER 13

Liquids

Summary of Terms

Pressure The ratio of force to the area over which that force is distributed: Liquidpressure = weight density depth

Buoyant force The net upward force that a fluid exerts on an immersed object.

Archimedesprinciple

An immersed body is buoyed up by a force equal to the weight of the fluid itdisplaces.

Principle of

flotation

A floating object displaces a weight of fluid equal to its own weight.

Pascals principle The pressure applied to a motionless fluid confined in a container istransmitted undiminished throughout the fluid.

Surface tension The tendency of the surface of a liquid to contract in area and thus to behave

like a stretched elastic membrane.

Capillarity The rise of a liquid in a fine, hollow tube or in a narrow space.

Review Questions

1. Give two examples of a fluid.

Pressure

2. Distinguish between force and pressure.

Pressure in a Liquid

3. What is the relationship between liquid pressure and the depth of a

liquid? Between liquid pressure and density?

4. If you swim beneath the surface in salt water, will the pressure be

greater than in freshwater at the same depth? Why or why not?

5. How does water pressure one meter below the surface of a small pond

compare with water pressure one meter below the surface of a hugelake?

6. If you punch a hole in a container filled with water, in what directiondoes the water initially flow outward from the container?

Buoyancy

7. Why does buoyant force act upward on an object submerged inwater?

8. Why is there no horizontal buoyant force on a submerged object?

9. How does the volume of a completely submerged object compare

with the volume of water displaced?

Archimedes Principle


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10. How does the buoyant force on a submerged object compare with the

weight of water displaced?

11. Distinguish between a submerged body and an immersed body.

12. What is the mass of 1 L of water? What is its weight in newtons?

13. If a 1-L container is immersed halfway into water, what is the volumeof water displaced? What is the buoyant force on the container?

What Makes an Object Sink or Float?

14. Is the buoyant force on a submerged object equal to the weight of theobject itself or equal to the weight of the fluid displaced by the

object?

15. There is a condition in which the buoyant force on an object doesequal the weight of the object. What is this condition?

16. Does the buoyant force on a submerged object depend on the volume

of the object or the weight of the object?

17. Fill in the blanks: An object denser than water will ______ in water.An object less dense than water will ______ in water. An object with

the same density of water will ____________ in water.

18. How is the density of a fish controlled? How is the density of a

submarine controlled?

Flotation

19. It was emphasized earlier that buoyant force does not equal an

objects weight but does equal the weight of displaced water. Now we

say buoyant force equals the objects weight. Isnt this a grandcontradiction? Explain.

20. What weight of water is displaced by a 100-ton ship? What is thebuoyant force that acts on a floating 100-ton ship?

Pascals Principle

21. What happens to the pressure in all parts of a confined fluid if the

pressure in one part is increased?

22. If the pressure in a hydraulic press is increased by an additional 10

N/cm2, how much extra load will the output piston support if its

cross-sectional area is 50 cm2

?

Surface Tension

23. What geometrical shape has the least surface area for a given

volume?

24. What is the cause of surface tension?

Capillarity


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25. Distinguish between adhesive and cohesive forces.

26. What determines how high water will climb in a capillary tube?

[previous page] [next page]Projects

1.Place an egg in a pan of tap water. Then dissolve salt in the water until the egg floats. Howdoes the density of an egg compare to that of tap water? To that of salt water?

2.If you punch a couple of holes in the bottom of a water-filled container, water will spurt out

because of water pressure. Now drop the container, and, as it freely falls, note that the water

no longer spurts out! If your friends dont understand this, could you figure it out and thenexplain it to them?

(Click image to enlarge)

3.Float a water-soaked Ping-Pong ball in a can of water held more than a meter above a rigidfloor. Then drop the can. Careful inspection will show the ball pulled beneath the surface as

both the ball and the can drop. (What does this say about surface tension?). Moredramatically, when the can makes impact with the floor, what happens to the ball, and why?

Try it and youll be astonished! (Caution: Unless youre wearing safety goggles, keep your

head away from above the can when it makes impact.)

4.Soap greatly weakens the cohesive forces between water molecules. You can see this byputting some oil in a bottle of water and shaking it so that the oil and water mix. Notice that

the oil and water quickly separate as soon as you stop shaking the bottle. Now add some

soap to the mixture. Shake the bottle again and you will see that the soap makes a fine filmaround each little oil bead and that a longer time is required for the oil to gather after you

stop shaking the bottle.This is how soap works in cleaning. It breaks the surface tension around each particle of

dirt so that the water can reach the particles and surround them. The dirt is carried away inrinsing. Soap is a good cleaner only in the presence of water.

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One-Step Calculations

Pressure = weight density depth

(Neglect the pressure due to the atmosphere in the calculations below.)

1. Calculate the water pressure at the bottom of the 100-m-high water

tower shown in Figure 13.2.

2. Calculate the water pressure at the base of a dam when the depth ofwater behind the dam is 100 m.

3. The top floor of a building is 50 m above the basement. Calculate how

much greater the water pressure is in the basement compared with the
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pressure at the top floor.

4. Water pressure at the bottom of a 1-m-tall closed barrel is 98 kPa.

What is the pressure at the bottom of the barrel when a 5-m pipe filled

with water is inserted into the top of the barrel?Exercises

1. What common liquid covers more than two-thirds of our planet,makes up 60% of our bodies, and sustains our lives and lifestyles in

countless ways?

2. Which is more likely to hurtbeing stepped on by a 200-lb man

wearing loafers or being stepped on by a 100-lb woman wearing high

heels?

3. Which do you suppose exerts more pressure on the groundanelephant or a lady standing on spike heels? (Which will be more likely

to make dents in a linoleum floor?) Approximate a rough calculation

for each.

4. Stand on a bathroom scale and read your weight. When you lift one

foot up so that youre standing on one foot, does the reading change?Does a scale read force or pressure?

5. Why are persons who are confined to bed less likely to develop

bedsores on their bodies if they use a waterbed rather than an ordinary

mattress?

6. You know that a sharp knife cuts better than a dull knife. Do youknow why this is so? Defend your answer.

7. If water faucets upstairs and downstairs are turned fully on, will more

water per second flow out of the upstairs faucets or the downstairsfaucets?

8. The photo shows physics instructor Marshall Ellenstein walkingbarefoot on broken glass bottles in his class. What physics concept is

Marshall demonstrating, and why is he careful that the broken pieces

are small and numerous? (The Band-Aids on his feet are for humor!)


9. Why does your body get more rest when youre lying down than itdoes when youre sitting? And why is blood pressure measured in the

upper arm, at the elevation of your heart? Is blood pressure in your


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legs greater?

10. When standing, blood pressure in your legs is greater than in your

upper body. Would this be true for an astronaut in orbit? Defend your

answer.

11. How does water pressure 1 meter beneath the surface of a lakecompare with water pressure 1 meter beneath the surface of a

swimming pool?

12. Which teapot holds more liquid?


13. The sketch shows a reservoir that supplies water to a farm. It is made

of wood and is reinforced with metal hoops. (a) Why is it elevated?

(b) Why are the hoops closer together near the bottom part of thetank?


14. A block of aluminum with a volume of 10 cm is placed in a beaker

of water filled to the brim. Water overflows. The same is done in

another beaker with a 10-cm3block of lead. Does the lead displacemore, less, or the same amount of water?

15. A block of aluminum with a mass of 1 kg is placed in a beaker of

water filled to the brim. Water overflows. The same is done in

another beaker with a 1-kg block of lead. Does the lead displace

more, less, or the same amount of water?


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16. A block of aluminum with a weight of 10 N is placed in a beaker of

water filled to the brim. Water overflows. The same is done inanother beaker with a 10-N block of lead. Does the lead displace

more, less, or the same amount of water? (Why are your answers to

this exercise and to Exercise 15 different from your answer to

Exercise 14?)

17. In 1960, the U.S. Navys bathyscaphe Trieste (a submersible)descended to a depth of nearly 11 kilometers in the Marianas Trench

near the Philippines in the Pacific Ocean. Instead of a large viewing

window, it was a small circular window 15 centimeters in diameter.What is your explanation for so small a window?

18. There is a story about Pascal in which it is said that he climbed a

ladder and poured a small container of water into a tall, thin, verticalpipe inserted into a wooden barrel full of water below. The barrel

burst when the water in the pipe reached about 12 m. This was all the

more intriguing because the weight of added water in the tube wasvery small. What two physical principles was Pascal demonstrating?

19. There is a legend of a Dutch boy who bravely held back the whole

North Sea by plugging a hole in a dike with his finger. Is this possible

and reasonable? (See also Problem 4.)

20. If youve wondered about the flushing of toilets on the upper floors of

city skyscrapers, how do you suppose the plumbing is designed sothat there is not an enormous impact of sewage arriving at the

basement level? (Check your speculations with someone who is

knowledgeable about architecture.)

21. Why does water seek its own level?

22. Suppose that you wish to lay a level foundation for a home on hilly

and bushy terrain. How can you use a garden hose filled with water todetermine equal elevations for distant points?

23. When you are bathing on a stony beach, why do the stones hurt yourfeet less when youre standing in deep water?

24. If liquid pressure were the same at all depths, would there be a

buoyant force on an object submerged in the liquid? Explain.

25. A can of diet soda floats in water, whereas a can of regular soda

sinks. Explain this phenomenon first in terms of density, then in terms

of weight versus buoyant force.

26. Why will a block of iron float in mercury but sink in water?

27. The mountains of the Himalayas are slightly less dense than the

mantle material upon which they float. Do you suppose that, like


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floating icebergs, they are deeper than they are high?

28. Why is a high mountain composed mostly of lead an impossibility on

the planet Earth?

29. How much force is needed to push a nearly weightless but rigid 1-L

carton beneath a surface of water?

30. Why will a volleyball held beneath the surface of water have morebuoyant force than if it is floating?

31. Why does an inflated beach ball pushed beneath the surface of waterswiftly shoot above the water surface when released?

32. Why is it inaccurate to say that heavy objects sink and that lightobjects float? Give exaggerated examples to support your answer.

33. Why is the buoyant force on a submerged submarine appreciably

greater than the buoyant force on it while it is floating?

34. A piece of iron placed on a block of wood makes it float lower in the

water. If the iron were instead suspended beneath the wood, would it

float as low, lower, or higher? Defend your answer.


35. Compared with an empty ship, would a ship loaded with a cargo ofStyrofoam sink deeper into the water or rise in the water? Defend

your answer.

36. If a submarine starts to sink, will it continue to sink to the bottom if

no changes are made? Explain.

37. A barge filled with scrap iron is in a canal lock. If the iron is thrown

overboard, does the water level at the side of the lock rise, fall, or

remain unchanged? Explain.

38. Would the water level in a canal lock go up or down if a battleship inthe lock sank?

39. Will a rock gain or lose buoyant force as it sinks deeper in water? Or


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will the buoyant force remain the same at greater depths? Defend

your answer.

40. Will a swimmer gain or lose buoyant force as she swims deeper in the

water? Or will her buoyant force remain the same at greater depths?

Defend your answer, and contrast it with your answer to Exercise 39.41. A balloon is weighted so that it is barely able to float in water. If it is

pushed beneath the surface, will it return to the surface, stay at the

depth to which it is pushed, or sink? Explain. (Hint: Does the

balloons density change?)


42. The density of a rock doesnt change when it is submerged in water,but your density changes when you are submerged. Explain.

43. In answering the question of why bodies float higher in salt water

than in freshwater, your friend replies that the reason is that salt wateris denser than freshwater. (Does your friend often answer questions

by reciting only factual statements that relate to the answers but dontprovide any concrete reasons?) How would you answer the same

question?

44. A ship sailing from the ocean into a freshwater harbor sinks slightly

deeper into the water. Does the buoyant force on the ship change? Ifso, does it increase or decrease?

45. Suppose that you are given the choice between two life preservers

that are identical in size, the first a light one filled with Styrofoam and

the second a very heavy one filled with gravel. If you submerge theselife preservers in the water, upon which will the buoyant force be

greater? Upon which will the buoyant force be ineffective? Why areyour answers different?

46. The weight of the human brain is about 15 N. The buoyant force

supplied by fluid around the brain is about 14.5 N. Does this mean

that the weight of fluid surrounding the brain is at least 14.5 N?


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Defend your answer.

47. The relative densities of water, ice, and alcohol are 1.0, 0.9, and 0.8,

respectively. Do ice cubes float higher or lower in a mixed alcoholic

drink? What comment can you make about a cocktail in which the ice

cubes lie submerged at the bottom of the glass?48. When an ice cube in a glass of water melts, does the water level in the

glass rise, fall, or remain unchanged? Does your answer change if the

ice cube has many air bubbles? How about if the ice cube contains

many grains of heavy sand?

49. When the wooden block is placed in the beaker, what happens to the

scale reading? Answer the same question for an iron block.


50. A half-filled bucket of water is on a spring scale. Will the reading ofthe scale increase or remain the same if a fish is placed in the bucket?

(Will your answer be different if the bucket is initially filled to the

brim?)

51. The weight of the container of water, as shown in a, is equal to the

weight of the stand and the suspended solid iron ball. When thesuspended ball is lowered into the water, as shown in b, the balance is

upset. Will the additional weight needed on the right side to restore

balance be greater than, equal to, or less than the weight of the solid

iron ball?


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52. If the gravitational field of the Earth were to increase, would a fish

float to the surface, sink, or stay at the same depth?

53. What would you experience when swimming in water in an orbiting

space habitat where simulated gravity is g? Would you float in

the water as you do on Earth?

54. We say that the shape of a liquid is that of its container. But, with no

container and no gravity, what is the natural shape of a blob of water?

Why?

55. If you release a Ping-Pong ball beneath the surface of water, it will

rise to the surface. Would it do the same if it were inside a big blob ofwater floating weightless in an orbiting spacecraft?

56. So youre on a run of bad luck, and you slip quietly into a small, quiet

pool as hungry crocodiles lurking at the bottom are relying on

Pascals principle to help them to detect atender morsel. What does

Pascals principle have to do with their delight at your arrival?

57. In the hydraulic arrangement shown, the larger piston has an area thatis fifty times that of the smaller piston. The strong man hopes to exert

enough force on the large piston to raise the 10 kg that rest on thesmall piston. Do you think he will be successful? Defend your

answer.


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58. In the hydraulic arrangement shown in Figure 13.22, themultiplication of force is equal to the ratio of the areas of the large

and small pistons. Some people are surprised to learn that the area of

the liquid surface in the reservoir of the arrangement shown in Figure13.23 is immaterial. What is your explanation to clear up this

confusion?

59. Why will hot water leak more readily than cold water through small

leaks in a car radiator?

60. On the surface of a pond, it is common to see water striders, insects

that can walk on the surface of water without sinking. What physicsconcept explains their ability?

[previous page] [next page]

2010 Pearson Education, Inc.

Problems

1. The depth of water behind the Hoover Dam in Nevada is 220 m. What

is the water pressure at the base of this dam? (Neglect the pressuredue to the atmosphere.)

2. A 6-kg piece of metal displaces 1 liter of water when submerged.What is its density?

3. A rectangular barge, 5 m long and 2 m wide, floats in freshwater. (a)Find how much deeper it floats when its load is a 400-kg horse. (b) If

the barge can only be pushed 15 cm deeper into the water before

water overflows to sink it, how many 400-kg horses can it carry?

4. A dike in Holland springs a leak through a hole of area 1 cm at adepth of 2 m below the water surface. How much force must a boy
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apply to the hole with his thumb to stop the leak? Could he do it?

5. A merchant in Kathmandu sells you a solid-gold 1-kg statue for a very

reasonable price. When you return home, you wonder whether or not

you got a bargain, so you lower the statue into a container of water

and measure the volume of displaced water. What volume will verifythat its pure gold?

6. When a 2.0-kg object is suspended in water, it masses 1.5 kg. What

is the density of the object?

7. An ice cube measures 10 cm on a side and floats in water. One cmextends above water level. If you shaved off the 1-cm part, how many

cm of the remaining ice would extend above water level?

8. A swimmer wears a heavy belt to make her average density exactlyequal to the density of water. Her mass, including the belt, is 60 kg.

(a) What is the swimmers weight in newtons? (b) What is the

swimmers volume in m3? (c) At a depth of 2 m below the surface of apond, what buoyant force acts on the swimmer? What net force acts

on her?

9. A vacationer floats lazily in the ocean with 90% of his body below the

surface. The density of the ocean water is 1,025 kg/m3. What is the

vacationers average density?

10. In the hydraulic pistons shown in the sketch, the small piston has a

diameter of 2 cm. The larger piston has a diameter of 6 cm. Howmuch more force can the larger piston exert compared with the force

applied to the smaller piston?

Solutions to Chapter 13 Exercises

1. Water.

2. Pressure would be appreciably greater by the woman, which would hurt you more.

3. A woman with spike heels exerts considerably more pressure on the ground than an elephant! Example: A 500-N woman with 1-cm

2spike heels puts half her weight on each foot, distributed (lets say) half on her heel and

half on her sole. So the pressure exerted by each heel will be (125 N/1 cm2) = 125 N/cm

2. A 20,000-N elephant

with 1000 cm2feet exerting

1/4its weight on each foot produces (5000N/1000 cm

2) = 5N/cm

2; about 25 times

less pressure. (So a woman with spike heels will make greater dents in a new linoleum floor than an elephant

will.)


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4. The scale measures force, not pressure, and is calibrated to read your weight. Thats why your weight on thescale is the same whether you stand on one foot or both.

5. There is less pressure with a waterbed due to the greater contact area.

6. A sharp knife cuts better than a dull knife because it has a thinner cutting area which results in more cutting

pressure for a given force.

7. More water will flow from a downstairs open faucet because of the greater pressure. Since pressure depends

on depth, the downstairs faucet is effectively deeper than the upstairs faucet. The pressure downstairs isgreater by an amount = weight density depth, where the depth is the vertical distance between faucets.

8. The concept of pressure is being demonstrated. He is careful that the pieces are small and numerous so thathis weight is applied over a large area of contact. Then the sharp glass provides insufficient pressure to cut the

feet.

9. Your body gets more rest when lying than when sitting or standing because when lying, the heart does not have

to pump blood to the heights that correspond to standing or sitting. Blood pressure is normally greater in the

lower parts of your body simply because the blood is deeper there. Since your upper arms are at the samelevel as your heart, the blood pressure in your upper arms will be the same as the blood pressure in your heart.

10. No, in orbit there are no pressure differences due to gravity.

11. Both are the same, for pressure depends on depth.

12. The water can be no deeper than the spouts, which are at the same height, so both teapots hold the same

amount of liquid.

13. (a) The reservoir is elevated so as to produce suitable water pressure in the faucets that it serves. (b) The

hoops are closer together at the bottom because the water pressure is greater at the bottom. Closer to the top,

the water pressure is not as great, so less reinforcement is needed there.

14. Both blocks have the same volume and therefore displace the same amount of water.


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15. A one-kilogram block of aluminum is larger than a one-kilogram block of lead. The aluminum therefore

displaces more water.

16. A 10-N block of aluminum is larger than a 10-N block of lead. The aluminum therefore displaces more water.Only in Exercise 10 were the volumes of the block equal. In this and the preceding exercise, the aluminumblock is larger. (These exercises serve only to emphasize the distinctions between volume, mass, and weight.)

17. The smaller the window area, the smaller the crushing force of water on it.

18. One, that water pressure depends on depth. The other, that the pressure due to the column of water is

transmitted to all parts of the barrel.

19. From a physics point of view, the event was quite reasonable, for the force of the ocean on his finger would

have been quite small. This is because the pressure on his finger has only to do with the depth of the water,

specifically the distance of the leak below the sea levelnot the weight of the ocean. For a numerical example,

see Problem 4.

20. A typical plumbing design involves short sections of pipe bent at 45-degree angles between vertical sections

two-stories long. The sewage therefore undergoes a succession of two-story falls which results in a moderate

momentum upon reaching the basement level.

21. Water seeking its own level is a consequence of pressure depending on depth. In a bent U-tube full of water, for

example, the water in one side of the tube tends to push water up the other side until the pressures at the same

depth in each tube are equal. If the water levels were not the same, there would be more pressure at a given

level in the fuller tube, which would move the water until the levels were equal.

22. The use of a water-filled garden hose as an elevation indicator is a practical example of water seeking its own

level. The water surface at one end of the hose will be at the same elevation above sea level as the water

surface at the other end of the hose.

23. In deep water, you are buoyed up by the water displaced and as a result, you dont exert as much pressureagainst the stones on the bottom. When you are up to your neck in water, you hardly feel the bottom at all.

24. Buoyant force is the result of differences in pressure; if there are no pressure differences, there is no buoyantforce. This can be illustrated by the following example: A Ping-Pong ball pushed beneath the surface of waterwill normally float back to the surface when released. If the container of water is in free fall, however, asubmerged Ping-Pong ball will fall with the container and make no attempt to reach the surface. In this casethere is no buoyant force acting on the ball because there are no pressure differences the local effects ofgravity are absent.


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25. The diet drink is less dense than water, whereas the regular drink is denser than water. (Water with dissolvedsugar is denser than pure water.) Also, the weight of the can is less than the buoyant force that would act on it iftotally submerged. So it floats, where buoyant force equals the weight of the can.

26. Mercury is more dense (13.6 g/cm3) than iron. A block of iron will displace its weight and still be partially

above the mercury surface. Hence it floats in mercury. In water it sinks because it cannot displace its weight.

27. Mountain ranges are very similar to icebergs: Both float in a denser medium, and extend farther down into that

medium than they extend above it. Mountains, like icebergs, are bigger than they appear to be. The concept of

floating mountains is isostacyArchimedes principle for rocks.28. A mostly-lead mountain would be more dense than the mantle and would sink in it. Guess where most of the

iron in the world is. In the Earths center!

29. The force needed will be the weight of 1 L of water, which is 9.8 N. If the weight of the carton is not negligible,

then the force needed would be 9.8 N minus the cartons weight, for then the carton would be helping to pushitself down.

30. When the ball is held beneath the surface, it displaces a greater weight of water.

31. The buoyant force on the ball beneath the surface is much greater than the force of gravity on the ball,

producing a large net force and large acceleration.

32. Heavy objects may or may not sink, depending on their densities (a heavy log floats while a small rock sinks, or

a boat floats while a paper clip sinks, for example). People who say that heavy objects sink really mean that

dense objects sink. Be careful to distinguish between how heavy an object is and how dense it is.

33. While floating, BF equals the weight of the submarine. When submerged, BF equals the submarines weightplus the weight of water taken into its ballast tanks. Looked at another way, the submerged submarine

displaces a greater weight of water than the same submarine floating.

34. The block of wood would float higher if the piece of iron is suspended below it rather than on top of it. By the law

of flotation: The iron-and-wood unit displaces its combined weight and the same volume of water whether theiron is on top or the bottom. When the iron is on the top, more wood is in the water; when the iron is on the

bottom, less wood is in the water. Or another explanation is that when the iron is belowsubmergedbuoyancy on it reduces its weight and less of the wood is pulled beneath the water line.

35. When a ship is empty its weight is least and it displaces the least water and floats highest. Carrying a load of

anything increases its weight and makes it float lower. It will float as low carrying a few tons of Styrofoam as it

will carrying the same number of tons of iron ore. So the ship floats lower in the water when loaded with


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Styrofoam than when empty. If the Styrofoam were outside the ship, below water line, then the ship would float

higher as a person would with a life preserver.

36. A sinking submarine will continue to sink to the bottom so long as the density of the submarine is greater thanthe density of the surrounding water. If nothing is done to change the density of the submarine, it will continue to

sink because the density of water is practically constant. In practice, water is sucked into or blown out of asubmarines tanks to adjust its density to match the density of the surrounding water.

37. The water level will fall. This is because the iron will displace a greater amount of water while being supported

than when submerged. A floating object displaces its weight of water, which is more than its own volume, while

a submerged object displaces only its volume. (This may be illustrated in the kitchen sink with a dish floating in

a dishpan full of water. Silverware in the dish takes the place of the scrap iron. Note the level of water at the

side of the dishpan, and then throw the silverware overboard. The floating dish will float higher and the water

level at the side of the dishpan will fall. Will the volume of the silverware displace enough water to bring the

level to its starting point? No, not as long as it is denser than water.)

38. For the same reason as in the previous exercise, the water level will fall. (Try this one in your kitchen sink also.

Note the water level at the side of the dishpan when a bowl floats in it. Tip the bowl so it fills and submerges,and youll see the water level at the side of the dishpan fall.)

39. Bouyant force will remain unchanged on the sinking rock because it displaces the same weight of water at any

depth.

40. Bouyant force on a sinking swimmer will decrease as she sinks. This is because her body, unlike the rock in the

previous exercise, will be compressed by the greater pressure of greater depths.

41. The balloon will sink to the bottom because its density increases with depth. The balloon is compressible, so the

increase in water pressure beneath the surface compresses it and reduces its volume, thereby increasing its

density. Density is further increased as it sinks to regions of greater pressure and compression. This sinking is

understood also from a buoyant force point of view. As its volume is reduced by increasing pressure as it

descends, the amount of water it displaces becomes less. The result is a decrease in the buoyant force that

initially was sufficient to barely keep it afloat.

42. You are compressible, whereas a rock is not, so when you are submerged, the water pressure tends to

squeeze in on you and reduce your volume. This increases your density. (Be careful when swimmingatshallow depths you may still be less dense than water and be buoyed to the surface without effort, but at

greater depths you may be pressed to a density greater than water and youll have to swim to the surface.)

43. A body floats higher in denser fluid because it does not have to sink as far to displace a weight of fluid equal to

its own weight. A smaller volume of the displaced denser fluid is able to match the weight of the floating body.

44. The buoyant force does not change. The buoyant force on a floating object is always equal to that objectsweight, no matter what the fluid.


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45. Since both preservers are the same size, they will displace the same amount of water when submerged and be

buoyed up with equal forces. Effectiveness is another story. The amount of buoyant force exerted on the heavy

gravel-filled preserver is much less than its weight. If you wear it, youll sink. The same amount of buoyant forceexerted on the lighter Styrofoam preserver is greater than its weight and it will keep you afloat. The amountof

the force and the effectivenessof the force are two different things.

46. No, there does not have to actually be 14.5 N of fluid in the skull to supply a buoyant force of 14.5 N on the

brain. To say that the buoyant force is 14.5 N is to say that the brain is taking up the space that 14.5 N of fluid

would occupy if fluid instead of the brain were there. The amount of fluid in excess of the fluid that immediately

surrounds the brain does not contribute to the buoyancy on the brain. (A ship floats the same in the middle of

the ocean as it would if it were floating in a small lock just barely larger than the ship itself. As long as there is

enough water to press against the hull of the ship, it will float. It is not important that the amount of water in this

tight-fitting lock weigh as much as the shipthink about that, and dont let a literal word explanation a floatingobject displaces a weight of fluid equal to its own weight and the idea it represents confuse you.)

47. Ice cubes will float lower in a mixed drink because the mixture of alcohol and water is less dense than water. In

a less dense liquid a greater volume of liquid must be displaced to equal the weight of the floating ice. In pure

alcohol, the volume of alcohol equal to that of the ice cubes weighs less than the ice cubes, and buoyancy is

less than weight and ice cubes will sink. Submerged ice cubes in a cocktail indicate that it is predominantly

alcohol.

48. When the ice cube melts the water level at the side of the glass is unchanged (neglecting temperature effects).

To see this, suppose the ice cube to be a 5 gram cube; then while floating it will displace 5 grams of water. But

when melted it becomes the same 5 grams of water. Hence the water level is unchanged. The same occurs

when the ice cube with the air bubbles melts. Whether the ice cube is hollow or solid, it will displace as much

water floating as it will melted. If the ice cube contains grains of heavy sand, however, upon melting, the waterlevel at the edge of the glass will drop. This is similar to the case of the scrap iron of Exercise 38.

49. The total weight on the scale is the same either way, so the scale reading will be the same whether or not the

wooden block is outside or floating in the beaker. Likewise for an iron block, where the scale reading shows the

total weight of the system.

50. If water doesnt overflow, the reading on the scale will increase by the ordinary weight of the fish. However, ifthe bucket is brim filled so a volume of water equal to the volume of the fish overflows, then the reading will not

change. We assume here that the fish and water have the same density.

51. When the ball is submerged (but not touching the bottom of the container), it is supported partly by the buoyant

force on the left and partly by the string connected to the right side. So the left pan must increase its upward

force to provide the buoyant force in addition to whatever force it provided before, and the right pans upwardforce decreases by the same amount, since it now supports a ball lighter by the amount of the buoyant force. To

bring the scale back to balance, the additional weight that must be put on the right side will equal twice the

weight of water displaced by the submerged ball. Why twice? Half of the added weight makes up for the loss of


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upward force on the right, and the other half for the equal gain in upward force on the left. (If each side initially

weighs 10 N and the left side gains 2 N to become 12 N, the right side loses 2 N to become 8 N. So an

additional weight of 4 N, not 2 N, is required on the right side to restore balance.) Because the density of water

is less than half the density of the iron ball, the restoring weight, equal to twice the buoyant force, will still be

less than the weight of the ball.

52. If the gravitational field of the Earth increased, both water and fish would increase in weight and weight densityby the same factor, so the fish would stay at its prior level in water.

53. Both you and the water would have half the weight density as on Earth, and you would float with the same

proportion of your body above the water as on Earth. Water splashed upward with a certain initial speed would

rise twice as high, since it would be experiencing only half the gravity force. Waves on the water surface wouldmove more slowly than on Earth (at about 70% as fast since vwave~g).

54. Because of surface tension, which tends to minimize the surface of a blob of water, its shape without gravity

and other distorting forces will be a spherethe shape with the least surface area for a given volume.

55. A Ping-Pong ball in water in a zero-g environment would experience no buoyant force. This is because

buoyancy depends on a pressure difference on different sides of a submerged body. In this weightless state, no

pressure difference would exist because no water pressure exists. (See the answer to Exercise 20, and Home

Project 2.)

56. Part of whatever pressure you add to the water is transmitted to the hungry crocodiles, via Pascals princip le. Ifthe water were confined, that is, not open to the atmosphere, the crocs would receive every bit of pressure you

exert. But even if you were able to slip into the pool to quietly float without exerting pressure via swimmingstrokes, your displacement of water raises the water level in the pool. This ever-so-slight rise, and

accompanying ever-so-slight increase in pressure at the bottom of the pool, is an ever-so-welcome signal to the

hungry crocodiles.

57. The strong man will be unsuccessful. He will have to push with 50 times the weight of the 10 kilograms. The

hydraulic arrangement is arranged to his disadvantage. Ordinarily, the input force is applied against the smaller

piston and the output force is exerted by the large pistonthis arrangement is just the opposite.

58. In Figure 13.21, the increased pressure in the reservoir is a result of the applied force distributed over the input

piston area. This increase in pressure is transmitted to the output piston. In Figure 13.23, however, the pressure

increase is supplied by the mechanical pump, which has nothing to do with the area of fluid interface between

the compressed air and the liquid.

59. When water is hot, the molecules are moving more rapidly and do not cling to one another as well as when they

are slower moving, so the surface tension is less. The lesser surface tension of hot water allows it to pass more

readily through small openings.


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60. Surface tension accounts for the walking of water striders, needles that appear to float, and even razor blades

that also appear to float. In these cases the weights of the objects are less than the restoring forces in the water

surface that tends to resist stretching.


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Chapter 13 Problem Solutions

1. Pressure = weight density depth = 10,000 N/m3220 m = 2,200,000 N/m

2=2200 kPa (or for density = 9800N/m

3, pressure = 2160 kPa.

2. Density = m/V = 6 kg/1 liter = 6 kg/liter. (Since there are 1000 liters in 1 cubic meter, density may be

expressed in units kg/m3. Density = 6 kg/1 liter 1000 liter/m

3= 6000 kg/m

3, six times the density of

water.)

3. (a) The volume of the extra water displaced will weigh as much as the 400-kg horse. And the volume of extrawater displaced will also equal the area of the barge times the extra depth. That is,

V = Ah, whereAis the horizontal area of the barge; Then h =V

A .

Now A = 5m 2m = 10 m2

; to find the volume V of barge pushed into the water by the horses weight, whichequals the volume of water displaced, we know that

density =mV

. Or from this, V=m

density =

400kg

1000kg/m3 = 0.4 m3.

So h =V

A =

0.4 m3

10 m2 = 0.04 m, which is 4 cm deeper.

(b) If each horse will push the barge 4 cm deeper, the question becomes: How many 4-cm increments will

make 15 cm? 15/4 = 3 .75, so 3 horses can be carried without sinking. 4 horseswill sink the barge.

4. First you must find the pressure. It is weight density depth = (10,000 N/m3)(2 m) = 20,000 N/m

2, or 20,000

Pa. Force is pressure area, and 1 cm2 = 10

-4 m

2, so F = (20,000 N/m

2)(10

-4m

2) = 2 N. It would be

easy for the boy to exert this force. It is about the weight of a notebook or a small box of cereal. (Note: Air

pressure is not figured into this calculation because its effect in pushing down on the water from above is

canceled by its effect in pushing from outside the hole against the leaking water.)

5. From Table 12.1 the density of gold is 19.3 g/cm3. Your gold has a mass of 1000 grams, so

1000 gV

= 19.3

g/cm

3

. Solving for V,

V =1000 g

19.3 g/cm3 = 51.8 cm

3.

6. Density =mass

volume =

2.0 kgvolume of (2.0 - 1.5) kg of water

=2.0 kg0.5 l


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= 4 kg/liter. And since 1 liter = 103cm

3= 10

-3m

3, density = 4,000 kg/m

3.

(Or this can be reasoned as follows: The buoyant force on the object is the force needed to support 0.5 kg, so

0.5 kg of water is displaced. Since density is mass/volume, volume is mass/density, and displaced volume =

(0.5 kg)/(1000 kg/m3) = 5 10

-4m3. The objects volume is the same as the volume it displaces, so the objects

density is mass/volume =

(2 kg)/(5 10-4

m3) = 4000 kg/m

3, four times the density of water.)

7. 10% of ice extends above water. So 10% of the 9-cm thick ice would float above the water line; 0.9 cm. So the

ice pops up. Interestingly, when mountains erode they become lighter and similarly pop up! Hence it takes a

long time for mountains to wear away.


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8. (a) Weight = mg= (60 kg)(10 m/s2) = 600 N(or 588 N if 9.8 m/s

2is used).

(b) She has the same density as water, 1000 kg/m3. Since density = mass/volume, volume = mass/density, so

volume = (60 kg)/(1000 kg/m3) = 0.06 m

3.

(c) Buoyant force = weight of water displaced = 600 N (or 588 N). Her weight balances the buoyant force, so net

force = 0.

9. The displaced water, with a volume 90 percent of the vacationers volume, weighs the same as the vacationer(to provide a buoyant force equal to his weight). Therefore his density is 90 percent of the waters density.Vacationers density = (0.90)(1,025 kg/m3) = 923 kg/m3.

10. The relative areas are as the squares of the diameters; 62/2

2= 36/4 = 9. The larger piston can lift 9 times the

input force to the smaller piston.

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