?Archimedes’ PrincipleThe Falkirk Wheel in Scotland (Figure 5.17) rotates with the same

Give two examples of a fluid.

Density What happens to the volume of a loaf of bread that is squeezed? What happens to the mass of the squeezed bread? What happens to the density of the squeezed bread?

Density Distinguish between mass density and weight density.

Pressure Distinguish between force and pressure. Compare their units of measurement.

Pressure How does the pressure exerted by a liquid change with depth of the liquid? How does the pressure exerted by a liquid change as the density of the liquid changes?

Pressure Ignoring the pressure of the atmosphere, if you swim twice as deep beneath the water surface, how much more water pressure is exerted on your ears? If you swim in salt water, is the pressure greater than in fresh water at the same depth?

Pressure How does water pressure 1 m below the surface of a small pond compare to water pressure 1 m below the surface of a huge lake?

Pressure If you punch a hole in the side of a container filled with water, in what direction does the water initially flow outward from the container?

Buoyancy in a Liquid Why does buoyant force act upward on an object submerged in water?

Buoyancy in a Liquid How does the volume of a completely submerged object compare with the volume of water displaced?

Archimedes’ Principle State Archimedes’ principle.

Archimedes’ Principle What is the difference between being immersed and being submerged?

Archimedes’ Principle How does the buoyant force on a fully submerged object compare with the weight of water displaced?

Archimedes’ Principle What is the mass in kilograms of 1 L of water? What is its weight in newtons?

Archimedes’ Principle If a 1-L container is immersed halfway in water, what is the volume of water displaced? What is the buoyant force on the container?

Archimedes’ Principle Does the buoyant force on a floating object depend on the weight of the object or on the weight of the fluid displaced by the object? Or are these two weights the same for the special case of floating? Defend your answer.

Archimedes’ Principle What weight of water is displaced by a 100-ton floating ship? What is the buoyant force that acts on this ship?

Pressure in a Gas By how much does the density of air increase when it is compressed to half its volume?

Pressure in a Gas What happens to the air pressure inside a balloon when the balloon is squeezed to half its volume at constant temperature?

Atmospheric Pressure What is the approximate mass in kilograms of a column of air that has a cross-sectional area of 1 \(\mathrm{cm}^{2}\) and extends from sea level to the upper atmosphere? What is the approximate weight in newtons of this amount of air? Text Transcription: cm^2

Atmospheric Pressure How does the downward pressure of the 76-cm column of mercury in a barometer compare with the air pressure at the bottom of the atmosphere?

Atmospheric Pressure How does the weight of mercury in a barometer tube compare with the weight of an equal cross section of air from sea level to the top of the atmosphere?

Atmospheric Pressure Why would a water barometer have to be 13.6 times as tall as a mercury barometer?

Atmospheric Pressure When you drink liquid through a straw, is it more accurate to say that the liquid is pushed up the straw rather than sucked up? What exactly does the pushing? Defend your answer.

Pascal’s Principle What happens to the pressure in all parts of a confined fluid when the pressure in one part is increased?

Pascal’s Principle Does Pascal’s principle provide a way to get more energy from a machine than is put into it? Defend your answer.

Buoyancy in a Gas A balloon that weighs 1 N is suspended in air, drifting neither up nor down. How much buoyant force acts upon it? What happens if the buoyant force decreases? If the buoyant force increases?

Bernoulli’s Principle What are streamlines? Is pressure greater or less in regions of crowded streamlines?

Bernoulli’s Principle Does Bernoulli’s principle refer to internal pressure changes in a fluid, to pressures that a fluid can exert on objects in the path of the flowing fluid, or to both?

Bernoulli’s Principle What do peaked roofs, convertible tops, and airplane wings have in common when air moves faster across their top surfaces?

Try to float an egg in water. Then dissolve salt in the water until the egg floats. How does the density of an egg compare to that of tap water? To that of salt water?

Punch a couple of holes in the bottom of a water-filled container, and water spurts 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 don’t understand this, could you explain it to them?

Place a wet Ping-Pong ball in a can of water held high above your head. Then drop the can on a rigid floor. Because of surface tension, the ball is pulled beneath the surface as the can falls. What happens when the can comes to an abrupt stop is worth watching!

Try this in the bathtub or when you’re washing dishes: Lower a drinking glass, mouth downward, over a small floating object such as a Ping-Pong ball. What do you observe? How deep must the glass be pushed in order to compress the enclosed air to half its volume? (You won’t be able to do this in your bathtub unless it’s 10.3 m deep!)

Compare the pressure exerted by the tires of your car on the road with the air pressure in the tires. For this project, you need to obtain your car’s weight (from the Internet) and then divide by 4 to get the approximate weight supported by one tire. You can closely approximate the area of contact of a tire with the road by tracing the edges of tire contact on a sheet of paper marked with 1-inch squares beneath the tire. After you get the pressure of the tire on the road, compare it with the air pressure in the tire. Are they nearly equal? Which one is greater?

You ordinarily pour water from a full glass into an empty glass simply by placing the full glass above the empty glass and tipping. Have you ever poured air from one glass to another? The procedure is similar. Lower two glasses in water, mouths downward. Let one fill with water by tilting its mouth upward. Then hold the mouth of the water filled glass downward above the air-filled glass. Slowly tilt the lower glass and let the air escape, filling the upper glass. You are pouring air from one glass into another!

Raise a filled glass of water above the waterline, but with its mouth beneath the surface. Why does the water not flow out? How tall would a glass have to be before water began to flow out? (You won’t be able to do this indoors unless you have a ceiling that is at least 10.3 m higher than the waterline.)

Place a card over the open top of a glass filled to the brim with water, and then invert it. Why does the card stay in place? Try it sideways.

Invert a water-filled soft-drink bottle or small-necked jar. Notice that the water doesn’t simply fall out, but instead gurgles out of the container. Air pressure doesn’t allow the water out until some air has pushed its way up inside the bottle to occupy the space above the liquid. How would an inverted, water-filled bottle pour out if you tried this on the Moon?

Do as Professor Dan Johnson does and pour about a quarter cup of water into a gallon or 5-liter metal can with a screw top. Place the can open on a stove, and heat it until the water boils and steam comes out of the opening. Quickly remove the can and screw the cap on tightly. Allow the can to stand. Steam inside condenses, which can be hastened by cooling the can with a dousing of cold water. What happens to the vapor pressure inside? (Don’t do this with a can you expect to use again.)

Heat a small amount of water to boiling in an aluminum soft-drink can and invert it quickly into a dish of cold water. What happens is surprisingly dramatic!

Make a small hole near the bottom of an open tin can. Fill the can with water, which then proceeds to spurt from the hole. If you cover the top of the can firmly with the palm of your hand, the flow stops. Explain.

Lower a narrow glass tube or drinking straw into water and place your finger over the top of the tube. Lift the tube from the water and then lift your finger from the top of the tube. What happens? (You’ll do this often in chemistry experiments.)

Push a pin through a small card and place it over the hole of a thread spool. Try to blow the card from the spool by blowing through the hole. Try it in all directions.

Hold a spoon in a stream of water as shown and feel the effect of the differences in pressure.

Neglect the pressure due to the atmosphere in the calculations that follow. A 1-m-tall barrel is filled with water (with a weight density of \(9800 \mathrm{~N} / \mathrm{m}^{3}\) ). Show that the water pressure on the bottom of the barrel is \(9800 \mathrm{~N} / \mathrm{m}^{2}\) , or, equivalently, 9.8 kPa. Text Transcription: 9800 N/m^3 9800 N/m^2

Neglect the pressure due to the atmosphere in the calculations that follow. Show that the water pressure at the bottom of the 50-m-high water tower in Figure 5.3 is \(490,000 \mathrm{~N} / \mathrm{m}^{2}\) , which is approximately 500 kPa. Text Transcription: 490,000 N/m^2

Neglect the pressure due to the atmosphere in the calculations that follow. The depth of water behind the Hoover Dam is 220 m. Show that the water pressure at the base of this dam is 2160 kPa.

Neglect the pressure due to the atmosphere in the calculations that follow. The top floor of a building is 20 m above the basement. Show that the water pressure in the basement is nearly 200 kPa greater than the water pressure on the top floor.

Suppose that you balance a 2-kg ball on the tip of your finger, which has an area of \(1 \mathrm{~cm}^{2}\) . Show that the pressure on your finger is \(20 \mathrm{~N} / \mathrm{cm}^{2}\) , which is 200 kPa. Text Transcription: 1 cm^2 20 N/cm^2

A 12-kg piece of metal displaces 2 L of water when submerged. Show that its density is \(6000 \mathrm{~kg} / \mathrm{m}^{3}\) . How does this compare with the density of water? Text Transcription: 6000 kg/m^3

A 1-m-tall barrel is closed on top except for a thin pipe extending 5 m up from the top. When the barrel is filled with water up to the base of the pipe (1 m deep) the water pressure on the bottom of the barrel is 9.8 kPa. What is the pressure on the bottom when water is added to fill the pipe to its top?

A rectangular barge, 5 m long and 2 m wide, floats in fresh water. Suppose that a 400-kg crate of auto parts is loaded onto the barge. Show that the barge floats 4 cm deeper.

Suppose that the barge in the preceding problem can be pushed only 15 cm deeper into the water before the water overflows to sink it. Show that it could carry three, but not four, 400-kg crates.

A merchant in Kathmandu sells you a 1-kg solid gold statue for a very reasonable price. When you arrive home, you wonder whether you got a bargain, so you lower the statue into a container of water and measure the volume of displaced water. Show that for 1 kg of pure gold, the volume of water displaced is \(51.8 \mathrm{~cm}^{3}\) . Text Transcription: 51.8 cm^3

A vacationer floats lazily in the ocean with 90% of her body below the surface. The density of the ocean water is \(1025 \mathrm{~kg} / \mathrm{m}^{3}\) . Show that the vacationer’s average density is \(923 \mathrm{~kg} / \mathrm{m}^{3}\) . Text Transcription: 1025 kg/m^3 923 kg/m^3

Your friend of mass 100 kg can just barely float in fresh water. Calculate her approximate volume.

In the hydraulic pistons shown, the smaller piston has a diameter of 2 cm. The larger piston has a diameter of 6 cm. How much more force can the larger piston exert compared with the force applied to the smaller piston?

On a perfect fall day, you are hovering at rest at low altitude in a hot-air balloon. The total weight of the balloon, including its load and the hot air in it, is 20,000 N. Show that the volume of the displaced air is about \(1700 \mathrm{~m}^{3}\) . Text Transcription: 1700 m^3

What change in pressure occurs in a party balloon that is squeezed to one-third its volume with no change in temperature?

A mountain climber of mass 80 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your legendary physics skills, he asks you. Share with him your calculations that show the volume of the balloon to be about \(17 \mathrm{~m}^{3}\) (slightly more than 3 m in diameter for a spherical balloon). Text Transcription: 17 m^3

The weight of the atmosphere above 1 square meter of Earth’s surface is about 100,000 N. Density, of course, becomes less with altitude. But suppose the density of air were a constant \(1.2 \mathrm{~kg} / \mathrm{m}^{3}\) . Calculate where the top of the atmosphere would be. How does this compare with the nearly 40-km-high upper part of the atmosphere? Text Transcription: 1.2 kg/m^3

The wings of a certain airplane have a total bottom surface area of \(100 \mathrm{~m}^{2}\) . At a particular speed, the difference in air pressure below and above the wings is 4% of atmospheric pressure. Show that the lift on the airplane is \(4 \times 10^{5} \mathrm{~N}\) Text Transcription: 100 m^2 4 times 10^5 N

Rank the following from most to least: (a) The pressure at the bottom of a 20-cm-tall container of salt water. (b) The pressure at the bottom of a 20-cm-tall container of fresh water. (c) The pressure at the bottom of a 5-cm-tall container of mercury

Rank, from most to least, the percentage of volume above the water line for: (a) A basketball floating in fresh water. (b) A basketball floating in salt water. (c) A basketball floating in mercury.

Think about what happens to the volume of an air-filled balloon on top of water, and what happens to its volume beneath the water. Then rank, from most to least, the buoyant force on a weighted balloon in water when it is: (a) Barely floating with its top at the surface. (b) Pushed 1 m beneath the surface. (c) 2 m beneath the surface.

Rank, from greatest to least, the volumes of air in the glass when it is held: (a) Near the surface, as shown in the figure. (b) 1 m beneath the surface. (c) 2 m beneath the surface.

Rank, from greatest to least, the buoyant forces supplied by the atmosphere for: (a) An elephant. (b) A helium filled party balloon. (c) A skydiver at terminal velocity.

Rank, from greatest to least, the amounts of lift on the following airplane wings. (a) Area \(1000 \mathrm{~m}^{2}\) with atmospheric pressure difference of \(2.0 \mathrm{~N} / \mathrm{m}^{2}\) . (b) Area \(800 \mathrm{~m}^{2}\) with atmospheric pressure difference of \(2.4 \mathrm{~N} / \mathrm{m}^{2}\) . (c) Area \(600 \mathrm{~m}^{2} \mathrm{v}\) with atmospheric pressure difference of \(3.8 \mathrm{~N} / \mathrm{m}^{2}\) . Text Transcription: 1000 m^2 2.0 N/m^2 800 m^2 2.4 N/m^2 600 m^2 v 3.8 N/m^2

Density When you squeeze a party balloon between your hands, what happens to the mass of the balloon? To its volume? To its density?

Density A can of diet soft drink floats in water, whereas a can of regular soft drink sinks. Discuss this phenomenon first in terms of density, then in terms of weight versus buoyant force.

Density The density of a rock doesn’t change when it is submerged in water. Does your density change when you are submerged in water? Discuss and defend your answer.

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

Pressure Which is more likely to hurt—being stepped on by a 200-lb man wearing loafers or being stepped on by a 100-lb woman wearing high heels?

Pressure Stand on a bathroom scale and read your weight. When you lift one foot up so that you’re standing on one foot, does the reading change? Does a scale read force or pressure?

Pressure Why are people who are confined to bed less likely to develop bedsores on their bodies if they use a waterbed rather than a standard mattress?

Pressure If water faucets upstairs and downstairs are turned fully on, does more water per second flow out the downstairs faucet? Or is the volume of water flowing from the faucets the same?

Buoyancy in a Liquid 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?

Buoyancy in a Liquid How much force is needed to push a nearly weightless but rigid 1-L carton beneath a surface of water?

Buoyancy in a Liquid Why is it inaccurate to say that heavy objects sink and that light objects float? Give exaggerated examples to support your answer.

Buoyancy in a Liquid Why does an inflated beach ball pushed beneath the surface of water swiftly shoot above the water surface when released?

Buoyancy in a Liquid A half-filled bucket of water is on a spring scale. Does the reading of the scale increase or remain the same when a fish is placed in the bucket? (Is your answer different if the bucket is initially filled to the brim?

Buoyancy in a Liquid When a wooden block is placed in a beaker that is brim full of water, what happens to the scale reading after water has overflowed? Answer the same question for an iron block.

Archimedes’ Principle Why will a block of iron float in mercury but sink in water?

Archimedes’ Principle Why does a volleyball that is held beneath the surface of water have more buoyant force than a volleyball that is floating?

Archimedes’ Principle The mountains of the Himalayas are slightly less dense than the mantle material upon which they “float.” Do you suppose that, like floating icebergs, they are deeper than they are high?

Archimedes’ Principle Give a reason why canal enthusiasts in Scotland appreciate the physics illustrated in Figure 5.16 (the block of wood floating in a vessel brim-filled with water).

Archimedes’ Principle The Falkirk Wheel in Scotland (Figure 5.17) rotates with the same low energy no matter what the weight of the boats it lifts. What would be different in its operation if, instead of carrying floating boats, it carried scrap metal that doesn’t float?

Archimedes’ Principle One gondola in the Falkirk Wheel carries a 50-ton boat, while the opposite gondola carries a 100-ton boat. Why do the gondolas nevertheless weigh the same?

Archimedes’ Principle Both a 50-ton boat and a 100-ton boat float side by side in the gondola of the Falkirk Wheel, while the opposite gondola carries no boats at all. Why do the gondolas nevertheless weigh the same?

Archimedes’ Principle A ship sailing from the ocean into a fresh-water harbor sinks slightly deeper into the water. Does the buoyant force on it change? If so, does it increase or decrease?

Archimedes’ Principle In a sporting goods store, you see what appear to be two identical life preservers of the same size. One is filled with Styrofoam and the other one with lead pellets. If you submerge these life preservers in the water, upon which is the buoyant force greater? Upon which is the buoyant force ineffective? Why are your answers different?

Pressure in a Gas Why is the pressure in an automobile’s tires slightly greater after the car has been driven several kilometers?

Pressure in a Gas How does the density of air in a deep mine compare with the air density at Earth’s surface?

Pressure in a Gas The “pump” in a vacuum cleaner is merely a high-speed fan. Would a vacuum cleaner pick up dust from a rug on the Moon? Explain.

Atmospheric Pressure It is said that a gas fills all the space available to it. Why, then, doesn’t the atmosphere go off into space?

Atmospheric Pressure Why is there no atmosphere on the Moon?

Atmospheric Pressure We can understand how pressure in water depends on depth by considering a stack of bricks. The pressure below the bottom brick is determined by the weight of the entire stack. Halfway up the stack, the pressure is half, because the weight of the bricks above is half. To explain atmospheric pressure, we should consider compressible bricks, like foam rubber. Why is this so?

Atmospheric Pressure If you could somehow replace the mercury in a mercury barometer with a denser liquid, would the height of the liquid column be greater or less than with mercury? Why?

Atmospheric Pressure Would it be slightly more difficult to draw soda through a straw at sea level or on top of a very high mountain? Explain.

Atmospheric Pressure Richard’s pump can operate at a certain maximum well depth in Pocatello, Idaho. Would this maximum depth be greater than, less than, or the same as if he pumps water in San Francisco?

Atmospheric Pressure Why is it so difficult to breathe when snorkeling at a depth of 1 m, and practically impossible at a depth of 2 m? Why can’t a diver simply breathe through a hose that extends to the surface?

Pascal’s Principle Say you’ve had a run of bad luck, and you slip quietly into a small, calm pool as hungry crocodiles lurking at the bottom are relying on Pascal’s principle to help them to detect a tender morsel. What does Pascal’s principle have to do with their delight at your arrival?

Pascal’s Principle In the hydraulic arrangement shown, the larger piston has an area that is 50 times that of the smaller piston. The strong man hopes to exert enough force on the large piston to raise the 10-kg block that rests on the small piston. Do you think he will be successful? Defend your answer.

Pascal’s Principle Why will the strong man in the previous exercise be more successful in lifting the 10-kg block if he switches places and pushes down on the smaller piston with the block on the larger piston?

Buoyancy in a Gas Your friend says that the buoyant force of the atmosphere on an elephant is significantly greater than the buoyant force of the atmosphere on a small helium-filled balloon. What do you say?

Buoyancy in a Gas When you replace helium in a balloon with hydrogen, which is less dense? Does the buoyant force on the balloon change if the balloon remains the same size? Explain.

Buoyancy in a Gas A steel tank filled with helium gas doesn’t rise in air, but a balloon containing the same gas easily does. Why?

Buoyancy in a Gas Two identical balloons of the same volume are pumped up with air to more than atmospheric pressure and suspended on the ends of a stick that is horizontally balanced. One of the balloons is then punctured. Is there a change in the stick’s balance? If so, which way does it tip?

Bernoulli’s Principle The force of the atmosphere at sea level against the outside of a 10-\(m^{2}\) store window is about 1 million N. Why does this not shatter the window? Why might the window shatter in a strong wind blowing past the window? Text Transcription: m^2

Bernoulli’s Principle How will two dangling vertical sheets of paper move when you blow between them? Try it and see.

Bernoulli’s Principle When a steadily flowing gas flows from a larger-diameter pipe to a smaller-diameter pipe, what happens to (a) its speed, (b) its pressure, and (c) the spacing between its streamlines?

Bernoulli’s Principle What physics principle underlies the following three observations? When passing an oncoming truck on the highway, your car tends to sway toward the truck. The canvas roof of a convertible automobile bulges upward when the car is traveling at high speeds. The windows of older passenger trains sometimes break when a high speed train passes by on the next track.

Bernoulli’s Principle How does an airplane adjust its angle of attack so that it is able to fly upside down?

The photo shows physics teacher Marshall Ellenstein walking barefoot on broken glass bottles in his class. What physics concept is Marshall demonstrating, and why is he careful to ensure that the broken pieces are small and numerous? (The Band-Aids on his feet are for humor!)

Why is blood pressure measured in the upper arm, at the elevation of your heart?

Which teapot holds more liquid?

Suppose 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 to determine equal elevations for distant points?

If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Discuss your explanation with your friends.

Compared to an empty ship, would a ship loaded with a cargo of Styrofoam sink deeper or less deeply into water? Discuss and defend your answer.

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? Discuss your explanation with your discussion group.

A discussion of the following question raises some eyebrows: Why is the buoyant force on a submerged submarine appreciably greater than the buoyant force on it while it is floating?

A balloon is weighted so that it is barely able to float in water. If it is pushed beneath the surface, does it rise back to the surface, stay at the depth to which it is pushed, or sink? Discuss your explanation. (Hint: Does the balloon’s density change?)

Greta Novak is treated to remarkable flotation in the very-salty Dead Sea. How does buoyant force on her compare when she is floating in fresh water? In answering this question, discuss differences between the volumes of water displaced in the two cases.

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 contains many air bubbles? Discuss whether or not your answer changes if the ice cube contains many grains of heavy sand.

Count the tires on a large tractor-trailer that is unloading food at your local supermarket, and you may be surprised to count 18 tires. Why so many tires? (Hint: See Activity 35.)

Two teams of eight horses each were unable to pull the Magdeburg hemispheres apart (Figure 5.20). Why? Suppose two teams of nine horses each could pull them apart. Then would one team of nine horses succeed if the other team were replaced with a strong tree? Discuss and defend your answer.

In the classroom demonstration at Lund University, a vacuum pump evacuates air from a large, empty oil drum, which slowly and dramatically crumples as shown. A student friend says that the vacuum sucks in the sides of the drum. What is your explanation?

If you bring an airtight bag of potato chips aboard an airplane, you’ll note that it puffs up as the plane ascends to high altitude. Why?

On a sensitive balance, weigh an empty, flat, thin plastic bag. Then weigh the bag filled with air. Will the readings differ? Explain.

Invoking ideas from Chapter 2 and this chapter, discuss why is it easier to throw a curve with a tennis ball than with a baseball.

Your study partner says he doesn’t believe in Bernoulli’s principle and cites as evidence the fact that a stream of water can knock over a building. The pressure that the water exerts on the building is not reduced, as Bernoulli claims. What distinction is your partner missing?