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

How does pressure at the bottom of a body of water relate to the weight of water above each square meter of the bottom surface?

What is the relationship between liquid pressure and the depth of a liquid? Between liquid pressure and weight density?

If you swim beneath the surface in saltwater, will the pressure be greater than in fresh water at the same depth?

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

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

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

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

Why isn’t there a horizontal buoyant force on a submerged object?

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

Distinguish between an immersed and a submerged body.

What is the mass of 1 L of water? Its weight in newtons?

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

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

What is the condition in which the buoyant force on an object does equal the weight of the object?

Does the buoyant force on a submerged object depend on the volume of the object or on the weight of the object?

How is the density of a fish controlled? How is the density of a submarine controlled?

Fill in the blanks: An object denser than water will ________ in water. An object less dense than water will ________ in water. An object that has the same density as water will ________ in water.

It was emphasized earlier that the buoyant force does not equal an object’s weight but does equal the weight of the displaced water. Now we say that the buoyant force equals the object’s weight. Isn’t this a grand contradiction? Explain.

Why do the gondolas of the Falkirk Wheel (see Figure 13.19) have the same weight whether or not they carry boats?

What happens to the pressure in all parts of a confined fluid if the pressure in one part is increased?

What geometrical shape has the smallest surface area for a given volume?

If the pressure in a hydraulic press is increased by an additional \(10\mathrm{\ N}/\mathrm{cm}^2\), how much extra load will the output piston support if its cross-sectional area is \(50\mathrm{\ cm}^2\)? Text Transcription: 10 N/cm^2 50 cm^2

What is the cause of surface tension?

Distinguish between adhesive and cohesive forces.

How does the height to which water is lifted in a capillary tube relate to adhesion and the weight of the water lifted?

Calculate the pressure a \(10-N\) block exerts on the table it rests on if its area of contact is \(50\mathrm{\ cm}^2\). . Pressure = weight density ? depth (Use \(10,000\mathrm{\ N}/\mathrm{m}^3\) for the weight density of water, and ignore the pressure due to the atmosphere in the calculations below.) Equation Transcription: Text Transcription: 10-N 50 cm^2 10,000 N/m^3

(Use \(10,000\mathrm{\ N}/\mathrm{m}^3\) for the weight density of water, and ignore the pressure due to the atmosphere in the calculations below.) A 1-m-tall barrel is filled with water (with a weight density of \(10,000\mathrm{\ N}/\mathrm{m}^3\)). Show that the water pressure on the bottom of the barrel is \(10,000\mathrm{\ N}/\mathrm{m}^2\) or, equivalently, 10 kPa. Text Transcription: times 10,000 N/m^3 10,000 N/m^2

(Use \(10,000\mathrm{\ N}/\mathrm{m}^3\) for the weight density of water, and ignore the pressure due to the atmosphere in the calculations below.) Show that the water pressure at the bottom of the 50-m-high water tower in the chapter-opening photo is \(500,000\mathrm{\ N}/\mathrm{m}^2\), which is approximately 500 kPa.

The depth of water behind the Hoover Dam is 220 m. Show that the water pressure at the base of this dam is 2200 kPa.

(Use \(10,000\mathrm{\ N}/\mathrm{m}^3\) for the weight density of water, and ignore the pressure due to the atmosphere in the calculations below.) 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. Text Transcription: times 10,000 N/m^3

Calculate the average force per nail when Sara, who weighs 120 pounds, lies on a bed of nails and is supported by 600 nails (see Figure 13.2).

Suppose that you balance a 5-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 \(50\mathrm{\ N}/\mathrm{cm}^2\), which is 500 kPa. Text Transcription: 1 cm^2 50 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 meter deep), the water pressure on the bottom of the barrel is 10 kPa. What is the pressure on the bottom when water is added to fill the pipe to its top?

A dike in Holland springs a leak through a hole of area \(1~\mathrm{cm}^2\) at a depth of 2 m below the water surface. How much force must a boy apply to the hole with his thumb to stop the leak? Could he do it?

A merchant in Katmandu sells you a solid gold 1-kg statue for a very reasonable price. When you get 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. Show that, for pure gold, the volume of water displaced will be \(51.8\mathrm{\ cm}^3\). Text Transcription: 51.8 cm^3

In lab you find that a \(1-kg\) rock suspended above water weighs \(10 \ N\). When the rock is suspended beneath the surface of the water, the scale reads \(8 \ N\). a. What is the buoyant force on the rock? b. If the container of water weighs \(10 \ N\) on the weighing scale, what is the scale reading when the rock is suspended beneath the surface of the water? c. What is the scale reading when the rock is released and rests at the bottom of the container? Equation Transcription: Text Transcription: 1-kg 10 N 8 N 10 N

In the hydraulic pistons shown in the sketch, the small piston has a diameter of \(2 \ cm\). The large 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? Equation Transcription: Text Transcription: 2 cm 6 cm

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

Think about what happens to the volume of an air-filled balloon on top of water and beneath the water. Then rank the buoyant forces on a weighted balloon in water, from greatest to least, when it is a. barely floating with its top at the surface. b. pushed \(1 \ m\) beneath the surface. c. pushed \(2 \ m\) beneath the surface. Equation Transcription: Text Transcription: 1 m 2 m

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?

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?

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

Which do you suppose exerts more pressure on the ground: a 5000-kg elephant or a 50-kg lady standing on spike heels? (Which will be more likely to make dents in a linoleum floor?) Approximate a rough calculation for each.

Why are persons who are confined to bed less likely to develop bedsores on their bodies if they rest on a waterbed rather than on an ordinary mattress?

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

When you are 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.

Why does your body get more rest when you’re lying down than when you’re sitting? Is blood pressure in your legs greater?

If water faucets upstairs and downstairs are turned fully on, will more water per second flow out of the upstairs faucets or the downstairs faucets?

How does water pressure 1 m beneath the surface of a lake compare with water pressure 1 m beneath the surface of a swimming pool?

The sketch shows a wooden reservoir reinforced with metal hoops that supplies water to a farm. (a) Why is it elevated? (b) Why are the hoops closer together near the bottom part of the tank?

A block of aluminum with a volume of \(10\mathrm{\ cm}^3\) is placed in a beaker of water filled to the brim. Water overflows. The same is done in another beaker with a \(10-\mathrm{cm}^{3}\) block of lead. Does the lead displace more, less, or the same amount of water? Text Transcription: 10 cm^3 10-cm^3

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?

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 in another beaker with a 10-N block of lead. Does the lead displace more, less, or the same amount of water? (Why do your answers differ from answers to the preceding two questions?)

In 1960, the U.S. Navy’s bathyscaphe Trieste (a submersible) descended to a depth of nearly 11 km in the Marianas Trench near the Philippines in the Pacific Ocean. Instead of a large viewing window, it had a small circular window 15 cm in diameter. What is your explanation for so small a window?

If you’ve wondered about the flushing of toilets on the upper floors of city skyscrapers, how do you suppose the plumbing is designed so that there is not an enormous impact of sewage arriving at the basement level? (Check your speculations with someone who is knowledgeable about architecture.)

Why does water “seek its own level”?

When you are bathing at a stony beach, why do the stones at the bottom hurt your feet less when you’re standing in deep water?

If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Explain.

Why is it easier to float in saltwater than in fresh water?

In answering the question of why bodies float higher in saltwater than in fresh water, your friend replies that the reason is that saltwater is denser than fresh water. (Does your friend often recite only factual statements that relate to the answers and not provide any concrete reasons?) How would you answer the same question?

A can of diet soda floats in water, whereas a can of regular soda sinks. Explain this phenomenon first in terms of density and then in terms of weight versus buoyant force.

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

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?

Why is a high mountain composed mostly of lead an impossibility on Earth?

How much force is needed to hold a nearly weightless but rigid 1-L carton beneath the surface of water?

Why will a volleyball held beneath the surface of water have more buoyant force than if it is floating?

Why does an inflated beach ball pushed beneath the surface of water swiftly shoot above the water surface when it is released?

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

Why is the buoyant force on a submerged submarine appreciably greater than the buoyant force on it while it is floating?

Will a rock gain or lose buoyant force as it sinks deeper in water? Or will the buoyant force remain the same at greater depths? Defend your answer.

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 the preceding question.

The density of a rock doesn’t change when it is submerged in water, but your density changes when you are submerged. Explain.

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? Defend your answer.

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

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? Comment on ice cubes submerged at the bottom of a cocktail.

When the wooden block is placed in the beaker, what happens to the scale reading? Answer the same question for an iron block.

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 in it? How about if the ice cube contains many grains of heavy sand?

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

Consider both a 50-ton boat and a 100-ton boat floating 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?

A small aquarium half-filled with water is on a spring scale. Will the reading of the scale increase or remain the same if a fish is placed in the aquarium? (Will your answer be different if the aquarium is initially filled to the brim?)

What would you experience when swimming in water in an orbiting space habitat where the simulated gravity is g? Would you float in the water as you do on Earth?

We say that the shape of a liquid is the same as the shape of its container. But, with no container and no gravity, what is the natural shape of a blob of water? Why?

So you’re having 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?

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 of water floating weightless in an orbiting spacecraft?

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 \(10 \ kg\) that rest on the small piston. Do you think he will be successful? Defend your answer. Equation Transcription: Text Transcription: 50 10 kg

In the hydraulic arrangement shown in Figure 13.22, the multiplication 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 Figure 13.23 is immaterial. What is your explanation to resolve this confusion?

Why will hot water flow more readily than cold water through small leaks in a car radiator?

A small, dry paper clip can rest on the surface of still water. Why can’t a heavier paper clip do the same without sinking?

A chunk of steel will sink in water. But a steel razor blade, carefully placed on the surface of water, will not sink. What is your explanation?

The photo shows physics instructor Marshall Ellenstein walking barefoot on broken glass bottles in his class. Discuss the physics concept that Marshall is demonstrating. Why is he careful to be sure that the broken pieces are small and numerous? (The Band-Aids on his feet are for humor!)

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. Discuss whether or not this is possible and reasonable. (See also Think and Solve 41.)

Discuss which teapot holds more liquid, and why.

There is a story about Pascal’s assistant climbing a ladder and pouring a small container of water into a tall, thin, vertical pipe 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 was very small. Discuss and explain.

Suppose you wish to lay a level foundation for a house on hilly, bushy terrain. Discuss how you could use a garden hose filled with water to determine equal elevations at distant points.

A piece of iron placed on a block of wood makes the block float lower in the water. If the iron were instead suspended beneath the wood, would the wood float as low, lower, or higher? Discuss.

Compared with an empty ship, would a ship loaded with a cargo of Styrofoam sink deeper into the water or rise in the water? Discuss.

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? This makes for a good discussion!

If a submarine starts to sink, will it continue to sink to the bottom if no changes are made? Discuss.

Would the water level in a canal lock go up or down if a battleship in the lock sank? Another good discussion.

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? In your discussion, consider any change in the balloon’s density change.

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 these life preservers in the water, upon which will the buoyant force be greater? Upon which will the buoyant force be ineffective? Discuss why your answers differ.

On a boat ride, the skipper gives you an extra-large life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear regular-sized Styrofoam-filled life preservers. Is he being truthful?

Would buoyancy occur in the absence of weight? Discuss the buoyancy that would or wouldn’t occur in the International Space Station.

If the gravitational field of Earth were to increase, would a fish float to the surface, sink, or stay at the same depth?