Solved: A mountain-climber friend with a mass of 80 kg

Problem 56E Is lower pressure the result of fast-moving air, or is fast-moving air the result of lower pressure? Give one example supporting each point of view. (In physics, when two things are related—such as force and acceleration or speed and pressure—it is usually arbitrary which one we call ?cause? and which one we call e ? ffect.?)

Problem 1E It is said that a gas fills all the space available to it. Why, then, doesn’t the atmosphere go off into space?

Problem 1R Rank the volume of air in the glass, from greatest to least, when it is held a. near the surface as shown. b. 1 m beneath the surface. c. 2 m beneath the surface.

Problem 1P What change in pressure occurs in a party balloon that is squeezed to one-third its volume with no change in temperature?

Problem 1RQ What is the energy source for the motion of gas in the atmosphere? What prevents atmospheric gases from flying off into space?

Problem 2E Why is there no atmosphere on the Moon?

Problem 2P Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)

Problem 2R Rank the buoyant force supplied by the atmosphere on the following, from most to least: a. An elephant b. A helium-filled party balloon c. A skydiver at terminal velocity

Problem 2RQ How high would you have to go in the atmosphere for half of the mass of air to be below you?

Problem 3E Why is the pressure in an automobile’s tires slightly greater after the car has been driven several kilometers?

Problem 3P A mountain-climber friend with a mass of 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 physics skills, he asks you. Share with him your calculations that show the volume of the balloon to be about 17 m3(slightly more than 3 m in diameter for a spherical balloon).

Problem 3RQ What is the cause of atmospheric pressure?

Problem 3R Rank from most to least, the amount of lift on the following airplane wings: a. Area 1000 m2 with atmospheric pressure difference of 2.0 N/m2 b. Area 800 m2 with atmospheric pressure difference of 2.4 N/m2 c. Area 600 m2 with atmospheric pressure difference of 3.8 N/m2

Problem 4RQ What is the mass of a cubic meter of air at room temperature (20°C)?

If you count the tires on a large tractor-trailer that is unloading food at your local supermarket, you may be surprised to count 18 tires. Why so many tires? (Hint: Consider Think and Do #31.) Think and Do #31 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 know the weight of your car, which you can get from a manual or a dealer. You divide the weight by 4 to get the approximate weight held up by one tire. You can closely approximate the area of contact of a tire with the road by tracing the edges of the tire contact on a sheet of paper marked with 1-inch squares beneath the tire. After you calculate the pressure of the tire against the road, compare it with the air pressure in the tire. Are they nearly equal? If not, which is greater?

Problem 5E The valve stem on a tire must exert a certain force on the air within to prevent any of that air from leaking out. If the diameter of the valve stem were doubled, by how much would the force exerted by the valve stem increase?

Problem 5P Consider an airplane with a total wing surface of 1002 m. At a certain speed the difference in air pressure below and above the wings is 4% of atmospheric pressure. Show that the lift on the airplane is 400,000 N.

Problem 5RQ What is the approximate mass of a column of air 1 cm2 in area that extends from sea level to the upper atmosphere? What is the weight of this amount of air?

Problem 6E Why is a soft, underinflated football at sea level much firmer when it is taken to a high elevation in the mountains?

Problem 6RQ What is the pressure at the bottom of the column of air referred to in the question 1? Question 1 What is the approximate mass of a column of air 1 cm2 in area that extends from sea level to the upper atmosphere? What is the weight of this amount of air?

Problem 7E What is the purpose of the ridges that prevent the funnel from fitting tightly in the mouth of a bottle?

Problem 7RQ How does the pressure at the bottom of a 76-cm column of mercury in a barometer compare with air pressure at the bottom of the atmosphere?

Problem 8E How does the density of air in a deep mine compare with the air density at Earth’s surface?

Problem 8RQ How does the weight of mercury in a barometer compare with the weight of an equal cross section of air from sea level to the top of the atmosphere?

Problem 9E When an air bubble rises in water, what happens to its mass, volume, and density?

Problem 9RQ Why would a water barometer have to be 13.6 times taller than a mercury barometer?

Problem 10E Two teams of eight horses each were unable to pull the Magdeburg hemispheres apart (shown at the top of the opening page of this chapter). Suppose that 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? Defend your answer.

Problem 10RQ When you drink liquid through a straw, is it more accurate to say the liquid is pushed up the straw rather than sucked up the straw? What exactly does the pushing? Defend your answer.

Problem 11E When boarding an airplane, you bring a bag of chips (or any other item packaged in an airtight foil package) and, while you are in flight, you notice that the bag puffs up. Explain why this happens.

Problem 11RQ Why will a vacuum pump not operate for a well that is more than 10.3 m deep?

Problem 12E Why do you suppose that airplane windows are smaller than bus windows?

Problem 12RQ Why is it that an aneroid barometer is able to measure altitude as well as atmospheric pressure?

Problem 13E 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 those made of foam rubber. Why is this so?

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

Problem 14E 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.

Problem 14RQ What happens to the air pressure inside a balloon when it is squeezed to half its volume at constant temperature?

Problem 15E Suppose that the pump shown in Figure 14.9 operated with a perfect vacuum. From how deep a well could water be pumped?

Problem 15RQ What is an ideal gas?

Problem 16E If a liquid only half as dense as mercury were used in a barometer, how high would its level be on a day of normal atmospheric pressure?

Problem 16RQ A balloon that weighs 1 N is suspended in air, drifting neither up nor down. (a) How much buoyant force acts on it? (b) What happens if the buoyant force decreases? (c) If it increases?

Why doesn’t the size of the cross-sectional area of a mercury barometer affect the height of the enclosed mercury column?

Problem 17RQ Does the air exert buoyant force on all objects in air or only on objects such as balloons that are very light for their size?

Problem 18E From how deep a container could mercury be drawn with a siphon?

Problem 18RQ What are streamlines? Is pressure greater or less in regions where streamlines are crowded?

Problem 19RQ What happens to the internal pressure in a fluid flowing in a horizontal pipe when its speed increases?

Problem 19E If you could somehow replace the mercury in a mercury barometer with a denser liquid, would the height of the liquid column be greater than or less than the height of the mercury? Why?

Problem 20E Would it be slightly more difficult to draw soda through a straw at sea level or on top of a very high mountain? Explain.

Problem 20RQ Does Bernoulli’s principle refer to changes in internal pressure of a fluid or to pressures the fluid may exert on objects?

Problem 21E The pressure exerted against the ground by an elephant’s weight distributed evenly over its four feet is less than 1 atmosphere. Why, then, would you be crushed beneath the foot of an elephant, while you’re unharmed by the pressure of the atmosphere?

Problem 21RQ How does Bernoulli’s principle apply to the flight of airplanes?

Problem 22E 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?

Problem 22RQ Why does a spinning ball curve in its flight?

Problem 23E Which will register the greater weight: an empty flattened balloon or the same balloon filled with air? Defend your answer, then try it and see.

Problem 24RQ How does a plasma differ from a gas?

Problem 25E Why is it so difficult to breathe when snorkeling at a depth of 1 m and practically impossible at a 2-m depth? Why can’t a diver simply breathe through a hose that extends to the surface?

Problem 23RQ Why do ships passing close together run a risk of sideways collisions?

Problem 24E On a sensitive balance, weigh an empty, flat, thin plastic bag. Then weigh the bag filled with air. Will the readings differ? Explain.

Problem 26E A little girl sits in a car at a traffic light holding a helium-filled balloon. The windows are closed and the car is relatively airtight. When the light turns green and the car accelerates forward, her head pitches backward but the balloon pitches forward. Explain why.

Problem 25RQ Cite at least three examples of plasma in your daily environment.

Problem 26RQ What can be produced when a plasma beam is directed into a magnet?

Problem 27E How does the concept of buoyancy complicate the old question “Which weighs more, a pound of lead or a pound of feathers”?

Would a bottle of helium gas weigh more or less than an identical bottle filled with air at the same pressure? Than an identical bottle with the air pumped out?

Problem 28E Why does the weight of an object in air differ from its weight in a vacuum (remembering that weight is the force exerted against a supporting surface)? Cite an example in which this would be an important consideration.

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

Problem 32E If the number of gas atoms in a container is doubled, the pressure of the gas doubles (assuming constant temperature and volume). Explain this pressure increase in terms of molecular motion of the gas.

Problem 30E When you replace helium in a balloon with less-dense hydrogen, does the buoyant force on the balloon change if the balloon remains the same size? Explain.

Problem 33E What, if anything, happens to the volume of gas in an atmospheric research-type balloon when it is heated?

Problem 34E What, if anything, happens to the pressure of the gas in a rubber balloon when the balloon is squeezed smaller?

Problem 35E What happens to the size of the air bubbles released by a diver as they rise?

The gas pressure inside an inflated rubber balloon is always greater than the air pressure outside. Explain.

Problem 40E The force of the atmosphere at sea level against the outside of a 10-m2 store window is about a million N. Why does this not shatter the window? Why might the window shatter in a strong wind blowing past the window?

Why does the fire in a fireplace burn more briskly on a windy day?

Problem 39E Two balloons that have the same weight and volume are filled with equal amounts of helium. One is rigid and the other is free to expand as the pressure outside decreases. When released, which will rise higher? Explain.

Problem 38E 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 the balance of the stick upset? If so, which way does it tip?

Problem 36E You and Tim float a long string of closely spaced helium- filled balloons over his used-car lot. You secure the two ends of the long string of balloons to different points on the ground so that the balloons float over the lot in an arc. What is the name of this arc? (Why could this exercise have been included in Chapter 12?)

Problem 42E What happens to the pressure in water as it speeds up when it is ejected by the nozzle of a garden hose?

Problem 43E Why do airplanes normally take off facing the wind?

Problem 44E What provides the lift to keep a Frisbee in flight?

Problem 45E Imagine a huge space colony that consists of a rotating air-filled cylinder. How would the density of air at “ground level” compare to the air densities “above”?

Problem 46E Would a helium-filled balloon “rise” in the atmosphere of a rotating space habitat? Defend your answer.

Problem 47E 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?

Problem 49E Why is it easier to throw a curve with a tennis ball than a baseball?

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

Compare the spacing of streamlines around a tossed baseball that doesn’t spin in flight with the spacing of streamlines around a ball that does. Why does the spinning baseball veer from the course of a nonspinning one?

Problem 52E Why are runways longer for takeoffs and landings at high-altitude airports, such as those in Denver and Mexico City?

Problem 51E How is an airplane able to fly upside down?

Problem 53E How will two dangling vertical sheets of paper move when you blow between them? Try it and see.

Problem 54E What physics principle underlies these 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 trains sometimes break when a high-speed train passes by on the next track.

When an air bubble rises in water, what happens to its mass, volume, and density?

What is the energy source for the motion of gas in the atmosphere? What prevents atmospheric gases from flying off into space?

How high would you have to go in the atmosphere for half of the mass of air to be below you?

What is the cause of atmospheric pressure?

What is the mass of a cubic meter of air at room temperature \(\left(20^{\circ} \mathrm{C}\right)\)?

What is the approximate mass of a column of air \(\mathrm{1~cm^2}\) in area that extends from sea level to the upper atmosphere? What is the weight of this amount of air?

What is the pressure at the bottom of the column of air referred to in the preceding question?

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

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

Why would a water barometer have to be 13.6 times taller than a mercury barometer?

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

Why won’t a vacuum pump operate for a well that is deeper than 10.3 m?

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

Why is it that an aneroid barometer is able to measure altitude as well as atmospheric pressure?

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

What is an ideal gas?

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

Does the air exert a buoyant force on all objects in air or on only objects such as balloons that are very light for their size?

Why are high-altitude research balloons only partially inflated when launched?

What are streamlines?

Is pressure greater or less in regions where streamlines are crowded?

What happens to the internal pressure in a fluid flowing in a horizontal pipe when its speed increases?

What happens to the internal pressure in a fluid flowing in a horizontal pipe when its speed decreases?

Does Bernoulli’s principle refer to changes in the internal pressure of a fluid or to pressures the fluid may exert on objects?

How does faster-moving air above an airplane wing affect the pressure on the wing?

How does faster-moving water between two ships affect the water pressure against the sides of the ships?

Are the ships in the preceding question sucked together or pushed together? Explain.

Is the fluid that goes up the inside tube in a hand sprayer pushed up the tube or sucked up the tube? Explain.

How does a plasma differ from a gas?

Cite at least three examples of plasma in your daily environment.

What can be produced when a plasma beam is directed into the field of a strong magnet?

Raise a submerged upside-down glass that is full of water above the waterline, but with its mouth beneath the surface. Why doesn’t the water run out? How tall would a glass have to be before water began to run 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.)

Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)

A mountain-climber friend with a mass of 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 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

On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N. a. Show that the weight of the displaced air is 20,000 N. b. Show that the volume of the displaced air is \(1700\mathrm{\ m}^3\). Text Transcription: 1700 m^3

Consider an airplane with a total wing surface of 100 square meters. At a certain speed the difference in the air pressure below and above the wings is 4% of atmospheric pressure. Show that the lift on the airplane is 400,000 N.

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

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

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

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

Why is there no atmosphere on the Moon?

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

The valve stem on a tire must exert a certain force on the air within to prevent any of that air from leaking out. If the diameter of the valve stem were doubled, by how much would the force exerted by the valve stem increase?

Why is a soft, underinflated football at sea level much firmer when it is taken to a high elevation in the mountains?

What is the purpose of the ridges that prevent the funnel from fitting tightly in the mouth of a bottle?

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

When an air bubble rises in water, what happens to its mass, volume, and density?

Why do you suppose that airplane windows are smaller than bus windows?

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 those made of foam rubber. Why is this so?

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.

Suppose that the pump shown in Figure 14.9 operated with a perfect vacuum. From how deep a well could water be pumped?

If a liquid only half as dense as mercury were used in a barometer, how high would its level be on a day of normal atmospheric pressure?

Why doesn’t the size of the cross-sectional area of a mercury barometer affect the height of the enclosed mercury column?

From how deep a container could mercury be drawn with a siphon?

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

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

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

A little girl sits in a car at a traffic light holding a helium-filled balloon. The windows are closed and the car is relatively airtight. When the light turns green and the car accelerates forward, her head pitches backward but the balloon pitches forward. Explain why.

Why does a precision scale give different readings for the weight of an object in air and in a vacuum (remembering that weight is the force exerted against a supporting surface)? Cite an example in which this would be an important consideration.

How does the concept of buoyancy complicate the old question “Which weighs more: a pound of lead or a pound of feathers?"

Would a bottle of helium gas weigh more or less than an identical bottle filled with air at the same pressure? Than an identical bottle with the air pumped out?

When you replace helium in a balloon with less-dense hydrogen, does the buoyant force on the balloon change if the balloon remains the same size? Explain.

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

If the number of gas atoms in a container is doubled, the pressure of the gas doubles (assuming constant temperature and volume). Explain this pressure increase in terms of the molecular motion of the gas.

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

What, if anything, happens to the volume of gas in an atmospheric research-type balloon when it is heated?

What, if anything, happens to the pressure of the gas in a rubber balloon when the balloon is squeezed smaller?

What happens to the size of the air bubbles released by a diver as they rise?

You and your friendly car dealer float a long string of closely spaced helium-filled balloons over his used-car lot. You secure the two ends of the long string of balloons to different points on the ground so that the balloons float over the lot in an arc. What is the name of this arc? (Why could this exercise have been included in Chapter 12?)

The gas pressure inside an inflated rubber balloon is always greater than the air pressure outside. Explain.

The force of the atmosphere at sea level against the outside of a \(10-\mathrm{m}^{2}\) store window is about a million N. Why doesn’t this shatter the window? Why might the window shatter in a strong wind blowing past the window?

Why does the fire in a fireplace burn more briskly on a windy day?

What happens to the pressure in water as it speeds up when it is ejected by the nozzle of a garden hose?

Why do airplanes normally take off facing the wind?

What provides the lift to keep a Frisbee in flight?

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?

Compare the spacing of streamlines around a tossed baseball that doesn’t spin in flight with the spacing of streamlines around a ball that does. Why does the spinning baseball veer from the course of a nonspinning one?

Why do airplanes extend wing flaps that increase the area and the angle of attack of the wing during takeoffs and landings? Why are these flaps pulled in when the airplane has reached cruising speed?

Why is it easier to throw a curve with a tennis ball than a baseball?

How is an airplane able to fly upside down?

Why are runways longer for takeoffs and landings at high-altitude airports, such as those in Denver and Mexico City?

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

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

Wharves are made with pilings that permit the free passage of water. Why would a solid-walled wharf be disadvantageous to ships attempting to pull alongside?

If you count the tires on a large tractor-trailer that is unloading food at your local supermarket, you may be surprised to count 18 tires. Why so many tires? (Hint: Consider Think and Do #31.)

Two teams of eight horses each were unable to pull the Magdeburg hemispheres apart (shown on the opening page of this chapter). Suppose that 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 this and defend your answer.

When boarding an airplane, you bring a bag of chips (or any other item packaged in an airtight foil package) and, while you are in flight, you notice that the bag puffs up. Discuss why this happens.

The pressure exerted against the ground by an elephant’s weight distributed evenly over its four feet is less than 1 atmosphere. Discuss why it is that you’d be crushed beneath the foot of an elephant, while you’re unharmed by the pressure of the atmosphere?

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. Discuss your response.

Discuss which will register the greater weight: an empty flattened balloon or the same balloon filled with air. Defend your answer: then try it and see.

On a sensitive balance, weigh an empty, flat, thin plastic bag. Then weigh the bag filled with air. Discuss whether or not the readings differ.

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. Discuss whether or not the balance of the stick is upset. If so, which way does it tip?

Two balloons that have the same weight and volume are filled with equal amounts of helium. One is rigid and the other is free to expand as the pressure outside decreases. When released, discuss which will rise higher.

A helium-filled balloon and a basketball have the same volume. Upon which is the buoyant force of the surrounding air greater? Discuss why the balloon is at the ceiling of a room whereas the basketball is on the floor.

Imagine a huge space colony that consists of a rotating air-filled cylinder. Discuss how the density of the air at “ground level” would compare to the air densities “above.”

Discuss whether or not a helium-filled balloon could “rise” in the atmosphere of a rotating space habitat.

Discuss whether or not lower pressure is the result of fast-moving air, or fast-moving air is the result of lower pressure. Give one example supporting each point of view. (In physics, when two things are related—such as force and acceleration or speed and pressure—it is usually arbitrary which one we call cause and which one we call effect.)