CHAPTER  14

Review QuestionsThe Atmosphere

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

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

Atmospheric Pressure3. What is the cause of atmospheric pressure?4. What is the mass of a cubic meter of air at room temperature (20°C)?5. 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?

6. What is the pressure at the bottom of the column of air referred to in the previous question?

Barometer7. 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?

8. 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?

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

10. 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.

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

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

Boyle’s Law13. By how much does the density of air increase when it is compressed to

half its volume?14. What happens to the air pressure inside a balloon when it is squeezed

to half its volume at constant temperature?15. What is an ideal gas?

Buoyancy of Air

16. 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?

17. 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?

18. What usually happens to a toy helium-filled balloon that rises high into the atmosphere?

Bernoulli’s Principle19. What are streamlines? Is pressure greater or less in regions where

streamlines are crowded?20. What happens to the internal pressure in a fluid flowing in a horizontal

pipe when its speed increases?21. Does Bernoulli’s principle refer to changes in internal pressure of a

fluid or to pressures the fluid may exert on objects?Applications of Bernoulli’s Principle22. How does Bernoulli’s principle apply to the flight of airplanes?23. Why does a spinning ball curve in its flight?24. Why do ships passing each other in open seas run a risk of sideways

collisions?Plasma25. How does a plasma differ from a gas?

Plasma in the Everyday World26. Cite at least three examples of plasma in your daily environment.27. Why is AM radio reception better at night?

Plasma Power28. What can be produced when a plasma beam is directed into a magnet?

[ previous page ] [ next page ]

  ©     2010 Pearson Education, Inc.

Projects

Pouring Air from One Glass to Another

  1.Find the pressure exerted by the tires of your car on the road and compare it with the air pressure in the tires. For this project, you need the weight of your car, which you can get from a manual or a dealer.

You divide the weight by four 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 tire contact on a sheet of paper marked with one-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?

(Click image to enlarge)  2. Try this in the bathtub or when you’re washing dishes. Lower a drinking

glass, mouth downward, over a small floating object (which makes the inside water level visible). What do you observe? How deep will the glass have to be pushed in order to compress the enclosed air to half its volume? (You won’t be able to get that much air compression in your bathtub unless it’s 10.3 m deep!)

(Click image to enlarge)  3. 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 into 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 water-filled glass mouth downward above the air-filled glass. Slowly tilt the lower glass and let the air escape, filling the upper glass. You will be pouring air from one glass into another!

(Click image to enlarge)  4. Hold a glass under water, letting it fill with water. Then turn it upside

down and raise it, but with its mouth beneath the surface. Why does the water not run out? How tall would a glass have to be before water began to run out? (If you could find such a glass, you might need to cut holes in your ceiling and roof to make room for it!)

(Click image to enlarge)  5. Place a card over the open top of a glass filled to the brim with water

and invert it. Why does the card stay in place? Try it sideways.

(Click image to enlarge)  6. Invert a water-filled pop bottle or a small-necked jar. Notice that the

water doesn’t simply fall out but gurgles out of the container. Air pressure won’t let it get 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 empty on the Moon?

  7. Do as Professor Dan Johnson does below. Pour about half a cup of water into a 5-or-so-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.)

(Click image to enlarge)  8. Heat a small amount of water to boiling in an aluminum soda-pop can

and invert it quickly into a dish of cooler water. Surprisingly dramatic!  9. Make a small hole near the bottom of an open tin can. Fill the can with

water, which will proceed to spurt from the hole. If you cover the top of the can firmly with the palm of your hand, the flow stops. Explain.

(Click image to enlarge)  10. 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 if you enroll in a chemistry lab.)

(Click image to enlarge)  11. Push a pin through a small card and place it in the hole of a thread

spool. Try to blow the card from the spool by blowing through the hole. Try it in all directions.

(Click image to enlarge)  12. Hold a spoon in a stream of water as shown and feel the effect of the

differences in pressure.

Exercises

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

2. Why is there no atmosphere on the Moon?3. 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: Consider Project 1.)

4. 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?

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

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

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

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

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

10. Two teams of eight horses each were unable to pull the Magdeburg hemispheres apart (Figure 14.2). 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? Defend your answer.

11. 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.

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

13. A half cup or so of water is poured into a 5-L can and is placed over a source of heat until most of the water has boiled away. Then the top of the can is screwed on tightly and the can is removed from the heat and allowed to cool. What happens to the can and why?

14. 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?

15. 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.

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

17. 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?

18. Why does the size of the cross-sectional area of a mercury barometer

not affect the height of the enclosed mercury column?19. From how deep a container could mercury be drawn with a siphon?20. 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 mercury? Why?

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

22. 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?

23. 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?

24. 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.

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

26. 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?

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

28. 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.

29. 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.

30. 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?

31. 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.

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

33. 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.

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

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

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

37. You and Tim float a long string of closely spaced helium-filled balloons over his used-car lot. You secure both ends of the string to the ground several meters apart 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?)

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

39. 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?

40. 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.

41. 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?

42. Why does the fire in a fireplace burn more briskly on a windy day?43. What happens to the pressure in water as it speeds up when it is

ejected by the nozzle of a garden hose?44. Why do airplanes normally take off facing the wind?45. What provides the lift to keep a Frisbee in flight?46. 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”?

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

48. 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?

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

50. Why is it easier to throw a curve with a tennis ball than a baseball?51. Why do airplanes extend wing flaps that increase the area of the wing

during takeoffs and landings? Why are these flaps pulled in when the airplane has reached cruising speed?

52. How is an airplane able to fly upside down?

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

54. When a jet plane is cruising at high altitude, the flight attendants have more of a “hill” to climb as they walk forward along the aisle than when the plane is cruising at a lower altitude. Why does the pilot have to fly with a greater angle of attack at a high altitude than at a low altitude?

55. 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.

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

57. A steady wind blows over the waves of an ocean. Why does the wind increase the peaks and troughs of the waves?

58. 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?

59. 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 effect.)

60. Why is the reception for far-away radio stations clearer at nighttime on your AM radio?

Problems

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

2. Air in a cylinder is compressed to one-tenth its original volume with no change in temperature. What happens to its pressure?

3. In the previous problem, if a valve is opened to let out enough air to bring the pressure back down to its original value, what percentage of the molecules escape?

4. 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.)

5. Nitrogen and oxygen in their liquid states have densities only 0.8 and 0.9 that of water. Atmospheric pressure is due primarily to the weight of nitrogen and oxygen gas in the air. If the atmosphere were somehow liquefied, would its depth be greater or less than 10.3 m?

6. 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. What answer can you provide, showing your calculations?

7. 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) What is the weight of the displaced air? (b) What is the volume of the displaced air?

8. How much lift is exerted on the wings of an airplane that have a total surface area of 100 m2 when the difference in air pressure below and above the wings is 4% of atmospheric pressure?

Solutions to Chapter 14 Exercises

1. Some of the molecules in the Earth’s atmosphere do go off into outer space—those like helium with speeds greater than escape speed. But the average speeds of most molecules in the atmosphere are well below escape speed, so the atmosphere is held to Earth by Earth gravity.

2. There is no atmosphere on the Moon because the speed of a sizable fraction of gas molecules at ordinary temperatures exceeds lunar escape velocity (because of the Moon’s smaller gravity). Any appreciable amounts of gas have long leaked away, leaving the Moon airless.

3. The weight of a truck is distributed over the part of the tires that make contact with the road. Weight/surface area = pressure, so the greater the surface area, or equivalently, the greater the

number of tires, the greater the weight of the truck can be for a given pressure. What pressure? The pressure exerted by the tires on the road, which is determined by (but is somewhat greater than) the air pressure in its tires. Can you see how this relates to Home Project 1?

4. When the diameter is doubled, the area is four times as much. For the same pressure, this would mean four times as much force.

5. The tires heat, giving additional motion to the gas molecules within.

6. At higher altitude, less atmospheric pressure is exerted on the ball’s exterior, making relative pressure within greater, resulting in a firmer ball.

7. The ridges near the base of the funnel allow air to escape from a container it is inserted into. Without the ridges, air in the container would be compressed and would tend to prevent filling as the level of liquid rises.

8. The density of air in a deep mine is greater than at the surface. The air filling up the mine adds weight and pressure at the bottom of the mine, and according to Boyle’s law, greater pressure in a gas means greater density.

9. The bubble’s mass does not change. Its volume increases because its pressure decreases (Boyle’s law), and its density decreases (same mass, more volume).

10. To begin with, the two teams of horses used in the Magdeburg hemispheres demonstration were for showmanship and effect, for a single team and a strong tree would have provided the same force on the hemispheres. So if two teams of nine horses each could pull the hemispheres apart, a single team of nine horses could also, if a tree or some other strong object were used to hold the other end of the rope.

11. If the item is sealed in an air-tight package at sea level, then the pressure in the package is about 1 atmosphere. Cabin pressure is reduced somewhat for high altitude flying, so the pressure in the package is greater than the surrounding pressure and the package therefore puffs outwards.

12. Airplane windows are small because the pressure difference between the inside and outside surfaces result in large net forces that are directly proportional to the window’s surface area. (Larger windows would have to be proportionately thicker to withstand the greater net force—windows on underwater research vessels are similarly small.)

13. The can collapses under the weight of the atmosphere. When water was boiling in the can, much of the air inside was driven out and replaced by steam. Then, with the cap tightly fastened, the steam inside cooled and condensed back to the liquid state, creating a partial vacuum in the can which could not withstand the crushing force of the atmosphere outside.

14. Unlike water, air is easily compressed. In fact, its density is proportional to its pressure. So, near the surface, where the pressure is greater, the air’s density is greater, and at high altitude, where the pressure is less, the air’s density is less.

15. A vacuum cleaner wouldn’t work on the Moon. A vacuum cleaner operates on Earth because the atmospheric pressure pushes dust into the machine’s region of reduced pressure. On the Moon there is no atmospheric pressure to push the dust anywhere.

16. A perfect vacuum pump could pump water no higher than 10.3 m. This is because the atmospheric pressure that pushes the water up the tube weighs as much as 10.3 vertical meters of water of the same cross-sectional area.

17. If barometer liquid were half as dense as mercury, then to weigh as much, a column twice as high would be required. A barometer using such liquid would therefore have to be twice the height of a standard mercury barometer, or about 152 cm instead of 76 cm.

18. The height of the column in a mercury barometer is determined by pressure, not force. Fluid pressures depend on density and depth—pressure at the bottom of a wide column of mercury is no different than the pressure at the bottom of a narrow column of mercury of the same depth. The weight of fluid per area of contact is the same for each. Likewise with the surrounding air. Therefore barometers made with wide barometer tubes show the same height as barometers with narrow tubes of mercury.

19. Mercury can be drawn a maximum of 76 cm with a siphon. This is because 76 vertical cm of mercury exert the same pressure as a column of air that extends to the top of the atmosphere. Or looked at another way; water can be lifted 10.3 m by atmospheric pressure. Mercury is 13.6 times denser than water, so it can only be lifted only 1/13.6 times as high as water.

20. The height would be less. The weight of the column balances the weight of an equal-area column of air. The denser liquid would need less height to have the same weight as the mercury column.

21. Drinking through a straw is slightly more difficult atop a mountain. This is because the reduced atmospheric pressure is less effective in pushing soda up into the straw.

22. If an elephant steps on you, the pressure that the elephant exerts is over and above the atmospheric pressure that is all the time exerted on you. It is the extra pressure the elephant’s foot produces that crushes you. For example, if atmospheric pressure the size of an elephant’s foot were somehow removed from a patch of your body, you would be in serious trouble. You would be soothed, however, if an elephant stepped onto this area!

23. You agree with your friend, for the elephant displaces far more air than a small helium-filled balloon, or small anything. The effects of the buoyant forces, however, is a different story. The large buoyant force on the elephant is insignificant relative to its enormous weight. The tiny buoyant force acting on the balloon of tiny weight, however, is significant.

24. The air-filled balloon is heavier and will weigh more. Although it has more buoyancy than the flattened balloon, the fact that it rests on the scale is evidence that the greater weight of air inside exceeds the buoyant force.

25. No, assuming the air is not compressed. The air filled bag is heavier, but buoyancy negates the extra weight and the reading is the same. The buoyant force equals the weight of the displaced air, which is the same as the weight of the air inside the bag (if the pressures are the same).

26. One’s lungs, like an inflated balloon, are compressed when submerged in water, and the air within is compressed. Air will not of itself flow from a region of low pressure into a region of higher pressure. The diaphragm in one’s body reduces lung pressure to permit breathing, but this limit is strained when nearly 1 m below the water surface. It is exceeded at more than 1 m.

27. Weight is the force with which something presses on a supporting surface. When the buoyancy of air plays a role, the net force against the supporting surface is less, indicating a smaller weight. Buoyant force is more appreciable for larger volumes, like feathers. So the mass of feathers that weigh 1 pound is more than the mass of iron that weighs 1 pound.

28. Objects that displace air are buoyed upward by a force equal to the weight of air displaced. Objects therefore weigh less in air than in a vacuum. For objects of low densities, like bags of compressed gases, this can be important. For high-density objects like rocks and boulders the difference is usually negligible.

29. The air tends to pitch toward the rear (law of inertia), becoming momentarily denser at the rear of the car, less dense in the front. Because the air is a gas obeying Boyle’s law, its pressure is greater where its density is greater. Then the air has both a vertical and a horizontal “pressure gradient.” The vertical gradient, arising from the weight of the atmosphere, buoys the balloon up. The horizontal gradient, arising from the acceleration, buoys the balloon forward. So the string of the balloon makes an angle. The pitch of the balloon will always be in the direction of the acceleration. Step on the brakes and the balloon pitches backwards. Round a corner and the balloon noticeably leans radially towards the center of the curve. Nice! (Another way to look at

this involves the effect of two accelerations, g and the acceleration of the car. The string of the balloon will be parallel to the resultant of these two accelerations. Nice again!)

30. Helium is less dense than air, and will weigh less than an equal volume of air. A helium-filled bottle would weigh less than the air bottle (assuming they are filled to the same pressure). However, the helium-filled bottle will weigh more than the empty bottle.

31. The buoyant force does not change, because the volume of the balloon does not change. The buoyant force is the weight of air displaced, and doesn’t depend on what is doing the displacing.

32. An object rises in air only when buoyant force exceeds its weight. A steel tank of anything weighs more than the air it displaces, so won’t rise. A helium-filled balloon weighs less than the air it displaces and rises.

33. A moving molecule encountering a surface imparts force to the surface. The greater the number of impacts, the greater the pressure.

34. The volume of gas in the balloon and the balloon increases.

35. The pressure increases, in accord with Boyle’s law.

36. Pressure of the water decreases and the bubbles expand.

37. The shape would be a catenary. It would be akin to Gateway Arch in St. Louis and the hanging chain discussed in Chapter 12.

38. The stretched rubber of an inflated balloon provides an inward pressure. So the pressure inside is balanced by the sum of two pressures; the outside air pressure plus the pressure of the stretched balloon. (The fact that air pressure is greater inside an inflated balloon than outside is evident when it is punctured—the air “explodes” outward.)

39. The end supporting the punctured balloon tips upwards as it is lightened by the amount of air that escapes. There is also a loss of buoyant force on the punctured balloon, but that loss of upward force is less than the loss of downward force, since the density of air in the balloon before puncturing was greater than the density of surrounding air.

40. The balloon which is free to expand will displace more air as it rises than the balloon which is restrained. Hence, the balloon, which is free to expand will have more buoyant force exerted on it than the balloon that does not expand, and will rise higher. (See also Problem 8.)

41. The force of the atmosphere is on both sides of the window; the net force is zero, so windows don’t normally break under the weight of the atmosphere. In a strong wind, however, pressure will be reduced on the windward side (Bernoulli’s Principle) and the forces no longer cancel to zero. Many windows are blown outward in strong winds.

42. According to Bernoulli’s principle, the wind at the top of the chimney lowers the pressure there, producing a better “draw” in the fireplace below.

43. As speed of water increases, internal pressure of the water decreases.

44. Air speed across the wing surfaces, necessary for flight, is greater when facing the wind.

45. Air moves faster over the spinning top of the Frisbee and pressure against the top is reduced. A Frisbee, like a wing, needs an “angle of attack” to ensure that the air flowing over it follows a longer path than the air flowing under it. So as with the beach ball in the previous exercise, there is a difference in pressures against the top and bottom of the Frisbee that produces an upward lift.

46. The rotating habitat is a centrifuge, and denser air is “thrown to” the outer wall. Just as on Earth, the maximum air density is at “ground level,” and becomes less with increasing altitude (distance toward the center). Air density in the rotating habitat is least at the zero-g region, the hub.

47. The helium-filled balloon will be buoyed from regions of greater pressure to regions of lesser pressure, and will “rise” in a rotating air-filled habitat.

48. (a) Speed increases (so that the same quantity of gas can move through the pipe in the same time). (b) Pressure decreases (Bernoulli’s principle). (c) The spacing between the streamlines decreases, because the same number of streamlines fit in a smaller area.

49. Spacing of airstreams on opposite sides of a nonspinning ball are the same. For a spinning ball, airstream spacings are less on the side where airspeed is increased by spin action.

50. A tennis ball has about the same size as a baseball, but much less mass. Less mass means less inertia, and more acceleration for the same force. A Ping-Pong ball provides a more obvious curve due to spinning because of its low mass.

51. Greater wing area produces greater lift, important for low speeds where lift is less. Flaps are pulled in to reduce area at cruising speed, reducing lift to equal the weight of the aircraft.

52. An airplane flies upside down by tilting its fuselage so that there is an angle of attack of the wing with oncoming air. (It does the same when flying right side up, but then, because the wings are designed for right-side-up flight, the tilt of the fuselage may not need to be as great.)

53. The thinner air at high-altitude airports produces less lift for aircraft. This means aircraft need longer runways to achieve correspondingly greater speed for takeoff.

54. The air density and pressure are less at higher altitude, so the wings (and, with them, the whole airplane) are tilted to a greater angle to produce the needed pressure difference between the upper and lower surfaces of the wing. In terms of force and air deflection, the greater angle of attack is needed to deflect a greater volume of lower-density air downward to give the same upward force.

55. Bernoulli’s Principle. For the moving car the pressure will be less on the side of the car where the air is moving fastest—the side nearest the truck, resulting in the car’s being pushed by the atmo-sphere towards the truck. Inside the convertible, atmospheric pressure is greater than outside, and the canvas rooftop is pushed upwards towards the region of lesser pressure. Similarly for the train windows, where the interior air is at rest relative to the window and the air outside is in motion. Air pressure against the inner surface of the window is greater than the atmospheric pressure outside. When the difference in pressures is significant enough, the window is blown out.

56. In accord with Bernoulli’s principle, the sheets of paper will move together because air pressure between them is reduced, and less than the air pressure on the outside surfaces.

57. The troughs are partially shielded from the wind, so the air moves faster over the crests than in the troughs. Pressure is therefore lower at the top of the crests than down below in the troughs. The greater pressure in the troughs pushes the water into even higher crests.

58. A solid-walled wharf is disadvantageous to ships pulling alongside because water currents are constrained and speed up between the ship and the wharf. This results in a reduced water pressure, and the normal pressure on the other side of the ship then forces the ship against the wharf. The pilings avoid this mishap by allowing the freer passage of water between the wharf and the ship.

59. According to Bernoulli’s principle, when a fluid gains speed in flowing through a narrow region, the pressure of the fluid is reduced. The gain in speed, the cause, produces reduced pressure, the effect. But one can argue that a reduced pressure in a fluid, the cause, will produce a flow in the

direction of the reduced pressure, the effect. For example, if you decrease the air pressure in a pipe by a pump or by any means, neighboring air will rush into the region of reduced pressure. In this case the increase in air speed is the result, not the cause of, reduced pressure. Cause and effect are open to interpretation. Bernoulli’s principle is a controversial topic with many physics types!

60. At nighttime when the energizing Sun no longer shines on the upper atmosphere, ionic layers settle closer together and better reflect the long radio waves of AM signals. The far-away stations you pick up at night are reflected off the ionosphere.

Chapter 14 Problem Solutions

1. According to Boyle’s law, the pressure will increase to three times its original pressure.

2. According to Boyle’s law, the product of pressure and volume is constant (at constant temperature), so one-tenth the volume means ten times the pressure.

3. To decrease the pressure ten-fold, back to its original value, in a fixed volume, 90% of the molecules must escape, leaving one-tenth of the original number.

4. To find the buoyant force that the air exerts on you, find your volume and multiply by the weight density of air (From Table 14.1 we see that the mass of 1 m3 of air is about 1.25 kg. Multiply this by 9.8 N/kg and you get 12.25 N/m3). You can estimate your volume by your weight and by assuming your density is approximately equal to that of water (a little less if you can float). The weight density of water is 104 N/m3, which we’ll assume is your density. By ratio and proportion:

= .

If your weight is a heavy 1000 N, for example (about 220 lb), your volume is 0.1 m 3. So buoyant force = 12.25 N/ m3 0.1 m3 = about 1.2 N, the weight of a big apple). (A useful conversion factor is 4.45 N = 1 pound.) Another way to do this is to say that the ratio of the buoyant force to your weight is the same as the ratio of air density to water density (which is your density). This ratio is 1.25/1000 = 0.00125. Multiply this ratio by your weight to get the buoyant force.

5. If the atmosphere were composed of pure water vapor, the atmosphere would condense to a depth of 10.3 m. Since the atmosphere is composed of gases that have less density in the liquid state, their liquid depths would be more than 10.3 m, about 12 m. (A nice reminder of how thin and fragile our atmosphere really is.)

6. To effectively lift (0.25)(80 kg) = 20 kg the mass of displaced air would be 20 kg. Density of air is about 1.2 kg/m3. From density = mass/volume, the volume of 20 kg of air, also the volume of the balloon (neglecting the weight of the hydrogen) would be volume = mass/density = (20 kg)/(1.2 kg/ m3) = 16.6 m3, slightly more than 3 m in diameter for a spherical balloon.

7. (a) The weight of the displaced air must be the same as the weight supported, since the total force (gravity plus buoyancy) is zero. The displaced air weighs 20,000 N.

(b) Since weight = mg, the mass of the displaced air is m = W/g = (20,000 N)/(10 m/s2) = 2,000 kg. Since density is mass/volume, the volume of the displaced air is volume = mass/density = (2,000 kg)/(1.2 kg/ m3) = 1,700 m3 (same answer to two figures if g = 9.8 m/ s2 is used).

8. From P = F

A ; F = PA = (0. 04 )(105 N

m2) (100 m2 ) = 4 ´ 105 N .