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# (b) If the height of the water column is 15 cm, what is the height of the gasoline column (a) (1) a higher (b) 22 cm 38 ( A 75-kg athlete does a single-hand hand..

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(b) If the height of the water column is 15 cm, what is the height of the gasoline column (a) (1) a higher (b) 22 cm 38 ( A 75-kg athlete does a single-hand handstand

thWilson, College Physics, 6 Edition

Chapter 9

Exercises

MC = Multiple Choice Question, CQ = Conceptual Question, and IE = Integrated Exercise. Throughout the text,

many exercise sections will include “paired” exercises. These exercise pairs, identified with red numbers, are

intended to assist you in problem solving and learning. In a pair, the first exercise (even numbered) is worked out in the Study Guide so that you can consult it should you need assistance in solving it. The second exercise (odd numbered) is similar in nature, and its answer is given at the back of the book.

9.1 Solids and Elastic Moduli

Use as many significant figures as you need to show small changes.

1. MC The pressure on an elastic body is described by (a) a modulus, (b) work, (c) stress, (d) strain. (c)

2. MC Shear moduli are not zero for (a) solids, (b) liquids, (c) gases, (d) all of these. (a)

3. MC A relative measure of deformation is (a) a modulus, (b) work, (c) stress, (d) strain. (d)

V,VV/.p,V,4. MC The volume stress for the bulk modulus is (a) (b) (c) (d) (a) oo

5. CQ Which has a greater Young’s modulus, a steel wire or a rubber band? Explain. steel wire

6. CQ Why are scissors sometimes called shears? Is this a descriptive name in the physical sense? see ISM

7. CQ Ancient stonemasons sometimes split huge blocks of rock by inserting wooden pegs into holes drilled in the

rock and then pouring water on the pegs. Can you explain the physics that underlies this technique? [Hint: Think

about sponges and paper towels.] see ISM

8. ; A tennis racket has nylon strings. If one of the strings with a diameter of 1.0 mm is under a tension of 15 N,

how much is it lengthened from its original length of 40 cm? 0.0015 m

9. ; Suppose you use the tip of one finger to support a 1.0-kg object. If your finger has a diameter of 2.0 cm, what

423.110 N/mis the stress on your finger?

10. ; A 5.0-m-long rod is stretched 0.10 m by a force. What is the strain in the rod? 0.020

11. ; A 250-N force is applied at a 37? angle to the surface of the end of a square bar. The surface is 4.0 cm on a side.

429.410 N/mWhat are (a) the compressional stress and (b) the shear stress on the bar? (a) (b)

521.210 N/m

1

12. ;; A 4.0-kg object is supported by an aluminum wire of length 2.0 m and diameter 2.0 mm. How much will the

wire stretch? 0.36 mm

13. ;; A copper wire has a length of 5.0 m and a diameter of 3.0 mm. Under what load will its length increase by

0.3 mm? 47 N

14. ;; A metal wire 1.0 mm in diameter and 2.0 m long hangs vertically with a 6.0-kg object suspended from it. If

the wire stretches 1.4 mm under the tension, what is the value of Young’s modulus for the

1121.110 N/mmetal?

15. IE ;; When railroad tracks are installed, gaps are left between the rails. (a) Should a greater gap be used if the

rails are installed on (1) a cold day or (2) a hot day? Or (3) Does it make any difference? Why? (b) Each steel rail

20.0025 m.is 8.0 m long and has a cross-sectional area of On a hot day, each rail thermally expands as much as

;33.010 m. If there were no gaps between the rails, what would be the force on the ends of each rail? (a) (1) a

51.910 Ncold day (b)

(20.0 cm15.0 cm)16. ;; A rectangular steel column supports a load of 12.0 metric tons. If the column is 2.00 m

;53.9210 min length before being stressed, what is the decrease in length?

17. IE ;; A bimetallic rod as illustrated in ;Fig 9.26 is composed of brass and copper. (a) If the rod is subjected to

a compressive force, will the rod bend toward the brass or the copper? Why? (b) Justify your answer

45.0010 N.mathematically if the compressive force is (a) bends toward brass (b) see ISM

18. IE ;; Two same-size metal posts, one aluminum and one copper, are subjected to equal shear stresses. (a)

Which post will show the larger deformation angle, (1) the copper post or (2) the aluminum post? Or (3) Is the

angle the same for both? Why? (b) By what factor is the deformation angle of one post greater than the other? (a)

，，1.5(2) the aluminium post (b) AlCu

19. ;; A 85.0-kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee

and hip jointthe femur. Assuming the femur is 0.650 m long and has a radius of 2.00 cm, by how much is the

;74.210 mbone compressed?

20. ;; Two metal plates are held together by two steel rivets, each of diameter 0.20 cm and length 1.0 cm. How

51.010 Nmuch force must be applied parallel to the plates to shear off both rivets?

2

21. IE ;; (a) Which of the liquids in Table 9.1 has the greatest compressibility? Why? (b) For equal volumes of

ethyl alcohol and water, which would require more pressure to be compressed by 0.10%, and how many times

？？？pp/2.2 more? (a) ethyl alcohol (b) wea

22. ;;; A brass cube 6.0 cm on each side is placed in a pressure chamber and subjected to a pressure of

721.210 N/m on all of its surfaces. By how much will each side be compressed under this

;63.210 mpressure?

23. ;;; A cylindrical eraser of negligible mass is dragged across a paper at a constant velocity to the right by its

pencil. The coefficient of kinetic friction between eraser and paper is 0.650. The pencil pushes down with 4.20 N.

The height of the eraser is 1.10 cm and its diameter is 0.760 cm. Its top surface is displaced horizontally 0.910

527.2810 N/mmm relative to the bottom. Determine the shear modulus of the eraser material.

24. ;;; A 45-kg traffic light is suspended from two steel cables of equal length and radii 0.50 cm. If each cable

makes a 15? angle with the horizontal, what is the fractional increase in their length due to the weight of the

;55.410light?

9.2 Fluids: Pressure and Pascal’s Principle

25. MC For a liquid in an open container, the total pressure at any depth depends on (a) atmospheric pressure, (b)

liquid density, (c) acceleration due to gravity, (d) all of the preceding. (d)

(),pgh26. MC For the pressuredepth relationship for a fluid it is assumed that (a) the pressure decreases with

depth, (b) a pressure difference depends on the reference point, (c) the fluid density is constant, (d) the

relationship applies only to liquids. (c)

27. MC When measuring automobile tire pressure, what type of pressure is this: (a) gauge, (b) absolute, (c) relative,

or (d) all of the preceding? (a)

28. CQ Figure 9.27 shows a famous ―bed of nails‖ trick. The woman lies on a bed of nails with a cinder block on

her chest. A person hits the anvil with a sledgehammer. The nails do not pierce the woman’s skin. Explain

why. see ISM

230 lb/in.,29. CQ Automobile tires are inflated to about whereas thin bicycle tires are inflated to 90 to

2115 lb/in.at least three times as much pressure! Why? see ISM

3

30. CQ (a) Why is blood pressure usually measured at the arm? (b) Suppose the pressure reading were taken on the

calf of the leg of a standing person. Would there be a difference, in principle? Explain. see ISM

31. CQ (a) Two dams form artificial lakes of equal depth. However, one lake backs up 15 km behind the dam, and

the other backs up 50 km behind. What effect does the difference in length have on the pressures on the dams? (b)

Dams are usually thicker at the bottom. Why? see ISM

32. CQ Water towers (storage tanks) are generally bulb shaped as shown in Fig. 9.28. Wouldn’t it be better to

have a cylindrical storage tank of the same height? Explain. see ISM

33. CQ (a) Liquid storage cans, such as gasoline cans, generally have capped vents. What is the purpose of the vents,

and what happens if you forget to remove the cap before you pour the liquid? (b) Explain how a medicine

dropper works. (c) Explain how we breathe (inhalation and exhalation). see ISM

34. CQ A water dispenser for pets has an inverted plastic bottle, as shown in Fig. 9.29. (The water is dyed blue for

contrast.) When a certain amount of water is drunk from the bowl, more water flows automatically from the

bottle into the bowl. The bowl never overflows. Explain the operation of the dispenser. Does the height of the

water in the bottle depend on the surface area of the water in the bowl? see ISM

35. IE ; In his original barometer, Pascal used water instead of mercury. (a) Water is less dense than mercury, so

the water barometer would have (1) a higher height than, (2) a lower height than, or (3) the same height as the

mercury barometer. Why? (b) How high would the water column have been? (a) (1) a higher height than (b) 10

m

36. ; If you dive to 10 m below the surface of a lake, (a) what is the pressure due to the water alone? (b) What is the

459.810 Pa2.010 Pa (b) total or absolute pressure at that depth? (a)

37. IE ; In an open U-tube, the pressure of a water column on one side is balanced by the pressure of a column of

gasoline on the other side. (a) Compared to the height of the water column, the gasoline column will have (1) a

higher, (2) a lower, or (3) the same height. Why? (b) If the height of the water column is 15 cm, what is the

height of the gasoline column? (a) (1) a higher (b) 22 cm

2125 cm,38. ; A 75-kg athlete does a single-hand handstand. If the area of the hand in contact with the floor is

45.910 Pawhat pressure is exerted on the floor?

4

39. ; The gauge pressure in both tires of a bicycle is 690 kPa. If the bicycle and the rider have a combined mass of

90.0 kg, what is the area of contact of each tire with the ground? (Assume that each tire supports half the total

;426.3910 mweight of the bicycle.)

40. ;; In a sample of seawater taken from an oil spill, an oil layer 4.0 cm thick floats on 55 cm of water. If the

330.7510 kg/m,density of the oil is what is the absolute pressure on the bottom of the

51.0710 Pacontainer?

41. IE ;; In a lecture demonstration, an empty can is used to demonstrate the force exerted by air pressure (Fig.

9.30). A small quantity of water is poured into the can, and the water is brought to a boil. Then the can is sealed

with a rubber stopper. As you watch, the can is slowly crushed with sounds of metal bending. (Why is a rubber

stopper used as a safety precaution?) (a) This is because of (1) thermal expansion and contraction, (2) a higher

steam pressure inside the can, or (3) a lower pressure inside the can as steam condenses. Why? (b) Assuming the

dimensions of the can are and the inside of the can is in a perfect vacuum, what is the 0.24 m0.16 m0.10 m，，

total force exerted on the can by the air pressure? (a) (3) a lower pressure inside the can as steam condenses (b)

41.610 N3600 lb，？

42. ;; What is the fractional decrease in pressure when a barometer is raised 40.0 m to the top of a building?

(Assume that the density of air is constant over that distance.) 0.50%

(29 028 ft)43. ;; A student decides to compute the standard barometric reading on top of Mt. Everest by

assuming that the density of air has the same constant density as at sea level. Try this yourself. What does the

result tell you? air density decreases rapidly with altitude; see ISM

44. ;; To drink a soda (assume same density as water) through a straw requires you to lower the pressure at the top

of the straw. What does the pressure need to be at the top of a straw that is 15.0 cm above the surface of the soda

49.9810 Pain order to get soda to your lips?

45. ;; During a plane flight, a passenger experiences ear pain due to a head cold that has clogged his Eustachian

tubes. Assuming the pressure in his tubes remained at 1.00 atm (from sea level) and the cabin pressure is

maintained at 0.900 atm, determine the air pressure force (including its direction) on one eardrum, assuming it

has a diameter of 0.800 cm. 0.51 N

5

46. ;; Here is a demonstration Pascal used to show the importance of a fluid’s pressure on the fluid’s depth (;Fig.

20.20 m is filled with water. A long, thin tube of cross-sectional area 9.31): An oak barrel with a lid of area

;525.010 m is inserted into a hole at the center of the lid, and water is poured into the tube. When the water

reaches 12 m high, the barrel bursts. (a) What was the weight of the water in the tube? (b) What was the pressure

of the water on the lid of the barrel? (c) What was the net force on the lid due to the water pressure? (a) 5.9 N (b)

541.210 Pa2.410 N (c)

47. ;; The door and the seals on an aircraft are subject to a tremendous amount of force during flight. At an altitude

422.710 Nm,33 000 ftof (about ), the air pressure outside the airplane is only while the inside is 10 000 m

still at normal atmospheric pressure, due to pressurization of the cabin. Calculate the net force due to the air

253.0 m.2.210 N50 000 lbpressure on a door of area (about )

48. ;; The pressure exerted by a person’s lungs can be measured by having the person blow as hard as possible into

one side of a manometer. If a person blowing into one side of an open-tube manometer produces an 80-cm

difference between the heights of the columns of water in the manometer arms, what is the gauge pressure of the

37.810 Palungs?

49. ;; In a head-on auto collision, the driver had his air bags disconnected and his head hits the windshield,

fracturing his skull. Assuming the driver’s head has a mass of 4.0 kg, the area of the head to hit the windshield to

225 cm,be and an impact time of 3.0 ms, with what speed does the head hit the windshield? (Take the

281.910 m/s1.010 Pa.compressive fracture strength of the cranial bone to be )

50. ;; A cylinder has a diameter of 15 cm (Fig. 9.32). The water level in the cylinder is maintained at a constant

height of 0.45 m. If the diameter of the spout pipe is 0.50 cm, how high is h, the vertical stream of water?

(Assume the water to be an ideal fluid.) 0.45 m

51. ;; In 1960, the U.S. Navy’s bathyscaphe Trieste (a submersible) descended to a depth of (about 10 912 m

35 000 ft) into the Mariana Trench in the Pacific Ocean. (a) What was the pressure at that depth? (Assume that

seawater is incompressible.) (b) What was the force on a circular observation window with a diameter of 15

861.110 Pa1.910 Ncm? (a) (b)

6

20.25 m. (a) How much pressure on the 52. ;; The output piston of a hydraulic press has a cross-sectional area of

61.510 N?input piston is required for the press to generate a force of (b) What force is applied to the input

646.010 Pa1.210 Npiston if it has a diameter of 5.0 cm? (a) (b)

24.00 cm53. ;; A hydraulic lift in a garage has two pistons: a small one of cross-sectional area and a large one of

2250 cm.cross-sectional area (a) If this lift is designed to raise a 3500-kg car, what minimum force must be

applied to the small piston? (b) If the force is applied through compressed air, what must be the minimum air

61.3710 Papressure applied to the small piston? (a) 549 N (b)

;3222.5 cm5.010-cm54. ;;; A hypodermic syringe has a plunger of area and a needle. (a) If a 1.0-N force is

applied to the plunger, what is the gauge pressure in the syringe’s chamber? (b) If a small obstruction is at the

end of the needle, what force does the fluid exert on it? (c) If the blood pressure in a vein is 50 mm Hg, what

324.010 N/mforce must be applied on the plunger so that fluid can be injected into the vein? (a) (b)

;32.010 N (c) 1.7 N

55. ;;; A funnel has a cork blocking its drain tube. The cork has a diameter of 1.50 cm and is held in place by

static friction with the sides of the drain tube. When water is filled to 10.0 cm above the cork, it comes flying out.

Determine the maximum force of static friction between the cork and drain tube. Neglect the weight of the

cork. 0.173 N

56. ;;; A hydraulic balance used to detect small changes in mass is shown in Fig. 9.33. If a mass m of 0.25 g is

placed on the balance platform, by how much will the height of the water in the smaller, 1.0-cm-diameter

cylinder have changed when the balance comes to equilibrium? 2.6 mm

9.3 Buoyancy and Archimedes’ Principle

57. MC A wood block floats in a swimming pool. The buoyant force exerted on the block by water depends on (a)

the volume of water in the pool, (b) the volume of the wood block, (c) the volume of the wood block under water,

(d) all of the preceding. (c)

58. MC If a submerged object displaces an amount of liquid of greater weight than its own and is then released, the

object will (a) rise to the surface and float, (b) sink, (c) remain in equilibrium at its submerged position. (a)

7

()(), to that of a fluid what is the condition for the object to float: (a) 59. MC Comparing an object’s density of

！！?！！, or (b) (a) foof

60. CQ (a) What is the most important factor in constructing a life jacket that will keep a person afloat? (b) Why is

it so easy to float in Utah’s Great Salt Lake? see ISM

61. CQ An ice cube floats in a glass of water. As the ice melts, how does the level of the water in the glass change?

Would it make any difference if the ice cube were hollow? Explain. see ISM

62. CQ Oceangoing ships in port are loaded to the so-called Plimsoll mark, which is a line indicating the maximum

safe loading depth. However, in New Orleans, located at the mouth of the Mississippi River, where the water is

brackish (partly salty and partly fresh), ships are loaded until the Plimsoll mark is somewhat below the water

line. Why? port water (partly fresh) is less dense than seawater

63. CQ Two blocks of equal volume, one iron and one aluminum, are dropped into a body of water. Which block

will experience the greater buoyant force? Why? same

64. CQ An inventor comes up with an idea for a perpetual motion machine, as illustrated in Fig. 9.34. It contains

(HO)a sealed chamber with mercury (Hg) in one half and water in the other. A cylinder is mounted in the 2

313.6 g/cmcenter and is free to rotate. He reasons that since mercury is much denser than water ( to

31.00 g/cm), the weight of the mercury displaced by half the cylinder is much greater than the water displaced

by the other half. Then, the buoyant force on the mercury side is greater than that on the water sidemore than

thirteen times greater. The difference in forces and torques should cause the cylinder to rotateperpetually.

Would you invest any money in this invention? Why or why not? see ISM

65. IE ; (a) If the density of an object is exactly equal to the density of a fluid, the object will (1) float, (2) sink, (3)

stay at any height in the fluid, as long as it is totally immersed. (b) A cube 8.5 cm on each side has a mass of 0.65

kg. Will the cube float or sink in water? Prove your answer. (a) (3) stay at any height (b) sink; see ISM

66. ; Suppose that Archimedes found that the king’s crown had a mass of 0.750 kg and a volume of

;533.98010 m. (a) What simple approach did Archimedes use to determine the crown’s volume? (b) Was the

crown pure gold? (a) water displacement (b) no; see ISM

8

67. ; A rectangular boat, as illustrated in Fig. 9.35, is overloaded such that the water level is just 1.0 cm below

32.610 kg the top of the boat. What is the combined mass of the people and the boat?

68. ;; An object has a weight of 8.0 N in air. However, it apparently weighs only 4.0 N when it is completely

332.010 kg/msubmerged in water. What is the density of the object?

69. ;; When a 0.80-kg crown is submerged in water, its apparent weight is measured to be 7.3 N. Is the crown pure

gold? no; see ISM

70. ;; A steel cube 0.30 m on each side is suspended from a scale and immersed in water. What will the scale

3700 kg/m71. ;; A wood cube 0.30 m on each side has a density of and floats levelly in water. (a) What is the

distance from the top of the wood to the water surface? (b) What mass has to be placed on top of the wood so that

its top is just at the water level? (a) 0.09 m (b) 8.1 kg

72. ;; (a) Given a piece of metal with a light string attached, a scale, and a container of water in which the piece of

metal can be submersed, how could you find the volume of the piece without using the variation in the water

level? (b) An object has a weight of 0.882 N. It is suspended from a scale, which reads 0.735 N when the piece is

submerged in water. What are the volume and density of the piece of metal? (a) see ISM (b)

;53331.5010 m, 6.0010 kg/m，，

73. ;; An aquarium is filled with a liquid. A cork cube, 10.0 cm on a side, is pushed and held at rest completely

submerged in the liquid. It takes a force of 7.84 N to hold it under the liquid. If the density of cork is

333HO200 kg/m,1.0010 kg/m find the density of the liquid. (probably ) 2

74. ;; A block of iron quickly sinks in water, but ships constructed of iron float. A solid cube of iron 1.0 m on each

side is made into sheets. To make these sheets into a hollow cube that will not sink, what should be the minimum

length of the sides of the sheets? 2.0 m

75. ;; Plans are being made to bring back the zeppelin, a lighter-than-air airship like the Goodyear blimp that

carries passengers and cargo, but is filled with helium, not flammable hydrogen as was used in the ill-fated

Hindenburg. (See opening Physics Facts.) One design calls for the ship to be 110 m long and to have a total mass

(without helium) of 30.0 metric tons. Assuming the ship’s ―envelope‖ to be cylindrical, what would its diameter

have to be so as to lift the total weight of the ship and the helium? 17.7 m

9

76. ;;; A girl floats in a lake with 97% of her body beneath the water. What are (a) her mass density and (b) her

23339.710 kg/m9.510 N/m (b) weight density? (a)

77. ;;; A spherical navigation buoy is tethered to the lake floor by a vertical cable (Fig. 9.36). The outside

diameter of the buoy is 1.00 m. The interior of the buoy consists of an aluminum shell 1.0 cm thick and the rest

332700 kg/m200 kg/m.is solid plastic. The density of aluminum is and the density of the plastic is The buoy

28.110 Nis set to float exactly halfway out of the water. Determine the tension in the cable.

78. ;;; Figure 9.37 shows a simple laboratory experiment. Calculate (a) the volume and (b) the density of the

suspended sphere. (Assume that the density of the sphere is uniform and that the liquid in the beaker is water.) (c)

Would you be able to make the same determinations if the liquid in the beaker were mercury? (See Table 9.2.)

33;439.810 m1.510 kg/mExplain. (a) (b) (c) see ISM

9.4 Fluid Dynamics and Bernoulli’s Equation

79. MC If the speed at some point in a fluid changes with time, the fluid flow is not (a) steady, (b) irrotational, (c)

incompressible, (d) nonviscous. (a)

80. MC An ideal fluid is not (a) steady, (b) compressible, (c) irrotational, or (d) nonviscous. (b) 81. MC Bernoulli’s equation is based primarily on (a) Newton’s laws, (b) conservation of momentum, (c) a

nonideal fluid, (d) conservation of energy. (d)

82. MC According to Bernoulli’s equation, if the pressure on the liquid in Fig. 9.19 is increased, (a) the flow speed

always increases, (b) the height of the liquid always increases, (c) both the flow speed and the height of the

liquid may increase, (d) none of the preceding. (c)

83. CQ The speed of blood flow is greater in arteries than in capillaries. However, the flow rate equation

(constant)Av seems to predict that the speed should be greater in the smaller capillaries. Can you resolve this

apparent inconsistency? there are many capillaries

84. CQ (a) Explain why water shoots out farther from a hose if you put your finger over the tip of the hose. (b) Give

a human analogy of constricted flow and greater speed. (a) smaller area, greater speed (b) arteries to capillaries

10

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