chapter 9

31. The spring of the pressure gauge shown in the figure has a force constant of 900 N/m, and the piston has a radius of 1.5 cm. As the gauge is lowered into water, what change in depth causes the piston to move in by 0.88 cm? The density of water is 1 000 kg/m3.

a. 1.1 m

71. How much power is theoretically available from a mass flow of 1 000 kg/s of water that falls a vertical distance of 120 m?

a. 1.18E+6 kW

56. A hole is poked through the metal side of a drum holding water. The hole is 16.0 cm below the water surface. What is the initial speed of outflow?

a. 1.77 m/s

12. A Boeing-737 airliner has a mass of 20 500 kg. The total area of the wings is 105 m2. What must be the pressure difference between the top and bottom of the wings to keep the airplane up?

a. 1.91E+3 Pa

86. A small sphere is allowed to fall through air, and when the sphere has a speed of 4.8 × 10-4 m/s, the viscous force on the sphere is 3.0 × 10-15 N. If the viscosity of air is 1.4 × 10-5 N·s/m2, what is the radius of the drop?

a. 2.4E-8 m

58. Water pressurized to 3.00 × 105 Pa is flowing at 5.25 m/s in a pipe which contracts to 1/2 of its former area. What are the pressure and speed of the water after the contraction? (Density of water = 1 × 103 kg/m3.)

a. 2.59E+5 Pa, 10.5 m/s

83. A centrifuge rotates at 100 rev/s (i.e., 628 rad/s). If the test tube places the suspension at 8.00 cm from the axis of rotation, by what factor are the terminal speeds of the settling particles increased as compared to sedimentation cause by gravity?

a. 3.2E+3

61. Water is being sprayed from a nozzle at the end of a garden hose of diameter 2.25 cm. If the nozzle has an opening of diameter 1.30 cm, and if the water leaves the nozzle at a speed of 14.0 m/s, what is the speed of the water inside the hose?

a. 4.67 m/s

32. When lying down, the gauge pressure of the blood at a patient's heart is 13.3 kPa. If the patient suddenly stands up and her body doesn't compensate quickly enough for the pressure changes, what would be the pressure at her head, 55.0 cm above her heart? The density of blood is 1 060 kg/m3.

a. 7.59E+3 Pa

14. A container is filled with water and the pressure at the bottom of the container is P. Then the container is emptied halfway and topped off with oil of density 0.8 × 103 kg/m3, which floats on top of the water. What is the pressure at the bottom of the container now?

a. a pressure < P

68. How much air must be pushed downward at 40.0 m/s to keep an 830-kg helicopter aloft?

b. 203 kg/s

67. Air pressure is 1.00 × 105 N/m2, air density is 1.30 kg/m3, and the density of soft drinks is 1.00 × 103 kg/m3. If one blows carefully across the top of a straw sticking up 0.10 m from the liquid in a soft drink can, it is possible to make the soft drink rise half way up the straw and stay there. How fast must the air be blown across the top of the straw?

b. 27 m/s

98. A machinist needs to punch a 5.0-cm-radius hole in a steel plate which is 0.45 cm thick. If the ultimate shear strength of steel is 2.50 × 108 Pa, what is the force required to accomplish this task?

b. 3.5E+5 N

96. How large a force is necessary to stretch a 1.1-mm-diameter steel wire (Y = 2.0 × 1011 N/m2) by 2.0%?

b. 3.8E+3 N

10. A solid object is made of two materials, one material having density of 2 500 kg/m3 and the other having density of 6 000 kg/m3. If the object contains equal volumes of the materials, what is its average density?

b. 4 250 kg/m3

59. A Venturi tube may be used as the inlet to an automobile carburetor. If the inlet pipe of 2.00 cm diameter narrows to 1.00 cm diameter, what is the pressure drop in the constricted section for airflow of 2.16 m/s in the 2.00-cm section? (Assume air density is 1.25 kg/m3.)

b. 43.7 Pa

30. A U-tube is partially filled with water and then an immiscible liquid is added to the right side. The top of the liquid is a distance h1 = 2.40 cm above the level of interface between the liquid and water. On the left side of the tube the top of the water is a distance h2 = 1.48 cm above the liquid-water interface on the right side. What is the density of the liquid in terms of the density of water, 1 000 kg/m3?

b. 617 kg/m3

36. What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 103 kg/m3 and water density = 1.0 × 103 kg/m3)

b. 7.4E-4 m3

89. The quantity "stress" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to

b. ML−1T−2.

29. A U-tube is partially filled with water and then an immiscible liquid is added to the right side. The top of the liquid is a distance h1 above the level of interface between the liquid and water. On the left side of the tube the top of the water is a distance h2 above the liquid-water interface on the right side. What is the density of the liquid in terms of the density of water ? Note that h2 < h1.

b. h2/h1 p H2O

1. Which state of matter is associated with the very highest of temperatures?

b. plasma

40. The bottom of a flat-bottomed aluminum boat has area = 4.10 m2 and mass = 65.0 kg. If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat, how much lower will the boat ride in the water? (H2O density = 1.0 × 103 kg/m3)

c. 0.0744 m

85. A substance is allowed to diffuse along a 10-cm length of tubing filled with water. The cross section of the tube is 5.3 cm2. If the diffusion coefficient is 5.0 × 10¯10 m2/s, and 6.5 × 10¯14 kg is transported along the tube in 16 s, what is the difference in the concentration levels of the substance at the two ends of the tube?

c. 1.5E-3 kg/m3

24. How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 105 Pa)

c. 10.3 m

73. The condition for onset of turbulent flow is that the Reynolds Number reaches what value?

c. 3 000

34. A piece of aluminum has density 2.70 g/cm3 and mass 770 g. The aluminum is submerged in a container of oil of density 0.650 g/cm3. A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal?

c. 585 g

22. Atmospheric pressure is 1.00 × 105 N/m2, and the density of air is 1.29 kg/m3. If the density of air is constant as you get higher and higher, calculate the height of the atmosphere needed to produce this pressure.

c. 7 900 m

51. Think of Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe. Imagine that you take measurements along the pipe in the direction of fluid flow. What happens to the sum of the pressure and energy per unit volume?

c. It remains constant as the pipe diameter increases.

26. Why do vapor bubbles get larger in boiling water as they approach the surface?

c. The pressure in the water decreases as the bubble moves toward the surface.

63. The equation of continuity applied to an incompressible ideal fluid flowing through a pipe of varying diameter is based on what of the following being conserved for the fluid in the pipe?

c. its flow rate

95. A tire stops a car by use of friction. What modulus should we use to calculate the stress and strain on the tire?

c. shear modulus

92. A uniform pressure of 5.7 × 105 N/m2 is applied to all six sides of a copper cube. What is the percentage change in volume of the cube? (for copper, B = 14 × 1010 N/m2)

d. 0.00041%

94. Consider two steel rods, A and B. B has three times the area and twice the length of A, so Young's modulus for B will be what factor times Young's modulus for A?

d. 1.0

87. A copper wire of length 5.0 m, cross sectional area 6.9 × 10−6 m2, and Young's modulus 11 × 1010 N/m2 has a 190-kg load hung on it. What is its increase in length? (g = 9.8 m/s2)

d. 1.2E-2 m

50. The flow rate of a liquid through a 4.0-cm-radius pipe is 0.0080 m3/s. The average fluid speed in the pipe is

d. 1.6 m/s.

42. A solid rock, suspended in air by a spring scale, has a measured mass of 8.50 kg. When the rock is submerged in water, the scale reads 4.00 kg. What is the density of the rock? (water density = 1 000 kg/m3)

d. 1.9E+3 kg/m3

25. A fountain sends water to a height of 113 m. What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 105 N/m2)

d. 11.1 atm

5. The pressure inside a commercial airliner is maintained at 1.00 atm (105 Pa). What is the net outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure is 0.30 atm?

d. 140 000 N

77. A pipe of diameter three cm is replaced by one of the same length but of diameter six cm. If the pressure difference between the ends of the pipe remains the same, by what factor is the rate of flow of a viscous liquid through it changed?

d. 16

8. The Greenland ice sheet can be one km thick. Estimate the pressure underneath the ice. (The density of ice is 918 kg/m3.)

d. 9.0 × 106 Pa (90 atm)

6. A stonecutter's chisel has an edge area of 0.50 cm2. If the chisel is struck with a force of 45.0 N, what is the pressure exerted on the stone?

d. 9.0E+5 Pa

17. In a large tank of liquid, the hydrostatic pressure at a given depth is a function of

d. Choices a and c are both valid.

62. A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm. If a force F is applied to the plunger, what is the force produced at the opening of the needle?

d. F/25

84. Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

d. It is zero

90. The quantity "strain" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to

d. a dimensionless quantity

44. A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the

d. difference between the weight of the stone and the weight of the displaced water.

93. Bar One has a Young's modulus that is bigger than that of Bar Two. This indicates Bar One

d. is made of material that is different from Bar Two.

64. The fluid to which Bernoulli's equation is applied is based on what being conserved for the fluid?

d. its total mechanical energy

27. At a pressure of 1 atmosphere a column of mercury in a barometer is supported to the height h = 0.76 m. The density of mercury is 13.6 × 103 kg/m3. A barometer of similar design filled with water would support a column of water how high at a pressure of 1 atmosphere?

d. more than ten times h

91. The bulk modulus of a material, as a meaningful physical property, is applicable to which of the following?

d. solids, liquids and gases

75. A pipe carrying water has a radius of 1.0 cm. If the flow velocity is 9.0 cm/s, which of the following characterizes the flow? Take the viscosity of water to be 1.0 × 10−3 N⋅s/m.

d. streamlined

88. In an elastic solid there is a direct proportionality between strain and

d. stress

76. In order to overcome a surface tension of a fluid, a force of 1.35 × 10−2 N is required to lift a wire ring of circumference 13.0 cm. What is the surface tension of the fluid?

a. 0.052 N/m

74. A fluid has a density of 1 040 kg/m3. If it rises to a height of 1.60 cm in a 1.50-mm diameter capillary tube, what is the surface tension of the liquid? Assume a contact angle of zero.

a. 0.0612 N/m

97. What is the minimum diameter of a steel wire if it is to support a mass of 80 kg? The elastic limit of steel is 5.0 × 108 Pa.

a. 1.4 mm

18. A 14 500-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.100 m. If a connecting cylinder with a piston of 0.050-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?

a. 1.45E+4 N

79. The SI units for viscosity are N·s/m2. Another commonly used unit for viscosity is the poise, where 10 poise = 1 N·s/m2. The poise is a fairly large unit, and it is more common to use the centipoise. Which of the following is equal to the centipoise?

a. 10−3 N·s/m2

54. Water (density = 1.00 × 103 kg/m3) flows at 15.0 m/s through a pipe with radius 0.0400 m. The pipe goes up to the second floor of the building, 2.50 m higher, and the pressure remains unchanged. What is the speed of the water flow in the pipe on the second floor?

a. 13.3 m/s

33. A piece of aluminum has density 2.70 g/cm3 and mass 769 g. The aluminum is submerged in a container of oil (oil's density = 0.650 g/cm3). How much oil does the metal displace?

a. 285 cm3

11. A solid object is made of two materials, one material having density of 2 500 kg/m3 and the other having density of 6 500 kg/m3. If the object contains equal masses of the materials, what is its average density?

a. 3 611 kg/m3

41. Legend says that Archimedes, in determining whether or not the king's crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 g/cm3, and the crown's mass is 600 g, what volume would be necessary to prove that it is pure gold?

a. 3.1E+1 cm3

3. A 1.00-kg platinum-iridium cylinder is 26.0 mm in height and 40.0 mm in diameter. What is the density of the material?

a. 30.6 g/cm3

69. A jet of water flowing from a hose at 18 m/s is directed against a wall. If the mass flow in the fluid stream is 2.0 kg/s, what force is the water applying to the wall if backsplash is negligible?

a. 36 N

20. If the column of mercury in a barometer stands at 73.0 cm, what is the atmospheric pressure? (The density of mercury is 13.6 × 103 kg/m3 and g = 9.80 m/s2)

a. 9.73E+4 N/m2

47. A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water. What happens to the surface level of the pond?

a. It stays the same.

13. A container is filled with water and the pressure at the container bottom is P. If the container is instead filled with oil having specific gravity 0.80, what new bottom pressure results?

a. a pressure < P

65. A water pipe with inner radius r1 is connected to a junction with two equal-diameter pipes. Water flows through each of the two pipes with a speed of v. If the diameter of each of the two pipes is ¼ the diameter of the single pipe, what is the flow rate in the single pipe?

a. v/8

39. The bottom of a flat-bottomed aluminum boat has an area of 4.20 m2 and the boat's mass is 63.0 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.00 × 103 kg/m3)

b. 0.0150 m

55. Water (density = 1.00 × 103 kg/m3) flows at 7.2 m/s through a pipe with radius 0.025 m. The pipe goes up to the second floor of the building, 2.00 m higher, and the pressure remains unchanged. What is the radius of the pipe on the second floor?

b. 0.036 m

60. It takes 4.00 minutes to fill a gas tank with 50.0 liters of gasoline. If the pump nozzle is 1.35 cm in radius, what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)

b. 0.364 m/s

15. A cube-shaped box is sitting on the floor. The pressure the box exerts on the floor is 235 Pa. If the density of the box is 21.0 kg/m3, what is the length of each side of the box?

b. 1.14 m

70. Water is sent from a fire hose at 34.5 m/s at an angle of 30.0° above the horizontal. What is the maximum height reached by the water, assuming the fire hose is level with the ground?

b. 15.2 m

35. A block of wood has density 0.500 g/cm3 and mass 2 000 g. It floats in a container of oil (the oil's density is 0.750 g/cm3). What volume of oil does the wood displace?

b. 2 670 cm3

48. A block of wood has specific gravity 0.80. When placed in water, what percent of the volume of the wood is above the surface?

b. 20%

19. By what factor is the total pressure greater at a depth of 900 m in water than at the surface where pressure is one atmosphere? (water density = 1.0 × 103 kg/m3, 1 atmosphere pressure = 1.01 × 105 N/m2, and g = 9.8 m/s2)

b. 88

4. The quantity "pressure" expressed in terms of the fundamental quantities (mass, length, time) is equivalent to

b. ML−1T−2.

53. An ideal fluid, of density 900 kg/m3, flows at 4.80 m/s through a level pipe with radius of 0.22 cm. The pressure in the fluid is 1.3 × 105 N/m2. This pipe connects to a second level pipe, with radius of 0.72 cm. Find the speed of flow in the second pipe.

c. 0.45 m/s

23. The water behind Grand Coulee Dam is 1 000 m wide and 200 m deep. Find the hydrostatic force on the back of the dam. (Hint: the total force = average pressure × area)

c. 1.96E+11 N

38. A cube of wood of density 0.780 g/cm3 is 11.2 cm on a side. When placed in water, what height of the block will float above the surface? (water density = 1.00 g/cm3)

c. 2.46 cm

28. A reading of a tire gauge tells you that the gauge pressure in a tire is 31 lb/in2. What is the absolute pressure in the tire? Assume that atmospheric pressure is 14 lb/in2.

c. 45 lb/in2

9. What is the total mass of the Earth's atmosphere? (The radius of the Earth is 6.4 × 106 m, and atmospheric pressure at the surface is 105 N/m2.)

c. 5 × 1018 kg

78. A fluid is drawn up through a tube as shown in the figure. If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m, then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet

c. 5.24 m/s

82. Spherical particles of density 1.8 g/cm3 are shaken in a container of water (viscosity = 1.0 × 10−3 N⋅s/m3). The water is 9.0 cm deep and is allowed to stand for 30 minutes. What is the radius of the largest particles still in suspension at that time?

c. 5.4E-6 m

57. Water comes down the spillway of a dam from an initial vertical height of 170 m. What is the highest possible speed of the water at the end of the spillway?

c. 57.7 m/s

21. Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at the top of both dams. The Dam #2 is twice as high and twice as wide as Dam #1. How much greater is the force of the water on Dam #2 than the force on Dam #1? (Ignore atmospheric pressure; it is pushing on both sides of the dams.)

c. 8

72. When an artery gets a constricted region due to plaque, how does the pressure in this region compare to the pressure in an unconstricted region adjacent?

c. In the constricted region the blood moves at a higher speed than in the unconstricted region resulting in a decreased pressure.

2. An ice cube with a small solid steel sphere frozen inside floats in a glass of water filled to the brim. What happens to the level of water in the glass as a result of the ice melting?

c. It goes down

46. A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond?

c. It goes down.

43. As ice floats in water, about 10% of the ice floats above the surface of the water. If we float some ice in a glass of water, what will happen to the water level as the ice melts?

c. The water level will remain unchanged.

37. A ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water?

d. 0.258 N

52. An ideal fluid, of density 850 kg/m3, flows at 0.560 kg/s through a pipe of radius 0.0250 m. What is the fluid speed?

d. 0.336 m/s

7. When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? (The bulk modulus of ice is 2.0 × 109 Pa, and 1 atm = 1.0 × 105 Pa.)

d. 1 800 atm

80. In addition to its weight, what force is needed to lift a wire ring of radius 2.0 cm from the surface of blood plasma? The surface tension of blood plasma is 7.3 × 10¯2 N/m.

d. 1.8E-2 N

16. What is the total force on the bottom of a 2.0-m-diameter by 1.5-m-deep round wading pool due to the weight of the air and the weight of the water? (Note the pressure contribution from the atmosphere is 1.0 × 105 N/m2, the density of water is 1 000 kg/m3, and g = 9.8 m/s2.)

d. 3.6E+5 N

66. The flow rate of blood through the average human aorta, of radius 0.95 cm, is about 90 cm3/s. What is the speed of the blood flow through the aorta?

d. 32 cm/s

45. A blimp is filled with 440 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3; the density of helium is 0.178 kg/m3.)

d. 489 kg

81. Spherical particles of density 2.0 g/cm3 are shaken in a container of water (viscosity = 1.0 × 10−3 N⋅s/m3). The water is 9.0 cm deep and is allowed to stand for 25 minutes. What is the greatest terminal velocity of the particles still in suspension at that time?​

d. 6.0E-5 m/s

49. An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 4.0 inches, respectively. The speed of the fluid flow through the 4.0-inch section will be what factor times that through the 1.0-inch section?

d.1/16