Chapter 10

115) A fluid is flowing with an average speed of 1.5 m/s through a tube that has a radius of 2.0 mm and is 18 cm long. The drop in pressure is 967 Pa. What is the viscosity of the fluid? 115) _____ A) 0.0018 N ∙ s/m2 B) 0.013 N ∙ s/m2 C) 0.028 N ∙ s/m2 D) 0.0034 N ∙ s/m2 E) 0.0056 N ∙ s/m2

A) 0.0018 N ∙ s/m2

104) Water flows through a horizontal pipe of cross-sectional area 10.0 cm2 at a pressure of 0.250 atm with a flow rate is 1.00 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to 5.00 cm2. What is the pressure at the valve? The density of water is 1000 kg/m3, and treat it as an ideal incompressible fluid. 104) _____ A) 0.235 atm B) 7700 Pa C) 0.157 atm D) 0.110 atm E) 0.200 atm

A) 0.235 atm

85) A hot air balloon along with its cargo has a mass of 4.0 x 105 kg, and it holds 7.0 x 105 m3 of hot air. It is floating at a constant height in air with a density of 1.29 kg/m3. What is the density of the hot air in the balloon? 85) ______ A) 0.72 kg/m3 B) 0.43 kg/m3 C) 0.57 kg/m3 D) 0.86 kg/m3 E) 1.4 kg/m3

A) 0.72 kg/m3

112) Glycerin, with a viscosity of 1.5 N ∙ s/m2, is flowing with an average speed of 1.2 m/s through a tube that has a radius of 5.0 mm and is 25 cm long. What is the drop in pressure over the length of this pipe? 112) _____ A) 140 kPa B) 130 kPa C) 72 kPa D) 46 kPa E) 76 kPa

A) 140 kPa

30) Two horizontal pipes have the same diameter, but pipe B is twice as long as pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe B is Q = deltaV/deltat what is the flow rate in pipe A? 30) ______ A) 2Q B) 16Q C) Q radical2 D) 4Q E) 8Q

A) 2Q

93) An incompressible ideal fluid flows steadily through a pipe that has a change in diameter. The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s. What is the fluid speed at a location where the diameter has narrowed to 4.0 cm? 93) ______ A) 5.1 m/s B) 1.3 m/s C) 0.64 m/s D) 0.32 m/s E) 2.6 m/s

A) 5.1 m/s

3) A styrofoam sphere of radius R has a density ρ. You now carefully compress the sphere so its radius is R/2. What is the density of the compressed sphere? 3) _______ A) 8 ρ B) 2 ρ C) 4 ρ D) ρ radical2 E) ρ radical8

A) 8 ρ

46) The deepest point of the Pacific Ocean is 11,033 m, in the Mariana Trench. What is the gauge pressure in the water at that point? The density of seawater is 1025 kg/m3. 46) ______ A) 8.88 × 107 Pa B) 1.11 × 108 Pa C) 2.22 × 108 Pa D) 5.55 × 107 Pa E) 3.33 × 108 Pa

B) 1.11 × 108 Pa

57) A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil with a density of 800 kg/m3 and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? For purposes of this problem, neglect the weight of the pistons. 57) ______ A) 3.67 kN B) 1.96 kN C) 0.954 kN D) 1.20 kN E) 1.88 kN

B) 1.96 kN

63) If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is 1000 kg/m3. 63) ______ A) 1010 m3 B) 104 m3 C) 1012 m3 D) 107 m3 E) 108 m3

B) 104 m3

29) Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is Q deltaV/deltat= , what is the flow rate in pipe B? 29) ______ A) 4Q B) 16Q C) Q radical2 D) 2Q E) 8Q

B) 16Q

37) How many grams of ethanol (density 0.80 g/cm3) should be added to 5.0 g of chloroform (density 1.5 g/cm3) if the resulting mixture is to have a density of 1.2 g/cm3? Assume that the fluids do not change their volumes when they are mixed. 37) ______ A) 4.4 g B) 2.0 g C) 2.4 g D) 1.8 g E) 1.6 g

B) 2.0 g

101) Ideal incompressible water is flowing in a drainage channel of rectangular cross-section. At one point, the width of the channel is 12 m, the depth of water is 6.0 m, and the speed of the flow is 2.5 m/s. At a point downstream, the width has narrowed to 9.0 m, and the depth of water is 8.0 m. What is the speed of the flow at the second point? 101) _____ A) 4.0 m/s B) 2.5 m/s C) 2.0 m/s D) 3.5 m/s E) 3.0 m/s

B) 2.5 m/s

76) A 200-N object floats with three-fourths of its volume beneath the surface of the water. What is the buoyant force on the object? The density of water is 1000 kg/m3. 76) ______ A) 50 N B) 200 N C) 150 N D) 267 N E) It cannot be determined because we do not know the volume of the object.

B) 200 N

102) Water is flowing in a drainage channel of rectangular cross-section. The width of the channel is 15 m, the depth of water is 8.0 m, and the speed of the flow is 2.5 m/s. What is the mass flow rate of the water? The density of water is 1000 kg/m3. 102) _____ A) 2.0 × 105 kg/s B) 3.0 × 105 kg/s C) 2.0 × 103 kg/s D) 3.0 × 103 kg/s E) 3.0 × 102 kg/s

B) 3.0 × 105 kg/s

65) A 4.0-kg cylinder of solid iron is supported by a string while submerged in water. What is the tension in the string? The density of iron is 7860 kg/m3 and that of water is 1000 kg/m3. 65) ______ A) 24 N B) 34 N C) 2.5 N D) 40 N E) 20 N

B) 34 N

35) A round coin has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.50 g. What is its density? 35) ______ A) 21.5 × 103 kg/m3 B) 5.37 × 103 kg/m3 C) 1.86 × 10-4 kg/m3 D) 2.68 × 103 kg/m3 E) 1.34 × 103 kg/m3

B) 5.37 × 103 kg/m3

103) In a section of horizontal pipe with a diameter of 3.0 cm, the pressure is 100 kPa and water is flowing with a speed of 1.5 m/s. The pipe narrows to 2.0 cm. What is the pressure in the narrower region? Treat the water as an ideal incompressible fluid. 103) _____ A) 230 kPa B) 95 kPa C) 44 kPa D) 48 kPa E) 67 kPa

B) 95 kPa

89) A rectangular wooden block measures 10.0 cm × 4.00 cm × 2.00 cm. When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is 1.00 g/cm3. 89) ______ A) 1.21 g/cm3 B) 0.350 g/cm3 C) 0.825 g/cm3 D) 1.65 g/cm3 E) 0.606 g/cm3

C) 0.825 g/cm3

82) A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/m3, hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values? 82) ______ A) 1600 kg/ B) 1400 kg/ C) 1900 kg/ D) 1700 kg/ E) 1500 kg/

C) 1900 kg/

87) The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of 880 kg/m3 to make it buoyant. If it is totally submerged in seawater with a density of 1025 kg/m3 and neither rising nor sinking, what is the weight of the Trieste craft? 87) ______ A) 527 kN B) 327 kN C) 227 kN D) 427 kN E) 127 kN

C) 227 kN

38) A 100-kg person sits on a 5-kg bicycle. The total weight is borne equally by the two wheels of the bicycle. The tires are 2.0 cm wide and are inflated to a gauge pressure of 8.0 × 105 Pa. What length of each tire is in contact with the ground? 38) ______ A) 2.4 cm B) 1.6 cm C) 3.2 cm D) 1.8 cm E) 6.4 cm

C) 3.2 cm

84) A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m3. How much deeper into the water does the barge sink when 3.0 x 105 kg of coal are loaded on the barge? 84) ______ A) 1.5 m B) 25 cm C) 50 cm D) 75 cm E) 1.0 m

C) 50 cm

83) A barge is 10 m wide and 60 m long and has vertical sides. The bottom of the boat is 1.2 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m3? 83) ______ A) 9.5 MN B) 6.8 MN C) 7.1 MN D) 3.5 MN E) 6.4 MN

C) 7.1 MN

2) A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is ρ. You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid. What is the density of the enlarged sphere? 2) _______ A) 4 ρ B) 8 ρ C) ρ D) ρ/8 E) ρ/2

C) ρ

Substance A has a density of 3 g/cm3 and substance B has a density of 4 g/cm3. In order to obtain equal masses of these two substances, what must be the ratio of the volume of A to the volume of B? 1) _______ A) Va/Vb = 1/3 B) Va/Vb = radical(3/4) C) Va/Vb = 4/3 D) Va/Vb = 3/4 E) Va/Vb = 3/1

C) Va/Vb = 4/3

114) Motor oil, with a viscosity of 0.25 N ∙ s/m2, is flowing through a tube that has a radius of 5.0 mm and is 25 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per second? 114) _____ A) 7.5 m3/s B) 4.7 m3/s C) 0.025 m3/s D) 0.0012 m3/s E) 0.00038 m3/s

D) 0.0012 m3/s

45) The Aswan High Dam on the Nile River in Egypt is 111 m high. What is the gauge pressure in the water at the foot of the dam? The density of water is 1000 kg/m3. 45) ______ A) 1.09 × 103 Pa B) 1.16 × 106 Pa C) 1.11 × 102 Pa D) 1.09 × 106 Pa E) 1.11 × 105 Pa

D) 1.09 × 106 Pa

49) A cubical box 25.0 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.40 kPa and the pressure on the bottom surface is 112.00 kPa. What is the density of the fluid? 49) ______ A) 1000 kg/m3 B) 1120 kg/m3 C) 1090 kg/m3 D) 1060 kg/m3 E) 1030 kg/m3

D) 1060 kg/m3

34) Under standard conditions, the density of air is 1.29 kg/m3. What is the mass of the air inside a room measuring 4.0 m × 3.0 m × 2.0 m? 34) ______ A) 0.32 kg B) 19 kg C) 3.1 kg D) 31 kg E) 1.9 kg

D) 31 kg

81) A 4.7-kg solid sphere, made of metal whose density is 4000 kg/, hangs by a light cord. When the sphere is immersed in water, what is the tension in the cord? The density of water is 1000 kg/m3. 81) ______ A) 40 N B) 52 N C) 46 N D) 35 N E) 58 N

D) 35 N

36) A 1938 nickel has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density? 36) ______ A) 1.37 × 10-4 kg/m3 B) 19.3 × 103 kg/m3 C) 1.82 × 103 kg/m3 D) 7.26 × 103 kg/m3 E) 3.63 × 103 kg/m3

D) 7.26 × 103 kg/m3

5) When a heavy metal block is supported by a cylindrical vertical post of radius R, it exerts a force F on the post. If the diameter of the post is increased to 2R, what force does the block now exert on the post? 5) _______ A) F/radical2 B) F/2 C) F/4 D) F E) 2F

D) F

7) Consider a brick that is totally immersed in water, with the long edge of the brick vertical. The pressure on the brick is 7) _______ A) the same on all surfaces of the brick. B) greatest on the sides of the brick. C) greatest on the top of the brick. D) greatest on the bottom of the brick. E) greatest on the face with largest area.

D) greatest on the bottom of the brick.

27) When you blow some air above a paper strip, the paper rises. This happens because 27) ______ A) the air above the paper moves slower and the pressure is lower. B) the air above the paper moves faster and the pressure is higher. C) the air above the paper moves faster and the pressure remains constant. D) the air above the paper moves faster and the pressure is lower. E) the air above the paper moves slower and the pressure is higher.

D) the air above the paper moves faster and the pressure is lower.

47) The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of 1.04 g/cm3, calculate the absolute (total) pressure at the bottom of the trench in atmospheres. (1.00 in = 2.54 cm, 1.00 atm = 1.01 × 105 Pa) 47) ______ A) 1.1 × 108 atm B) 1.1 × 106 atm C) 1.1 × 105 atm D) 2.1 atm E) 1.1 × 103 atm

E) 1.1 × 103 atm

86) A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m3 while suspended from a harness. Her apparent weight is now 21.2 N. What is her density? 86) ______ A) 960 kg/m3 B) 1050 kg/m3 C) 56.1 kg/m3 D) 1030 kg/m3 E) 1040 kg/m3

E) 1040 kg/m3

48) What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 44.0 cm at a depth of 9400 m in sea water? The density of sea water is 1025 kg/m3. 48) ______ A) 5.74 × 1011 N B) 1.83 × 107 N C) 2.87 × 1011 N D) 2.87 × 107 N E) 5.74 × 107 N

E) 5.74 × 107 N