Physics Chapter 10
B
37) A crane lifts a steel submarine of density 7800 kg/m3 and mass 20,000 kg. What is the tension in the lifting cable (a) when the submarine is submerged in water of density 1000 kg/m3, and (b) when it is entirely out of the water? A) (a) 2.0 × 105 N (b) 1.7 × 105 N B) (a) 1.7 × 105 N (b) 2.0 × 105 N C) (a) 2.6 × 103 N (b) 2.0 × 105 N D) (a) 2.0 × 105 N (b) 2.6 × 103 N
E
7) Consider a brick that is totally immersed in water, with the long edge of the brick vertical. The pressure on the brick is A) the same on all surfaces of the brick. B) greatest on the face with largest area. C) greatest on the top of the brick. D) greatest on the sides of the brick. E) greatest on the bottom of the brick.
B
67) A hole of radius 1.0 mm forms in the bottom of a very large water storage tank that holds water to a depth of 15 m. At what volume rate will water flow out of the hole? A) 5.4 × 10-4 m3/s B) 5.4 × 10-5 m3/s C) 5.4 × 10-6 m3/s D) 5.4 × 10-7 m3/s
A
11) Calculate the pressure exerted on the ground due to the weight of person standing on one foot. if the bottom of the person's foot is wide and long. A) 2.1 × 104 Pa B) 2.2 × 103 Pa C) 4.8 × 104 Pa D) 5.3 × 104 Pa
C, E
11) If atmospheric pressure increases by an amount Δp, which of the following statements about the pressure in a lake is true? (There could be more than one correct choice.) A) The absolute (total) pressure does not change. B) The absolute (total) pressure increases, but by an amount less than Δp. C) The absolute (total) pressure increases by Δp. D) The gauge pressure increases by Δp. E) The gauge pressure does not change.
A, E
12) A closed cubical chamber resting on the floor contains oil and a piston. If you push down on the piston hard enough to increase the pressure just below the piston by an amount Δp, which of the following statements is correct? (There could be more than one correct choice.) A) The pressure everywhere in the oil will increase by Δp. B) The pressure at the bottom of the oil will increase by more than Δp. C) The pressure at the top of the oil will increase by less than Δp. D) The pressure on the sides of the chamber will not increase. E) The increase in the force on the top of the chamber will be the same as the increase in the force on the bottom of the chamber.
C
13) A person weighing 900 N is standing on snowshoes. Each snowshoe has area 2500 cm2 and has negligible weight. What pressure does this person's weight exert on the snow? A) 0.18 N/m2 B) 0.36 N/m2 C) 1800 N/m2 D) 3600 N/m2
D
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? A) F/4 B) F/2 C) F/ D) F E) 2F
C
33) 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. A) 1010 m3 B) 1012 m3 C) 104 m3 D) 107 m3 E) 108 m3
D
34) An object has a volume of 4.0 m3 and weighs 40,000 N. What will its apparent weight be in water of density 1000 kg/m3? A) 40,000 N B) 39,200 N C) 9,800 N D) 800 N
D
35) 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. A) 2.5 N B) 20 N C) 24 N D) 34 N E) 40 N
A
4) When a box rests on a round sheet of wood on the ground, it exerts an average pressure p on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure? A) 4p B) 2p C) p D) p/2 E) p/4
D
12) A brick weighs 50.0 N, and measures 30.0 cm × 10.0 cm × 4.00 cm. What is the maximum pressure it can exert on a horizontal surface due to its weight? A) 1.25 Pa B) 12.5 Pa C) 1.25 kPa D) 12.5 kPa
C
1) A plastic block of dimensions 2.00 cm × 3.00 cm × 4.00 cm has a mass of 30.0 g. What is its density? A) 0.80 g/cm3 B) 1.20 g/cm3 C) 1.25 g/cm3 D) 1.60 g/cm3
B
1) 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? A) = B) = C) = D) = E) =
C
10) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the absolute (total) pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?
A
10) One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. What net outward force is exerted on a square window of the house that is on each side? (1.00 atm = 1.01 × 105 Pa) A) 4.59 × 104 N B) 5.19 × 104 N C) 4.82 × 105 N D) 5.42 × 105 N
C
13) The water pressure to an apartment is increased by the water company. The water enters the apartment through an entrance valve at the front of the apartment. Where will the increase in the static water pressure be greatest when no water is flowing in the system? A) at a faucet close to the entrance valve B) at a faucet far from the entrance valve C) It will be the same at all faucets. D) There will be no increase in the pressure at the faucets.
A
14) A waiter fills your water glass with ice water (containing many ice cubes) such that the liquid water is perfectly level with the rim of the glass. As the ice melts, A) the liquid-water level remains flush with the rim of the glass. B) the liquid water level rises, causing water to run down the outside of the glass. C) the liquid-water level decreases.
A
14) A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is 1000 kg/m3. A) 3.9 × 105 N/m2 B) 2.0 × 104 N/m2 C) 9.2 N/m2 D) The question cannot be answered because the cross sectional area of the tank is needed.
C
15) A spherical ball of lead (density 11.3 g/cm3) is placed in a tub of mercury (density 13.6 g/cm3). Which answer best describes the result? A) The lead ball will float with about 83% of its volume above the surface of the mercury. B) The lead ball will float with its top exactly even with the surface of the mercury. C) The lead ball will float with about 17% of its volume above the surface of the mercury. D) The lead will sink to the bottom of the mercury.
A
15) 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. A) 1.09 × 106 Pa B) 1.16 × 106 Pa C) 1.09 × 103 Pa D) 1.11 × 105 Pa E) 1.11 × 102 Pa
C
16) A wooden block contains some nails so that its density is exactly equal to that of water. If it is placed in a tank of water and released from rest when it is completely submerged, it will A) rise to the surface. B) sink to the bottom. C) remain where it is released.
C
16) 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. A) 5.55 × 107 Pa B) 8.88 × 107 Pa C) 1.11 × 108 Pa D) 2.22 × 108 Pa E) 3.33 × 108 Pa
B
17) A boat loaded with rocks is floating in a swimming pool. If the rocks are thrown into the pool, the water level in the pool, after the rocks have settled to the bottom, A) rises. B) falls. C) stays the same.
A
17) 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) A) 1.1 × 103 atm B) 1.1 × 108 atm C) 1.1 × 105 atm D) 1.1 × 106 atm E) 2.1 atm
C
18) Salt water has greater density than fresh water. A boat floats in both fresh water and in salt water. Where is the buoyant force greater on the boat? A) in salt water B) in fresh water C) The buoyant force is the same in both cases.
A
18) 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. A) 5.74 × 107 N B) 5.74 × 1011 N C) 2.87 × 1011 N D) 1.83 × 107 N E) 2.87 × 107 N
C
19) 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? A) 1000 kg/m3 B) 1030 kg/m3 C) 1060 kg/m3 D) 1090 kg/m3 E) 1120 kg/m3
B
19) Salt water is denser than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of water displaced in the salt water is A) more. B) less. C) the same. D) Cannot be determined because we do not know the volume of the ship.
A
2) A compressed gas with a total mass of is stored in a spherical container having a radius of 0.521 m. What is the density of the compressed gas? A) 181 kg/m3 B) 110 kg/m3 C) 134 kg/m3 D) 161 kg/m3
D
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? A) 8 ρ B) 4 ρ C) ρ/2 D) ρ E) ρ/8
D
20) A circular window 30 cm in diameter in a submarine can withstand a net maximum force of 5.20 × 105 N without damage. What is the maximum depth in a fresh-water lake to which the submarine can go without damaging the window? The density of fresh water is 1000 kg/m3. A) 680 m B) 740 m C) 1200 m D) 750 m
A
20) A steel ball sinks in water but floats in a pool of mercury, which is much denser than water. Where is the buoyant force on the ball greater? A) floating on the mercury B) submerged in the water C) It is the same in both cases. D) It cannot be determined from the information given.
A
21) A 10-kg piece of aluminum sits at the bottom of a lake, right next to a 10-kg piece of lead, which is much denser than aluminum. Which one has the greater buoyant force on it? A) the aluminum B) the lead C) Both have the same buoyant force. D) It cannot be determined without knowing their volumes.
A
21) A container has a vertical tube, whose inner radius is 24.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The mass of the oil is closest to A) 210 B) 410 C) 620 D) 820 E) 1000
A
22) A container has a vertical tube, whose inner radius is 12.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The gauge pressure at level B is closest to A) 630 Pa B) 310 Pa C) 470 Pa D) 790 Pa E) 940 Pa
B
22) A piece of iron rests on top of a piece of wood floating in a bathtub. If the iron is removed from the wood, and kept out of the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) It is impossible to determine from the information given.
A
23) A container has a vertical tube, whose inner radius is 20.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C, whose density is The density of the unknown liquid is closest to A) 3600 kg/ B) 3900 kg/ C) 2800 kg/ D) 3100 kg/ E) 3300 kg/
C
23) A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub? A) It goes up. B) It goes down. C) It does not change. D) It cannot be determined without knowing the volumes of the two pieces of wood.
C
24) As a rock sinks deeper and deeper into water of constant density, what happens to the buoyant force on it if it started above the surface of the water? A) The buoyant force keeps increasing steadily. B) The buoyant force remains constant. C) The buoyant force first increases and then remains constant. D) The buoyant force steadily decreases.
13 m
24) As shown in the figure, a large open tank contains a layer of oil ( density 450 kg/ ) floating on top of a layer of water (density 1000 kg/m3) that is 3.0 m thick, as shown in the sketch. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be
10.6 kg
25) A container consists of two vertical cylindrical columns of different diameter connected by a narrow horizontal section, as shown in the figure. The open faces of the two columns are closed by very light plates that can move up and down without friction. The tube diameter at A is 35.0 cm and at B it is 10.2 cm. This container is filled with oil of density 0.820 g/cm3. If a 125-kg object is placed on the larger plate at A, how much mass should be placed on the smaller plate at B to balance it?
B
25) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the buoyant force B on this block as a function of time t if the block just enters the water at time t = 0 s?
B
26) 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 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 initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons. A) 727 N B) 926 N C) 2.90 kN D) 3.33 kN E) 1.20 kN
B
26) A 50-cm3 block of wood is floating on water, and a 50-cm3 chunk of iron is totally submerged in the water. Which one has the greater buoyant force on it? A) the wood B) the iron C) Both have the same buoyant force. D) It cannot be determined without knowing their densities.
C
27) 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. A) 0.954 kN B) 1.88 kN C) 1.96 kN D) 3.67 kN E) 1.20 kN
B
27) When you blow some air above a paper strip, the paper rises. This happens because A) the air above the paper moves faster and the pressure is higher. B) the air above the paper moves faster and the pressure is lower. C) the air above the paper moves faster and the pressure remains constant. D) the air above the paper moves slower and the pressure is higher. E) the air above the paper moves slower and the pressure is lower.
C
28) A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of 2.0 cm2. If the large piston has an area of 40 cm2, how much weight can the large piston support? Assume the pistons each have negligible weight. A) 25 N B) 500 N C) 10000 N D) 40000 N
B
28) Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water pressure greatest? A) at point A B) at point B C) It is the same at both A and B.
D
29) In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight. A) 6.7 × 103 N B) 5.0 × 103 N C) 2.9 × 103 N D) 2.2 × 103 N
D
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 = , what is the flow rate in pipe B? A) 2Q B) 4Q C) 8Q D) 16Q E) Q
C
4) 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? A) 0.32 kg B) 3.1 kg C) 31 kg D) 1.9 kg E) 19 kg
E
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? A) 2 ρ B) 4 ρ C) ρ D) ρ E) 8 ρ
A
3) The density of material at the center of a neutron star is approximately 1.00 × 1018 kg/m3. What is the mass of a cube of this material that is on each side. (One micron is equal to 1.00 × 10-6 m.) A) 5.45 kg B) 4.74 kg C) 6.16 kg D) 6.70 kg
B
30) A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston. What force needs to be applied to a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible weight. A) 260 N B) 520 N C) 2600 N D) 5200 N
A
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 = what is the flow rate in pipe A? A) 2Q B) 4Q C) 8Q D) 16Q E) Q
(a) 600 N (b) 1.2 × 105 Pa
31) The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. Assume the pistons each have negligible weight. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.
A
32) A block of metal weighs 40 N in air and 30 N in water. What is the buoyant force on the block due to the water? The density of water is 1000 kg/m3. A) 10 N B) 30 N C) 40 N D) 70 N
D
36) What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is 19.3 × 103 kg/m3 and that of water is 1000 kg/m3. A) 3.0 × 10-5 N B) 3.0 × 10-4 N C) 3.0 × 10-2 N D) 0.30 N
C
38) An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m3. What is the density of the object? A) 6000 kg/m3 B) 7000 kg/m3 C) 8000 kg/m3 D) 9000 kg/m3
B
39) When a container of water is placed on a laboratory scale, the scale reads 120 g. Now a 20-g piece of copper (of density 8.9 g/cm3) is suspended from a thread and lowered into the water, not touching the bottom of the container. What will the scale now read? The density of water is 1.0 g/cm3. A) 120 g B) 122 g C) 138 g D) 140 g
(a) 3.7 × 10-4 m3 (b) 6.2 N
40) A piece of aluminum with a mass of 1.0 kg and density of 2700 kg/m3 is suspended from a light cord and then completely immersed in a container of water having density 1000 kg/m3. (a) Determine the volume of the piece of aluminum. (b) Determine the tension in the cord when the aluminum is immersed in the container of water.
A
41) A cylindrical rod of length 12 cm and diameter 2.0 cm will just barely float in water of density 1000 kg/m3. What is its mass? A) 38 g B) 75 g C) 150 g D) 300 g
C
42) A rectangular box of negligible mass measures 5.0 m long, 1.0 m wide, and 0.50 m high. How many kilograms of mass can be loaded onto the box before it sinks in a lake having water of density 1000 kg/m3? A) 0.50 × 103 kg B) 1.5 × 103 kg C) 2.5 × 103 kg D) 3.5 × 103 kg
B
43) A 1.00-m3 object floats in water with 20.0% of its volume above the waterline. What does the object weigh out of the water? The density of water is 1000 kg/m3. A) 1,960 N B) 7,840 N C) 9,800 N D) 11,800 N
B
44) An object floats with half its volume beneath the surface of the water. The weight of the displaced water is 2000 N. What is the weight of the object? The density of water is 1000 kg/m3. A) 1000 N B) 2000 N C) 4000 N D) It cannot be determined because we do not know the volume of the object.
C
45) A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density? The density of water is 1000 kg/m3. A) 1333 kg/m3 B) 1000 kg/m3 C) 750 kg/m3 D) 250 kg/m3
C
46) 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. A) 50 N B) 150 N C) 200 N D) 267 N E) It cannot be determined because we do not know the volume of the object.
D
47) A polar bear of mass 200 kg stands on an ice floe that is a uniform 1.0 m thick. What is the minimum area of the floe that will just support the bear in saltwater of density 1030 kg/m3? The density of ice is 980 kg/m3. A) 1.0 m2 B) 2.0 m2 C) 3.0 m2 D) 4.0 m2
31 kg
48) A wooden raft has a mass of 55 kg. When empty it floats in water (density with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?
A
49) A hollow steel ball of diameter 3.0 m just barely floats in water. What is the wall thickness of the ball? (ρFe = 7.87 g/cm3, ρwater = 1.00 g/cm3) A) 6.6 cm B) 37 cm C) 131 cm D) 79 cm
A
5) 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? A) 5.37 × 103 kg/m3 B) 21.5 × 103 kg/m3 C) 1.34 × 103 kg/m3 D) 2.68 × 103 kg/m3 E) 1.86 × 10-4 kg/m3
A
50) A 200-kg flat-bottomed boat floats in fresh water, which has a density of 1000 kg/m3. If the base of the boat is 1.42 m wide and 4.53 m long, to what depth is the bottom of the boat submerged when it carries three passengers whose total mass is A) 7.10 cm B) 7.53 cm C) 7.95 cm D) 8.52 cm
A
51) 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. A) 35 N B) 40 N C) 46 N D) 52 N E) 58 N
A
52) A solid sphere of mass 8.6 kg, made of metal whose density is 3400 kg/ , 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? A) 1900 kg/ B) 1700 kg/ C) 1600 kg/ D) 1500 kg/ E) 1400 kg/
D
53) 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? A) 3.5 MN B) 6.4 MN C) 6.8 MN D) 7.1 MN E) 9.5 MN
B
54) 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? A) 25 cm B) 50 cm C) 75 cm D) 1.0 m E) 1.5 m
B
55) 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? A) 1.4 kg/m3 B) 0.72 kg/m3 C) 0.57 kg/m3 D) 0.86 kg/m3 E) 0.43 kg/m3
B
56) 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? A) 1050 kg/m3 B) 1040 kg/m3 C) 1030 kg/m3 D) 960 kg/m3 E) 56.1 kg/m3
B
57) 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? A) 127 kN B) 227 kN C) 327 kN D) 427 kN E) 527 kN
E
58) A cylinder, semicircular in cross-section, is 10 m long and 5.0 m in radius. It is completely submerged, with its flat bottom side horizontal and 8.0 m below the water surface, as shown in the figure. What is the magnitude of the net force on the curved upper surface of the half-cylinder? Neglect atmospheric pressure. A) 2.0 × 106 N B) 2.5 × 106 N C) 3.0 × 106 N D) 3.5 × 106 N E) 4.0 × 106 N
A
59) 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. A) 0.825 g/cm3 B) 1.21 g/cm3 C) 1.65 g/cm3 D) 0.606 g/cm3 E) 0.350 g/cm3
E
6) 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? A) 1.37 × 10-4 kg/m3 B) 1.82 × 103 kg/m3 C) 19.3 × 103 kg/m3 D) 3.63 × 103 kg/m3 E) 7.26 × 103 kg/m3
E
6) As shown in the figure, fluid fills a container having several sections. At which of the indicated points is the pressure greatest? A) A B) B C) C D) D E) The pressure is the same at each of the labeled points.
A
60) Consider a very small hole in the bottom of a tank that is in diameter and filled with water to a height of Find the speed at which the water exits the tank through the hole. A) 4.20 m/s B) 17.64 m/s C) 44.1 m/s D) 48.3 m/s
A
61) Water flowing through a cylindrical pipe suddenly comes to a section of pipe where the diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was what is its speed in this smaller section if the water behaves like an ideal incompressible fluid? A) 43 m/s B) 37 m/s C) 28 m/s D) 24 m/s
A
62) A pump uses a piston of 15 cm diameter that moves at 2.0 cm/s as it pushes a fluid through a pipe. What is the speed of the fluid when it enters a portion of the pipe that is 3.0 mm in diameter? Treat the fluid as ideal and incompressible. A) 50 m/s B) 50 cm/s C) 6.0 cm/s D) 22 cm/s
E
63) 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? A) 0.32 m/s B) 0.64 m/s C) 1.3 m/s D) 2.6 m/s E) 5.1 m/s
A
64) Fluid flows at 2.0 m/s through a pipe of diameter 3.0 cm. What is the volume flow rate of the fluid? A) 1.4 × 10-3 m3/s B) 5.7 × 10-3 m3/s C) 14 m3/s D) 57 m3/s
D
65) Ideal incompressible fluid flows through a 4.0-cm-diameter pipe at 1.0 m/s. There is a 2.0 cm diameter constriction in the line. What is the speed of the fluid in this constriction? A) 0.25 m/s B) 0.50 m/s C) 2.0 m/s D) 4.0 m/s
D
66) Water, which we can treat as ideal and incompressible, flows at 12 m/s in a horizontal pipe with a pressure of 3.0 × 104 Pa. If the pipe widens to twice its original radius, what is the pressure in the wider section? A) 3.0 × 104 Pa B) 4.9 × 104 Pa C) 7.4 × 104 Pa D) 9.8 × 104 Pa
D
68) Ideal incompressible water flows through a horizontal pipe of cross-sectional area 10.0 cm2 at a pressure of 0.250 atm with a volume flow rate of 1.00 × 10-3 m3/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? A) 0.112 atm B) 0.157 atm C) 0.200 atm D) 0.235 atm
B
69) For a certain patient, the build-up of fatty tissue on the wall of an artery has decreased the arterial radius by 10%. By how much would the pressure provided by the heart have to be increased to maintain a constant volume of blood flow? Model the blood as an ideal incompressible fluid. A) 48% B) 52% C) 46% D) 54%
A
7) 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. A) 2.0 g B) 2.4 g C) 1.8 g D) 4.4 g E) 1.6 g
(a) 0.13 m/s (b) 23 L/min
70) An ideal incompressible fluid flows at 0.252 m/s through a 44-mm diameter cylindrical pipe. The pipe widens to a square cross sectional area that is 5.5 cm on a side. Assume steady flow throughout the system. (a) What is the speed of the fluid through the square section of pipe? (b) What is the flow rate in liters per minute?
C
8) 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? A) 1.6 cm B) 1.8 cm C) 3.2 cm D) 2.4 cm E) 6.4 cm
A
8) An air bubble underwater has the same pressure as that of the surrounding water. As the air bubble rises toward the surface (and its temperature remains constant), the volume of the air bubble A) increases. B) decreases. C) remains constant. D) increases or decreases, depending on the rate it rises.
A
9) A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the gauge pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?
C
9) The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is 100 cm2? A) 12 × 105 Pa B) 12 × 104 Pa C) 2.9 × 105 Pa D) 2.9 × 104 Pa
