Deck 11: Static Fluids

Question 1

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.

Answer 1

A

Question 2

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.

Answer 2

B

Question 3

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.

Answer 3

B

Question 4

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 exerted on this block by the water as a function of time t if the block just enters the water at time t = 0 s?

Question 5

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.

Question 6

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 exerted on it by the water?

A)the aluminum
B)the lead
C)The same buoyant force is exerted on both.
D)It cannot be determined without knowing their volumes.

Question 7

The water company increased the water pressure in the water flowing to an apartment.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.

Question 8

A wooden block contains some nails so that its average 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.

Question 9

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 exerted on the top of the chamber will be the same as the increase in the force exerted on the bottom of the chamber.

Question 10

As a rock sinks deeper and deeper into water of constant density,what happens to the buoyant force exerted on it by water 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.

Question 11

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.

Question 12

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.

Question 13

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.

Question 14

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.

Question 15

Salt water has greater density than fresh water.A boat floats in both fresh water and in salt water.Where is the buoyant force exerted on the boat by the water greater?

A)in salt water
B)in fresh water
C)The buoyant force is the same in both cases.

Question 16

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?

Question 17

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.

Question 18

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?

Question 19

A steel ball sinks in water but floats in a pool of mercury,which is much denser than water.Where is the buoyant force exerted on the ball by the liquid 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.

Question 20

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.

Question 21

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

Question 22

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

Question 23

A 500-N object 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

Question 24

A block of metal weighs 40 N in air and 30 N in water.What is the buoyant force that the water exerts on the block? The density of water is 1000 kg/m³.

A)10 N
B)30 N
C)40 N
D)70 N

Question 25

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

Question 26

A 50-cm³ block of wood is floating on water,and a 50-cm³ chunk of iron is totally submerged in the water.On which one the water exerts the greater buoyant force?

A)on the wood
B)on the iron
C)The same buoyant force is exerted on both.
D)It cannot be determined without knowing their densities.

Question 27

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

Question 28

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?

Question 29

A 13,000-N vehicle is to be lifted by a 25-cm diameter hydraulic piston.What force needs to be exerted on a 5.0 cm diameter piston to accomplish this? Assume the pistons each have negligible mass.

A)260 N
B)520 N
C)2600 N
D)5200 N

Question 30

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 oil must exert on the smaller piston in order to lift the car after it has been raised 1.20 m? For purposes of this problem,neglect the mass of the pistons.

A)0.954 kN
B)1.88 kN
C)1.96 kN
D)3.67 kN
E)1.20 kN

Question 31

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

Question 32

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

Question 33

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

Question 34

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 × 10^{5 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

Question 35

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 oil must exert on the smaller piston in order to start lifting the car? For purposes of this problem,neglect the mass of the pistons.

A)727 N
B)926 N
C)2.90 kN
D)3.33 kN
E)1.20 kN

Question 36

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

Question 37

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/

Question 38

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

Question 39

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.

Question 40

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 mass.
(a)Determine the force that must be exerted by the fluid in the lift on the small piston.
(b)Determine the pressure applied to the fluid in the lift.

Question 41

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

Question 42

A hollow steel ball of diameter 3.0 m just barely floats in water.What is the wall thickness of the ball? (ρ_Fe = 7.87 g/cm³, ρ_water = 1.00 g/cm³)

A)6.6 cm
B)37 cm
C)131 cm
D)79 cm

Question 43

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?

Question 44

You use a spring scale to suspend an object.The spring scale reads 7.84 N when the object is in air and 6.86 N when the object 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

Question 45

A crane lifts a steel submarine of density 7800 kg/m³ and mass 20,000 kg.What is the tension force that the lifting cable exerts on the submarine (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

Question 46

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.

Question 47

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 force the cord exerts on the sphere? The density of water is 1000 kg/m³.

A)35 N
B)40 N
C)46 N
D)52 N
E)58 N

Question 48

A rectangular box of negligible mass measures 5.0 m long,1.0 m wide,and 0.50 m high.How many kilograms of material 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

Question 49

An object floats with half its volume beneath the surface of the water.The weight (force that Earth exerts in it)of the displaced water is 2000 N.What is the weight (force that Earth exerts on it)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.

Question 50

A 4.0-kg cylinder of solid iron is supported by a string while submerged in water.What is the force that the string exerts on the cylinder? 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

Question 51

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

Question 52

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

Question 53

A 1.00-m³ object floats in water with 20.0% of its volume above the waterline.What is the force that Earth exerts on the object? The density of water is 1000 kg/m³.

A)1,960 N
B)7,840 N
C)9,800 N
D)11,800 N

Question 54

What buoyant force is exerted by water on a 0.60-kg solid gold crown 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

Question 55

A 200-N object floats with three-fourths of its volume beneath the surface of the water.What is the buoyant force exerted by the water 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.

Question 56

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 force that the cord exerts on the sphere 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/

Question 57

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

Question 58

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 (apparent weight is the reading of a scale which supports the object)

A)40,000 N
B)39,200 N
C)9,800 N
D)800 N

Question 59

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

Question 60

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 (force exerted on them by Earth),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

Question 61

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

Question 62

A 550- N person empties her lungs as much as possible and is then completely immersed in water of density 1000 kg/m³ while suspended from a harness connected to a spring scale.The spring scale reads 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

Question 63

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

Question 64

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

Question 65

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