Question 1

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water.The upper face is 2.50 m below the surface of the water.The net force on this cylinder is observed to be 1120 N downward.Atmospheric pressure is 1.01 × 10⁵ Pa.What is the weight of the cylinder? A)2430 N B)3550 N C)4670 N D)10,900 N E)12,100 N

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Question 2

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m³),what is the tension in the cord? A)46 N B)61 N C)76 N D)92 N E)110 N

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Question 3

An incompressible 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)1.28 m/s
D)2.56 m/s
E)5.12 m/s

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Question 4

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible oil with a density of 820 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm? A)0.045 m B)0.025 m C)0.065 m D)0.115 m E)0.205 m

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Question 5

A barge is 15.0 m wide and 75.0 m long and has vertical sides.The bottom of the hull is 1.20 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)22.6 MN B)13.2 MN C)1.35 MN D)1.13 MN E)11.3 MN

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Question 6

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible 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,you can neglect the weight of the pistons.)
A)727 N
B)926 N
C)2900 N
D)3330 N
E)1.20 kN

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Question 7

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³)that is 3.0 m thick,as shown.What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

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Question 8

A 12,000-N car is raised using a hydraulic lift,which consists of a U-tube with arms of unequal areas,filled with incompressible 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,you can 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

Accepted Answer

First, we need to find the pressure in the system. Since the pistons are at the same level initially, the pressure at the bottom of both sides of the U-tube is atmospheric pressure, 1.013x10^5 N/m^2. Since the oil is incompressible, the pressure at any point in the oil must be the same on both sides of the U-tube. Using Pascal's Law, this means that the pressure at the piston on the larger arm of the U-tube is the same as the pressure at the bottom of the smaller arm.

The pressure at the bottom of the smaller arm can be found using the equation:

P = ρgh

where P is pressure, ρ is density, g is acceleration due to gravity, and h is the height of the oil column above the piston in the smaller arm.

The height of the oil column can be found using the fact that the volume of oil in the U-tube is constant. This means that the product of the area and height of the oil column on each side of the U-tube is the same. Letting h1 and h2 be the heights of the oil column in the larger and smaller arms respectively, we have:

A1h1 = A2h2

where A1 is the area of the larger piston and A2 is the area of the smaller piston. Rearranging this equation, we get:

h2 = (A1/A2)h1

Plugging in the values given, we get:

h2 = (π(0.18^2)/(π(0.05^2))) x 1.20 m = 25.92 m

Now we can use the equation for pressure to find the pressure at the bottom of the smaller arm:

P = ρgh = (800 kg/m^3)(9.81 m/s^2)(25.92 m) = 2.01x10^5 N/m^2

This is the pressure that must be exerted on the oil in the smaller arm in order to lift the car. We can find the force needed to create this pressure using the equation:

F = PA

where F is the force needed, P is the pressure, and A is the area of the smaller piston. Plugging in the values given, we get:

F = (2.01x10^5 N/m^2)(π(0.05^2)) = 1.96 kN

Therefore, the best choice is C.

Question 9

A hollow steel ball of diameter 3.0 m barely floats in water.What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³. A)6.6 cm B)37 cm C)131 cm D)79 cm

Accepted Answer

For the steel ball to barely float, its average density must equal the density of water. The volume of the steel (Vs) can be found from the total volume of the ball minus the volume of the hollow part. The mass of the steel (Ms) is its volume times its density. Setting the mass of the steel equal to the mass of the water displaced by the ball gives us the equation for density: Ms/V = 1000 kg/m^3, where V is the total volume of the ball. By solving this equation with the given densities and the diameter of the ball, we find the thickness of the wall to be 6.6 cm.

Question 10

On planet X,the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 10⁵ N/m².At a depth 5.00 m below the surface,the absolute pressure is 8.00 × 10⁵ N/m².The density of liquid nitrogen is 808 kg/m³. (a)What is the atmospheric pressure on planet X? (b)What is the acceleration due to gravity on planet X?

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Question 11

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

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Question 12

A 6.1-kg solid sphere,made of metal whose density is 2600 kg/  ,is suspended by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 26 N.Find the density of the liquid.
A)1500 kg/ 
B)1400 kg/ 
C)1300 kg/ 
D)1200 kg/ 
E)1100 kg/

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Question 13

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water.The upper face is 2.50 m below the surface of the water.The net force on this cylinder is observed to be 1120 N downward.Atmospheric pressure is 1.01 × 10⁵ Pa.What net force does the water exert on the lower face of the cylinder? A)7.40 × 10³ N B)1.09 × 10⁴ N C)3.79 × 10⁴ N D)4.14 × 10⁴ N E)1.37 × 10⁵ N

Accepted Answer

The buoyant force on the cylinder is equal to the weight of water displaced by the cylinder. The weight of water displaced is given by the volume of water displaced times the density of water, or
$$
V_{	ext{disp}}=\pi\left(\dfrac{0.620}{2}ight)^2	imes1.20=0.442	ext{ m}^3
$$
$$
W_{	ext{disp}}=V_{	ext{disp}}	imesho_{	ext{water}}=0.442	imes10^3=442	ext{ N}
$$
The net force on the cylinder is the difference between the weight of the cylinder and the buoyant force acting on it. Therefore,
$$
F_{	ext{net}}=W_{	ext{cyl}}-W_{	ext{disp}}+P_{	ext{atm}}A_{	ext{bottom}}-P_{	ext{water}}A_{	ext{top}}=1120	ext{ N}
$$
where $W_{	ext{cyl}}$ is the weight of the cylinder, $P_{	ext{water}}$ is the pressure of water at 2.50 m depth, and $A_{	ext{bottom}}$ is the area of the bottom face of the cylinder. Since the cylinder is completely submerged and its axis is vertical, the pressure at the bottom face is
$$
P_{	ext{bottom}}=P_{	ext{water}}+gho_{	ext{water}}h=1.01	imes10^5+\left(9.81	imes10^0ight)\left(1.00	imes10^3ight)\left(2.50ight)=1.26	imes10^5	ext{ Pa}
$$
Thus, the force exerted by water on the bottom face is
$$
F_{	ext{bottom}}=P_{	ext{bottom}}A_{	ext{bottom}}=P_{	ext{atm}}A_{	ext{top}}+W_{	ext{cyl}}-W_{	ext{disp}}-F_{	ext{net}}\approx4.14	imes10^{14}	ext{ N}
$$
Therefore, the answer is D.

Question 14

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density 350 kg/m³.The board is floating partially submerged in water of density 1000 kg/m³.What fraction of the volume of the board is above the surface of the water? A)0.350 B)0.650 C)zero D)0.200 E)The answer depends on which edge of the board is vertical.

Accepted Answer

To solve the problem, we need to compare the weight of the board to the weight of the water it displaces. The weight of the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of the board, density is its density, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of the board can be found using the formula: 
volume = width x thickness x length 
Plugging in the given values, we get: 
volume = 20.0 cm x 5.00 cm x 3.00 m = 3000 cm^3 = 0.003 m^3

The weight of the board is then: 
weight = 0.003 m^3 x 350 kg/m^3 x 9.81 m/s^2 = 10.3 N

The weight of the water displaced by the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of water displaced by the board, density is the density of water, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of water displaced by the board is equal to the volume of the submerged part of the board. Let h be the height of the submerged part of the board. Then: 
volume of water = width x h x length 
Plugging in the given values, we get: 
volume of water = 20.0 cm x h x 3.00 m = 0.6 h m^3

The weight of the water displaced by the board is then: 
weight of water = 0.6 h m^3 x 1000 kg/m^3 x 9.81 m/s^2 = 5886 h N

Since the board is floating partially submerged, the weight of the board is equal to the weight of the water displaced by the submerged part of the board. Thus, we have: 
10.3 N = 5886 h N 
Solving for h, we get: 
h = 0.00175 m

Therefore, the fraction of the volume of the board above the surface of the water is: 
fraction = (width x thickness x length - width x h x length) / (width x thickness x length) 
Plugging in the given values, we get: 
fraction = (20.0 cm x 5.00 cm x 3.00 m - 20.0 cm x 0.00175 m x 3.00 m) / (20.0 cm x 5.00 cm x 3.00 m) = 0.65

So, the answer is (B) 0.650.

Question 15

A rock is suspended from a scale reads 20.0 N.A beaker of water (having a density of 1000 kg/m³)is raised up so the rock is totally submerged in the water.The scale now reads 12.5 N.What is the density of the rock? A)1.60 × 10³ kg/m³ B)2.50 × 10³ kg/m³ C)2.33 × 10³ kg/m³ D)3.00 × 10³ kg/m³ E)2.67 × 10³ kg/m³

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Question 16

As shown in the figure,a container has a vertical tube,whose inner radius is 32.00 mm,connected to it at its side.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 20.0-cm high column of oil,between levels B and C,whose density is 460 kg/m³.What is the density of the unknown liquid? A)1800 kg/m³ B)2000 kg/m³ C)1400 kg/m³ D)1600 kg/m³ E)1700 kg/m³

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Question 17

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

Accepted Answer

The rate of flow of water can be found using the formula:
rate of flow = cross-sectional area x velocity
The cross-sectional area of the channel can be found by multiplying the width and depth of the channel:
cross-sectional area = 15 m x 8.0 m = 120 m^2
Substituting the given values, we get:
rate of flow = 120 m^2 x 2.5 m/s
rate of flow = 300 kg/s
Therefore, the answer is:
C) 3.0 × 10^15 kg/s

Question 18

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

Accepted Answer

When the person is completely immersed in water, the buoyant force acting on her is equal to the weight of the water displaced. Let V be the volume of water displaced by the person.
Buoyant force = weight of water displaced
Density of water × V × g = (550 − 21.2) N
V = (528.8 N) / (1000 kg/m³ × 9.81 m/s²) = 0.054 m³
The volume of the person is the same as the volume of water displaced. Let M be the mass of the person and ρ be her density.
M / ρ = V
M / ρ = 0.054 m³
M = 550 N / 9.81 m/s² = 56.1 kg
ρ = M / V = (56.1 kg) / (0.054 m³) ≈ 1040 kg/m³
Therefore, the answer is B.

Question 19

A wooden raft has a mass of 50 kg.When empty it floats in water (density  with 69% of its volume submerged.What mass of sand can be put on the raft without it sinking?

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Question 20

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible mercury with a density of 13,600 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm? A)1.58 m B)4.20 m C)3.75 m D)3.40 m E)3.15 m

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Quiz 14: Fluids and Elasticity

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m³) ,what is the tension in the cord?

An incompressible 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?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible oil with a density of 820 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm?

A barge is 15.0 m wide and 75.0 m long and has vertical sides.The bottom of the hull is 1.20 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?

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³)that is 3.0 m thick,as shown.What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

A hollow steel ball of diameter 3.0 m barely floats in water.What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

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

A 6.1-kg solid sphere,made of metal whose density is 2600 kg/ ,is suspended by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 26 N.Find the density of the liquid.

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density 350 kg/m³.The board is floating partially submerged in water of density 1000 kg/m³.What fraction of the volume of the board is above the surface of the water?

A rock is suspended from a scale reads 20.0 N.A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water.The scale now reads 12.5 N.What is the density of the rock?

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s.At what rate is water flowing in this channel?

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 wooden raft has a mass of 50 kg.When empty it floats in water (density with 69% of its volume submerged.What mass of sand can be put on the raft without it sinking?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible mercury with a density of 13,600 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm?

Quiz 14: Fluids and Elasticity

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m3) ,what is the tension in the cord?

An incompressible 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?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m3.The manometer contains incompressible oil with a density of 820 kg/m3.What is the difference in elevation h if the manometer reading m is 25.0 cm?

A barge is 15.0 m wide and 75.0 m long and has vertical sides.The bottom of the hull is 1.20 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?

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m3)that is 3.0 m thick,as shown.What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

A hollow steel ball of diameter 3.0 m barely floats in water.What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3.

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

A 6.1-kg solid sphere,made of metal whose density is 2600 kg/ ,is suspended by a cord.When the sphere is immersed in a liquid of unknown density,the tension in the cord is 26 N.Find the density of the liquid.

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density 350 kg/m3.The board is floating partially submerged in water of density 1000 kg/m3.What fraction of the volume of the board is above the surface of the water?

A rock is suspended from a scale reads 20.0 N.A beaker of water (having a density of 1000 kg/m3) is raised up so the rock is totally submerged in the water.The scale now reads 12.5 N.What is the density of the rock?

Water,of density 1000 kg/m3,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s.At what rate is water flowing in this channel?

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 wooden raft has a mass of 50 kg.When empty it floats in water (density with 69% of its volume submerged.What mass of sand can be put on the raft without it sinking?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m3.The manometer contains incompressible mercury with a density of 13,600 kg/m3.What is the difference in elevation h if the manometer reading m is 25.0 cm?

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m³) ,what is the tension in the cord?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible oil with a density of 820 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm?

A barge is 15.0 m wide and 75.0 m long and has vertical sides.The bottom of the hull is 1.20 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?

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³)that is 3.0 m thick,as shown.What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be The density of the oil is 510 kg/ .

A hollow steel ball of diameter 3.0 m barely floats in water.What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density 350 kg/m³.The board is floating partially submerged in water of density 1000 kg/m³.What fraction of the volume of the board is above the surface of the water?

A rock is suspended from a scale reads 20.0 N.A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water.The scale now reads 12.5 N.What is the density of the rock?

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is 2.5 m/s.At what rate is water flowing in this channel?

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?

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density 1000 kg/m³.The manometer contains incompressible mercury with a density of 13,600 kg/m³.What is the difference in elevation h if the manometer reading m is 25.0 cm?