Question 1

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.

Accepted Answer

The answer of The small piston of a hydraulic lift...

Question 2

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.)

Accepted Answer

The force needed is determined by the principle of hydraulic lift, which states that the force applied is proportional to the area of the pistons. The force on the smaller piston is calculated using the formula: F1/A1 = F2/A2, where F1 is the force on the smaller piston, A1 is the area of the smaller piston, F2 is the weight of the car, and A2 is the area of the larger piston. After calculating the areas and solving for F1, the force required is approximately 1.96 kN.

Question 3

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.)

Accepted Answer

The answer of A 12,000-N car is raised using a...

Question 4

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?

Accepted Answer

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Question 5

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ m³, 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.

Accepted Answer

The buoyant force on the sphere is equal to the weight of the liquid displaced by the sphere. The weight of the liquid displaced is equal to the difference between the weight of the sphere in air and the tension in the cord. Therefore, the density of the liquid is equal to the weight of the liquid displaced divided by the volume of the liquid displaced. The volume of the liquid displaced is equal to the volume of the sphere, which is (4/3)πr^3, where r is the radius of the sphere. The radius of the sphere can be found from the density of the sphere and its mass. The mass of the sphere is 6.1 kg and the density of the sphere is 2600 kg/m^3. Therefore, the radius of the sphere is 0.1 m. The volume of the liquid displaced is therefore (4/3)π(0.1 m)^3 = 0.00419 m^3. The weight of the liquid displaced is equal to the difference between the weight of the sphere in air and the tension in the cord, which is 6.1 kg * 9.8 m/s^2 - 26 N = 34.78 N. Therefore, the density of the liquid is 34.78 N / 0.00419 m^3 = 8300 kg/m^3.

Question 6

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?

Accepted Answer

To determine the weight of the barge and its cargo, we need to calculate the buoyant force acting on it, which is equal to the weight of the water displaced by the barge.

The volume of water displaced by the barge can be calculated as follows:

volume = width x length x height 
volume = 15.0 m x 75.0 m x 1.20 m 
volume = 13500 m^3

The weight of the water displaced can be calculated using the density of fresh water:

weight = volume x density x gravity 
weight = 13500 m^3 x 1000 kg/m^3 x 9.81 m/s^2 
weight = 1324980 N = 1324.98 kN

Therefore, the weight of the barge and its cargo must be equal to the buoyant force, which is 1324.98 kN or 13.2 MN.

The correct answer is B.

Question 7

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.

Accepted Answer

The volume of water displaced by the ball equals the volume of the ball's outer sphere. The weight of the displaced water equals the weight of the steel. By equating these and solving for the thickness, we find it to be approximately 6.6 cm.

Question 8

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?

Accepted Answer

First, we need to find the volume of the cylinder.
$V = \pi r^2 h = \pi (\frac{0.62}{2})^2 (1.2) \approx 0.44 m^3$
Next, we need to find the weight of the cylinder.
$W = mg = \rho Vg = (1000)(0.44)(9.81) \approx 4300 N$
Since the cylinder is immersed in water, there is a buoyant force acting on it in the upward direction. We can find the buoyant force using Archimedes' principle.
$F_b = \rho_{water} V_{submerged} g = (1000)(0.44)(2.5)(9.81) \approx 4320 N$
The net force on the cylinder is 1120 N downward, so the force from the water on the lower face of the cylinder must be larger than the weight of the cylinder minus the buoyant force. 
$F_{lower} - W + F_b = 1120$
$F_{lower} = W - F_b + 1120$
$F_{lower} = 4300 - 4320 + 1120$
$F_{lower} \approx 4140 N$
Therefore, the best choice is D.

Question 9

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?

Accepted Answer

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Question 10

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 36m/s, what is its speed in this smaller section?

Accepted Answer

According to the principle of continuity for incompressible fluids, the product of cross-sectional area and velocity is constant. If the diameter decreases to 86%, the area decreases to (0.86)^2. Therefore, the velocity increases by a factor of 1/(0.86)^2, resulting in a new speed of approximately 49 m/s.

Question 11

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?

Accepted Answer

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Question 12

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

Accepted Answer

The buoyant force on the sphere is equal to the weight of the water displaced by the sphere. The volume of the sphere is:$$V = \frac{m}{ho} = \frac{7.8 	ext{ kg}}{2500 	ext{ kg/m}^3} = 0.00312 	ext{ m}^3$$The weight of the water displaced by the sphere is:$$F_b = ho g V = (1000 	ext{ kg/m}^3)(9.8 	ext{ m/s}^2)(0.00312 	ext{ m}^3) = 30.6 	ext{ N}$$The tension in the cord is equal to the weight of the sphere minus the buoyant force:$$T = mg - F_b = (7.8 	ext{ kg})(9.8 	ext{ m/s}^2) - 30.6 	ext{ N} = 46 	ext{ N}$$

Question 13

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?

Accepted Answer

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Question 14

A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

Accepted Answer

The answer of A wooden raft has a mass of...

Question 15

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 5.0 × 10⁴ Pa? The density of the oil is 510 kg/m³.

Accepted Answer

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Question 16

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?

Accepted Answer

The answer of The two water reservoirs shown in the...

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?

Accepted Answer

The rate of water flowing through the channel can be found using the formula:

flow rate = area x velocity x density

The area of the cross-section can be found by multiplying the width by the depth:

area = 15 m x 8.0 m = 120 m^2

Substituting the given values,

flow rate = 120 m^2 x 2.5 m/s x 1000 kg/m^3 
= 300,000 kg/s

So the answer is (C) 3.0 x 10^15 kg/s.

Question 18

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?

Accepted Answer

First, we need to find the weight of the board.
Volume of the board = (20.0 cm) x (5.00 cm) x (3.00 m) = 0.3 m^3
Weight of the board = Volume x Density = 0.3 m^3 x 350 kg/m^3 = 105 kg
Next, we need to find the buoyant force acting on the board.
Buoyant force = Volume of water displaced x Density of water x Gravity
Volume of water displaced = (20.0 cm) x (3.00 m) x (x m) where x is the fraction of the volume above the surface of the water.
Volume of water displaced = 0.6 m^3 x
Density of water = 1000 kg/m^3
Gravity = 9.81 m/s^2
Buoyant force = (0.6 m^3 x x) x 1000 kg/m^3 x 9.81 m/s^2 = 5886 x x N
Since the board is floating, the weight of the board is equal to the buoyant force acting on it.
105 kg = 5886 x x N
x ≈ 0.0179 or 1.79%
Therefore, the fraction of the volume of the board above the surface of the water is approximately 1.79%, or 0.0179 as a decimal. The fraction of the volume below the surface of the water is approximately 98.21%, or 0.9821 as a decimal. Therefore, the fraction of the volume above the surface of the water is 0.9821, which is closest to choice B, 0.650.

Question 19

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?

Accepted Answer

The answer of A person who weighs 550 N empties...

Question 20

Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

Accepted Answer

The answer of Water is flowing in a horizontal pipe...

Quiz 11: Fluid Mechanics

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/ m³, 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 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 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 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 flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 36m/s, what is its speed in this smaller section?

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 7.8-kg solid sphere, made of metal whose density is 2500 kg/m³, 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 wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

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 5.0 × 10⁴ Pa? The density of the oil is 510 kg/m³.

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?

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 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 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?

Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

Quiz 11: Fluid Mechanics

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/ m3, 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 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 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 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 flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value. If the speed of the water in the larger section of the pipe was 36m/s, what is its speed in this smaller section?

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 7.8-kg solid sphere, made of metal whose density is 2500 kg/m3, 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 wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m3) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

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 5.0 × 104 Pa? The density of the oil is 510 kg/m3.

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?

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 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 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?

Water is flowing in a horizontal pipe of diameter d. If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was, what should be the new diameter?

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/ m³, 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 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 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 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 7.8-kg solid sphere, made of metal whose density is 2500 kg/m³, 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 wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

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 5.0 × 10⁴ Pa? The density of the oil is 510 kg/m³.

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?

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 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 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?