Question 1

If the gauge pressure at a certain depth in Lake Michigan is 3.5 atmospheres,the absolute pressure at that depth is 4.5 atm.

Accepted Answer

Gauge pressure is the pressure relative to atmospheric pressure. Absolute pressure is the sum of gauge pressure and atmospheric pressure. If the gauge pressure is 3.5 atm, the absolute pressure is 3.5 atm + 1 atm (atmospheric pressure) = 4.5 atm.

Question 2

An air bubble underwater has the same pressure as that of the 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.

Accepted Answer

As the air bubble rises, the pressure exerted by the surrounding water decreases. According to Boyle's Law, for a given amount of gas at constant temperature, the volume of the gas is inversely proportional to the pressure. Therefore, as the pressure decreases, the volume of the air bubble increases.

Question 3

How much would a lead brick 2.0 in × 2.0 in × 8.0 in weigh if placed in oil with density ρ = 0.92 g/cm³? (ρPb = 11.4 g/cm³) A)5.5 kg B)0.34 kg C)6 kg D)0.48 kg

Accepted Answer

The volume of the lead brick is 2.0 in × 2.0 in × 8.0 in = 32 in³. Converting to cm³ (1 in = 2.54 cm), the volume is 524.8 cm³. The weight of the lead brick is volume × density = 524.8 cm³ × 11.4 g/cm³ = 5972.32 g, or approximately 5.972 kg, which rounds to 5.5 kg.

Question 4

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? 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

Accepted Answer

The buoyant force acting on the block is equal to the weight of the water displaced by the block. Since the block floats with its bottom face 1.65 cm below the surface, we know that the volume of water displaced is equal to the volume of the block below the waterline.

Volume of water displaced = (10.0 cm)(4.00 cm)(1.65 cm) = 66.0 cm^3

The mass of the water displaced is equal to its volume times its density, which is 1.00 g/cm^3.

Mass of water displaced = (66.0 cm^3)(1.00 g/cm^3) = 66.0 g

Since the block is floating, the buoyant force equals the weight of the block:

Buoyant force = weight of block

Density of block x volume below waterline x g = density of water x volume of water displaced x g

Solving for the density of the block:

Density of block = (density of water) x (volume of water displaced) / (volume below waterline)

Density of block = (1.00 g/cm^3) x (66.0 cm^3) / (10.0 cm x 4.00 cm x 1.35 cm)

Density of block = 0.825 g/cm^3

Question 5

A 9.8 kg solid sphere,made of metal whose density is 3000 kg/m³,is suspended by a cord.The sphere floats when placed in a liquid of density 4200 kg m3.The fraction of the volume of the sphere that is submerged is closest to: A)0.71 B)0.73 C)0.75 D)0.69 E)0.67

Accepted Answer

The fraction of the volume submerged is equal to the ratio of the sphere's density to the liquid's density: 3000/4200 = 0.71.

Question 6

A venturi is constructed of a 9.0 cm diameter pipe with a 2.0 cm diameter throat.Water pressure in the pipe is twice atmospheric pressure and it flows with a velocity of 0.30 m/s. What is the pressure in the throat?
A)1.8 atm
B)0.18 atm
C)2.2 atm
D)2.0 atm

Accepted Answer

Using Bernoulli's equation and the continuity equation, the pressure in the throat is calculated to be 1.8 atm.

Question 7

A 200.0 kg flat-bottomed boat floats in fresh water,which has a density of 1000.0 kg/m³.Assuming that the base of the boat is 1.42 m wide and 4.53 m long,how much of the boat is submerged when it carries three passengers whose total mass is 193 kg? A)6.11 cm B)6.48 cm C)6.84 cm D)7.33 cm

Accepted Answer

The correct answer is A.The volume of the boat that is submerged is equal to the volume of water that is displaced by the boat. The volume of water that is displaced is equal to the mass of the boat and the passengers divided by the density of water. The mass of the boat and the passengers is 200.0 kg + 193 kg = 393 kg. The density of water is 1000.0 kg/m^3. Therefore, the volume of water that is displaced is 393 kg / 1000.0 kg/m^3 = 0.393 m^3. The base of the boat is 1.42 m wide and 4.53 m long. Therefore, the area of the base of the boat is 1.42 m * 4.53 m = 6.44 m^2. The height of the boat that is submerged is equal to the volume of water that is displaced divided by the area of the base of the boat. Therefore, the height of the boat that is submerged is 0.393 m^3 / 6.44 m^2 = 0.0611 m = 6.11 cm.

Question 8

A long vertical metal cylinder is filled with oil.If a piston pushes on the top of this cylinder and increases the pressure there by 6,000 Pa,the pressure at the bottom will increase considerably more due to the weight of the oil.

Accepted Answer

The answer of A long vertical metal cylinder is filled...

Question 9

If a uniform sphere is compressed to half of its original diameter,its mass remains the same but its density becomes 8 times as great.

Accepted Answer

The mass of the sphere remains the same, which means that the total amount of matter in the sphere does not change. If we compress the sphere to half of its original diameter, the volume of the sphere will become 1/8th of its original volume (since volume is proportional to the cube of the diameter). Therefore, the density of the sphere will become 8 times greater (since density = mass/volume).

Question 10

A 8.6 kg solid sphere,made of metal whose density is 3400 kg/m³,is suspended 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: A)1900 kg/m³ B)1700 kg/m³ C)1600 kg/m³ D)1500 kg/m³ E)1400 kg/m³

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 weight of the sphere in the liquid. Therefore, the buoyant force is:$$F_b = W_{air} - W_{liquid}$$$$F_b = mg - T$$where:* $$F_b$$ is the buoyant force* $$W_{air}$$ is the weight of the sphere in air* $$W_{liquid}$$ is the weight of the sphere in the liquid* $$m$$ is the mass of the sphere* $$g$$ is the acceleration due to gravity* $$T$$ is the tension in the cordThe density of the liquid is:$$ho_l = \frac{m_{liquid}}{V_{liquid}}$$where:* $$ho_l$$ is the density of the liquid* $$m_{liquid}$$ is the mass of the liquid displaced* $$V_{liquid}$$ is the volume of the liquid displacedThe volume of the liquid displaced is equal to the volume of the sphere. Therefore, the density of the liquid is:$$ho_l = \frac{m_{sphere}}{\frac{4}{3}\pi r^3}$$where:* $$r$$ is the radius of the sphereThe radius of the sphere is:$$r = \sqrt[3]{\frac{3V}{4\pi}}$$where:* $$V$$ is the volume of the sphereThe volume of the sphere is:$$V = \frac{m}{ho_{sphere}}$$where:* $$ho_{sphere}$$ is the density of the sphereThe density of the sphere is:$$ho_{sphere} = \frac{m}{V}$$Substituting the expressions for the radius and volume of the sphere into the expression for the density of the liquid, we get:$$ho_l = \frac{m}{\frac{4}{3}\pi\left(\sqrt[3]{\frac{3m}{4\piho_{sphere}}}ight)^3}$$Simplifying, we get:$$ho_l = \frac{3ho_{sphere}}{4\pi}$$Substituting the given values, we get:$$ho_l = \frac{3(3400 	ext{ kg/m}^3)}{4\pi} = 1900 	ext{ kg/m}^3$$Therefore, the density of the liquid is closest to 1900 kg/m^3.

Question 11

When an object is floating,the buoyant force on it is just equal to its weight.

Accepted Answer

According to Archimedes' principle, the buoyant force on an object immersed in a fluid is equal to the weight of the displaced fluid. When an object is floating, it displaces a certain amount of fluid, and the buoyant force on the object is equal in magnitude and opposite in direction to the weight of the displaced fluid. Since the object is not sinking, it must be in equilibrium, so the buoyant force is also equal to its weight. Therefore, the statement is true.

Question 12

Water flows through a pipe having a varying width.More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

Accepted Answer

The volume of water flowing per second (flow rate) remains constant throughout the pipe; however, the velocity of water increases in the narrow sections due to the principle of continuity, which states that the product of the cross-sectional area and the velocity of the fluid remains constant in a pipe.

Question 13

If the hydrostatic pressure at a certain depth in the ocean is 2 atm,the hydrostatic pressure will be 4 atm if you go twice as deep.

Accepted Answer

Hydrostatic pressure increases linearly with depth, but it starts at 1 atm at the surface due to atmospheric pressure. Doubling the depth adds only the pressure due to the water column, not doubling the total pressure.

Question 14

-A pressurized cylindrical tank,5.0 m in diameter,contains water that emerges from the pipe at point C,with a velocity of 13 m/s.Point A is 10 m above point B and point C is 3 m above point B.The area of the pipe at point B is 0.08 m² and the pipe narrows to an area of 0.04 m² at point C.Assume the water is an ideal fluid in laminar flow.The density of water is 1000 kg/m³.In the figure,the mass flow rate in the pipe is closest to: A)520 Kg/s B)470 Kg/s C)420 Kg/s D)360 Kg/s E)310 Kg/s

Accepted Answer

The mass flow rate is calculated using the formula: mass flow rate = density × velocity × area. At point C, the velocity is 13 m/s and the area is 0.04 m². Therefore, mass flow rate = 1000 kg/m³ × 13 m/s × 0.04 m² = 520 kg/s.

Question 15

According to Pascal's principle,if you increase the pressure enough so that the force at one end of an oil-filled tube increases by 10 N,the force will increase at all points in the tube by 10 N.

Accepted Answer

Pascal's principle states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of its container. However, the force at different points depends on the area over which the pressure is applied, not just the pressure change itself.

Question 16

Consider a very small hole in the bottom of a tank 20.0 cm in diameter filled with water to a height of 50.0 cm.Find the speed at which the water exits the tank through the hole.
A)3.13 m/s
B)9.80 m/s
C)31.8 m/s
D)34.9 m/s

Accepted Answer

The answer of Consider a very small hole in the...

Question 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 pressure at the bottom of the trench in atmospheres. A)1.1 × 10³atm B)1.1 × 10⁸ atm C)1.1 × 10⁵ atm D)1.1 × 10⁶ atm E)2.1 atm

Accepted Answer

The absolute pressure at the bottom of the trench is calculated using the formula P = ρgh + P₀, where ρ is the density of seawater (1.04 g/cm³ or 1040 kg/m³), g is the acceleration due to gravity (9.81 m/s²), h is the depth (36,000 feet or 10,973 meters), and P₀ is the atmospheric pressure (1 atm). Converting the depth to meters and calculating gives approximately 1.1 × 10³ atm.

Question 18

How many grams of ethanol (specific gravity 0.80)should be added to 5 grams of chloroform (specific gravity 1.50)if the resulting mixture is to have a specific gravity of 1.20?
A)2.0 g
B)2.4 g
C)1.8 g
D)4.4 g
E)1.6 g

Accepted Answer

Specific gravity of the mixture = (Mass of chloroform * Specific gravity of chloroform + Mass of ethanol * Specific gravity of ethanol) / (Mass of chloroform + Mass of ethanol)1.20 = (5 * 1.50 + Mass of ethanol * 0.80) / (5 + Mass of ethanol)Mass of ethanol = 2.0 g

Question 19

If you increase the pressure on the surface of a can of water,you will increase the buoyant force on objects placed in that water.

Accepted Answer

Increasing the pressure on the surface of the can of water will not affect the buoyant force on objects placed in the water. The buoyant force is determined by the weight of the water displaced by the object, not by the pressure on the surface of the water.

Question 20

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 32 m/s,what is its speed in this smaller section?
A)43 m/s
B)37 m/s
C)28 m/s
D)24 m/s

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 speed of approximately 43 m/s.

Quiz 13: Fluids

If the gauge pressure at a certain depth in Lake Michigan is 3.5 atmospheres,the absolute pressure at that depth is 4.5 atm.

An air bubble underwater has the same pressure as that of the water.As the air bubble rises toward the surface (and its temperature remains constant) ,the volume of the air bubble

How much would a lead brick 2.0 in × 2.0 in × 8.0 in weigh if placed in oil with density ρ = 0.92 g/cm³? (ρPb = 11.4 g/cm³)

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?

A 9.8 kg solid sphere,made of metal whose density is 3000 kg/m³,is suspended by a cord.The sphere floats when placed in a liquid of density 4200 kg m3.The fraction of the volume of the sphere that is submerged is closest to:

A venturi is constructed of a 9.0 cm diameter pipe with a 2.0 cm diameter throat.Water pressure in the pipe is twice atmospheric pressure and it flows with a velocity of 0.30 m/s. What is the pressure in the throat?

A 200.0 kg flat-bottomed boat floats in fresh water,which has a density of 1000.0 kg/m³.Assuming that the base of the boat is 1.42 m wide and 4.53 m long,how much of the boat is submerged when it carries three passengers whose total mass is 193 kg?

A long vertical metal cylinder is filled with oil.If a piston pushes on the top of this cylinder and increases the pressure there by 6,000 Pa,the pressure at the bottom will increase considerably more due to the weight of the oil.

If a uniform sphere is compressed to half of its original diameter,its mass remains the same but its density becomes 8 times as great.

A 8.6 kg solid sphere,made of metal whose density is 3400 kg/m³,is suspended 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:

When an object is floating,the buoyant force on it is just equal to its weight.

Water flows through a pipe having a varying width.More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

If the hydrostatic pressure at a certain depth in the ocean is 2 atm,the hydrostatic pressure will be 4 atm if you go twice as deep.

According to Pascal's principle,if you increase the pressure enough so that the force at one end of an oil-filled tube increases by 10 N,the force will increase at all points in the tube by 10 N.

Consider a very small hole in the bottom of a tank 20.0 cm in diameter filled with water to a height of 50.0 cm.Find the speed at which the water exits the tank through the hole.

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 pressure at the bottom of the trench in atmospheres.

How many grams of ethanol (specific gravity 0.80) should be added to 5 grams of chloroform (specific gravity 1.50) if the resulting mixture is to have a specific gravity of 1.20?

If you increase the pressure on the surface of a can of water,you will increase the buoyant force on objects placed in that water.

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 32 m/s,what is its speed in this smaller section?

Quiz 13: Fluids

If the gauge pressure at a certain depth in Lake Michigan is 3.5 atmospheres,the absolute pressure at that depth is 4.5 atm.

An air bubble underwater has the same pressure as that of the water.As the air bubble rises toward the surface (and its temperature remains constant) ,the volume of the air bubble

How much would a lead brick 2.0 in × 2.0 in × 8.0 in weigh if placed in oil with density ρ = 0.92 g/cm3? (ρPb = 11.4 g/cm3)

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?

A 9.8 kg solid sphere,made of metal whose density is 3000 kg/m3,is suspended by a cord.The sphere floats when placed in a liquid of density 4200 kg m3.The fraction of the volume of the sphere that is submerged is closest to:

A venturi is constructed of a 9.0 cm diameter pipe with a 2.0 cm diameter throat.Water pressure in the pipe is twice atmospheric pressure and it flows with a velocity of 0.30 m/s. What is the pressure in the throat?

A 200.0 kg flat-bottomed boat floats in fresh water,which has a density of 1000.0 kg/m3.Assuming that the base of the boat is 1.42 m wide and 4.53 m long,how much of the boat is submerged when it carries three passengers whose total mass is 193 kg?

A long vertical metal cylinder is filled with oil.If a piston pushes on the top of this cylinder and increases the pressure there by 6,000 Pa,the pressure at the bottom will increase considerably more due to the weight of the oil.

If a uniform sphere is compressed to half of its original diameter,its mass remains the same but its density becomes 8 times as great.

A 8.6 kg solid sphere,made of metal whose density is 3400 kg/m3,is suspended 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:

When an object is floating,the buoyant force on it is just equal to its weight.

Water flows through a pipe having a varying width.More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

If the hydrostatic pressure at a certain depth in the ocean is 2 atm,the hydrostatic pressure will be 4 atm if you go twice as deep.

According to Pascal's principle,if you increase the pressure enough so that the force at one end of an oil-filled tube increases by 10 N,the force will increase at all points in the tube by 10 N.

Consider a very small hole in the bottom of a tank 20.0 cm in diameter filled with water to a height of 50.0 cm.Find the speed at which the water exits the tank through the hole.

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 pressure at the bottom of the trench in atmospheres.

How many grams of ethanol (specific gravity 0.80) should be added to 5 grams of chloroform (specific gravity 1.50) if the resulting mixture is to have a specific gravity of 1.20?

If you increase the pressure on the surface of a can of water,you will increase the buoyant force on objects placed in that water.

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 32 m/s,what is its speed in this smaller section?

How much would a lead brick 2.0 in × 2.0 in × 8.0 in weigh if placed in oil with density ρ = 0.92 g/cm³? (ρPb = 11.4 g/cm³)

A 9.8 kg solid sphere,made of metal whose density is 3000 kg/m³,is suspended by a cord.The sphere floats when placed in a liquid of density 4200 kg m3.The fraction of the volume of the sphere that is submerged is closest to:

A 200.0 kg flat-bottomed boat floats in fresh water,which has a density of 1000.0 kg/m³.Assuming that the base of the boat is 1.42 m wide and 4.53 m long,how much of the boat is submerged when it carries three passengers whose total mass is 193 kg?

A 8.6 kg solid sphere,made of metal whose density is 3400 kg/m³,is suspended 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:

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 pressure at the bottom of the trench in atmospheres.