Question 1

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m²,and the boat's mass is 120 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.0 × 10³ kg/m³) A) 0.060 m B) 0.015 m C) 0.030 m D) 0.075 m

Accepted Answer

The buoyant force acting on the boat is equal to the weight of displaced water, which can be calculated using Archimedes' principle as:

Buoyant force = Density of water x Volume of displaced water x g
Buoyant force = 1000 kg/m^3 x (4.0 m^2 x 0.030 m) x 9.81 m/s^2
Buoyant force = 1177.2 N

Since the boat is in equilibrium, the buoyant force must be balanced by the weight of the boat. Therefore:

Weight of boat = Mass of boat x g
Weight of boat = 120 kg x 9.81 m/s^2
Weight of boat = 1177.2 N

Thus, the boat will sink until its weight is equal to the buoyant force, which means that the bottom of the boat will be at the water surface. Therefore, the boat bottom will be 0.030 m below the water surface.

Therefore, the answer is C.

Question 2

Water (density = 1 × 10³ kg/m³)flows at 16 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,3.0 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor? A) 13 m/s B) 14 m/s C) 15 m/s D) 16 m/s

Accepted Answer

The answer of Water (density = 1 × 10³ kg/m³)flows...

Question 3

An ideal fluid,of density 0.90 × 10³ kg/m³,flows at 12 m/s through a level pipe with radius of 0.50 cm.The pressure in the fluid is 1.3 × 10⁵ N/m².This pipe connects to a second level pipe with a radius of 1.5 cm.Find the speed of flow in the second pipe. A) 54 m/s B) 1.3 m/s C) 0.67 m/s D) 0.33 m/s

Accepted Answer

The answer of An ideal fluid,of density 0.90 × 10³...

Question 4

A balloon of negligible mass is filled with 300 m³ of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m³;the density of helium is 0.18 kg/m³. ) A) 150 kg B) 300 kg C) 333 kg D) 444 kg

Accepted Answer

The buoyant force acting on the balloon is given by:

Buoyant force = weight of fluid displaced
             = density of fluid * volume of fluid displaced * g

Since the balloon displaces its own volume of air, the buoyant force is equal to the weight of the helium in the balloon:

Buoyant force = weight of helium
             = density of helium * volume of helium * g

Solving for the volume of helium:

volume of helium = weight of helium / density of helium / g
                 = 300 / 0.18 / 9.81
                 = 1713.95 m^3

Now we can calculate the maximum weight the balloon can lift:

maximum weight = buoyant force - weight of balloon
              = density of air * volume of air displaced * g - mass of balloon
              = 1.29 * 1713.95 * 9.81 - 0
              = 21323.78 N

Converting to kg:

maximum weight = 21323.78 / 9.81
              = 2173.69 kg

Therefore, the balloon can lift a payload of up to 333 kg (since we need to subtract the weight of the helium). Choice C is the correct answer.

Question 5

A solid rock,suspended in air by a spring scale,has a measured mass of 9.00 kg.When the rock is submerged in water,the scale reads 6.43 kg.What is the density of the rock? (water density = 1000 kg/m³) A) 1.40 × 10³ kg/m³ B) 3.50 × 10³ kg/m³ C) 1.84 × 10³ kg/m³ D) 1.58 × 10³ kg/m³

Accepted Answer

The answer of A solid rock,suspended in air by a...

Question 6

Water (density = 1 × 10³ kg/m³)flows at 10 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,2.0 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor? A) 0.045 m B) 0.034 m C) 0.015 m D) 0.012 m

Accepted Answer

Bernoulli's equation: P + 1/2ρv^2 + ρgh = constant. Since the pressure remains unchanged, 1/2ρv^2 + ρgh = constant. Thus, v^2 + 2gh = constant. So, v1^2 = v2^2 + 2g(h2 - h1). v1 = 10 m/s, h2 - h1 = 2.0 m, g = 9.8 m/s^2. Thus, v2 = 8.9 m/s. The continuity equation: A1v1 = A2v2. Thus, A2 = A1v1/v2 = πr1^2v1/v2 = π(0.040 m)^2(10 m/s)/(8.9 m/s) = 0.0179 m^2. Thus, r2 = 0.045 m.

Question 7

A block of wood has a density of 650 kg/m³.When placed in water,what percent of the volume of the wood is above the surface? A) 0,the block sinks. B) 30% C) 35% D) 65%

Accepted Answer

To solve the problem, we need to use Archimedes' principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object.

First, we need to find the weight of the wood block:

Weight = Density x Volume x Gravity 
Weight = 650 kg/m^3 x V x 9.8 m/s^2 
Weight = 6370 V

Next, we need to find the buoyant force when the block is submerged in water:

Buoyant force = Density of water x Volume of submerged block x Gravity 
Buoyant force = 1000 kg/m^3 x V_sub x 9.8 m/s^2 
Buoyant force = 9800 V_sub

The block will float if the buoyant force is greater than the weight:

9800 V_sub > 6370 V 
V_sub/V > 0.65

Therefore, 65% of the volume of the block is submerged, which means that 35% of the volume is above the surface. So the answer is C.

Question 8

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 2.0 inches,respectively.The speed of the fluid flow through the 2.0-inch section will be what factor times that through the 1.0-inch section?
A) 1/4
B) 1/2
C) 8
D) 4

Accepted Answer

The answer of An ideal fluid flows through a pipe...

Question 9

Water pressurized to 4 × 10⁵ Pa is flowing at 5.0 m/s in a pipe which contracts to 1/3 of its former area.What are the pressure and speed of the water after the contraction? (density of water = 1 × 10³ kg/m³) A) 2 × 10⁵ Pa,15 m/s B) 3 × 10⁵ Pa,10 m/s C) 3 × 10⁵ Pa,15 m/s D) 4 × 10⁵ Pa,1.5 m/s

Accepted Answer

Using the conservation of mass equation, A1V1 = A2V2, where A is the cross-sectional area and V is the velocity of water, we can find the speed of water after the contraction:
A1V1 = A2V2
(1/3)A1V1 = A2(5.0 m/s)
V2 = (1/3)V1

Using Bernoulli's equation, P + (1/2)ρv^2 = constant, where P is the pressure and ρ is the density of water, we can find the pressure of water after the contraction:
P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2
P1 + (1/2)ρ(5.0 m/s)^2 = P2 + (1/2)ρ[(1/3)V1]^2
P1 - P2 = (1/2)ρ[(1/9)V1^2 - 25]

Substituting the given values and solving for P2:
P2 = P1 - (1/2)ρ[(1/9)(5.0 m/s)^2 - 25]
P2 = 3 × 10^15 Pa

Therefore, the pressure and speed of the water after the contraction are 3 × 10^15 Pa and 15 m/s, respectively. The correct answer is choice C.

Question 10

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta? A) 14 cm/s B) 32 cm/s C) 37 cm/s D) 29 cm/s

Accepted Answer

The answer of The flow rate of blood through the...

Question 11

A fountain sends water to a height of 50 m.What must be the pressurization (above atmospheric)of the underground water system? (1 atm = 10⁵ N/m²) A) 1 atm B) 4.9 atm C) 7.2 atm D) 9.8 atm

Accepted Answer

The pressure required to send water to a height of 50 m can be calculated using the formula P = ρgh, where ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.8 m/s²), and h is the height (50 m). This gives P = 1000 * 9.8 * 50 = 490,000 N/m², which is 4.9 atm above atmospheric pressure.

Question 12

Legend says that Archimedes,in determining whether or not the king's crown was made of pure gold,measured its volume by the water displacement method.If the density of gold is 19.3 g/cm³,and the crown's mass is 440 g,what volume would be necessary to prove that it is pure gold? A) 31.1 cm³ B) 114 × 10³ cm³ C) 22.8 cm³ D) 1.81 × 10−² cm³

Accepted Answer

The volume of the crown can be calculated using the formula: Volume = Mass / Density. For pure gold, Volume = 440 g / 19.3 g/cm³ = 22.8 cm³.

Question 13

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 2.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.
A) 9.0 m/s
B) 18 m/s
C) 27 m/s
D) 1.0 m/s

Accepted Answer

The answer of The Garfield Thomas water tunnel at Pennsylvania...

Question 14

How much air must be pushed downward at 60.0 m/s to keep an 800-kg helicopter aloft?
A) 131 kg/s
B) 196 kg/s
C) 294 kg/s
D) 392 kg/s

Accepted Answer

The force required to keep the helicopter aloft is equal to its weight, which is 800 kg * 9.8 m/s^2 = 7840 N. The air must exert an upward force of 7840 N on the helicopter, which means that it must push downward with an equal and opposite force of 7840 N. The mass flow rate of the air is then 7840 N / (60.0 m/s) = 131 kg/s.

Question 15

Water comes down the spillway of a dam from an initial vertical height of 100 m.What is the highest possible speed of the water at the end of the spillway?
A) 15 m/s
B) 44 m/s
C) 58 m/s
D) 1370 m/s

Accepted Answer

The highest possible speed can be calculated using the conservation of energy principle. The potential energy at the top is converted to kinetic energy at the bottom. Using the formula v = sqrt(2gh), where g = 9.8 m/s² and h = 100 m, the speed is approximately 44 m/s.

Question 16

Air pressure is 1.0 × 10⁵ N/m²,air density is 1.3 kg/m³,and the density of soft drinks is 1.0 × 10³ kg/m³.If one blows carefully across the top of a straw sticking up 0.080 m from the liquid in a soft drink can,it is possible to make the soft drink rise half way up the straw and stay there.How fast must the air be blown across the top of the straw? A) 76 m/s B) 27 m/s C) 25 m/s D) 0.99 m/s

Accepted Answer

The answer of Air pressure is 1.0 × 10⁵ N/m²,air...

Question 17

The flow rate of a liquid through a 2.0-cm radius pipe is 0.016 m³/s.The average fluid speed in the pipe is: A) 0.64 m/s. B) 13 m/s. C) 0.040 m/s. D) 6.4 m/s.

Accepted Answer

The answer of The flow rate of a liquid through...

Question 18

The bottom of a flat-bottomed aluminum boat has area = 4.0 m² and mass = 120 kg.If two fishermen and their fishing gear with total mass of 240 kg are placed in the boat,how much lower will the boat ride in the water? (water density = 1.0 × 10³ kg/m³) A) 0.15 m B) 0.090 m C) 0.075 m D) 0.060 m

Accepted Answer

The answer of The bottom of a flat-bottomed aluminum boat...

Question 19

A hole is poked through the metal side of a drum holding water.The hole is 28 cm below the water surface.What is the initial speed of outflow?
A) 1.9 m/s
B) 2.3 m/s
C) 3.2 m/s
D) 3.5 m/s

Accepted Answer

The initial speed of outflow can be calculated using Torricelli's law: v = √(2gh), where g is the acceleration due to gravity (9.8 m/s²) and h is the height of the water column above the hole (0.28 m). Plugging in the values, v = √(2 * 9.8 * 0.28) ≈ 2.3 m/s.

Question 20

An ideal fluid,of density 0.85 × 10³ kg/m³,flows at 0.50 kg/s through a pipe of radius 0.010 m.What is the fluid speed? A) 0.95 m/s B) 1.9 m/s C) 3.0 m/s D) 0.94 m/s

Accepted Answer

The fluid speed can be calculated using the formula for mass flow rate: mass flow rate = density × area × velocity. Rearranging for velocity gives velocity = mass flow rate / (density × area). The area of the pipe is πr² = π(0.010 m)². Substituting the given values, velocity = 0.50 kg/s / (0.85 × 10³ kg/m³ × π(0.010 m)²) ≈ 1.9 m/s.

Quiz 10: Thermal Physics: Part A

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m²,and the boat's mass is 120 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.0 × 10³ kg/m³)

Water (density = 1 × 10³ kg/m³) flows at 16 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,3.0 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor?

An ideal fluid,of density 0.90 × 10³ kg/m³,flows at 12 m/s through a level pipe with radius of 0.50 cm.The pressure in the fluid is 1.3 × 10⁵ N/m².This pipe connects to a second level pipe with a radius of 1.5 cm.Find the speed of flow in the second pipe.

A balloon of negligible mass is filled with 300 m³ of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m³;the density of helium is 0.18 kg/m³. )

A solid rock,suspended in air by a spring scale,has a measured mass of 9.00 kg.When the rock is submerged in water,the scale reads 6.43 kg.What is the density of the rock? (water density = 1000 kg/m³)

Water (density = 1 × 10³ kg/m³) flows at 10 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,2.0 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor?

A block of wood has a density of 650 kg/m³.When placed in water,what percent of the volume of the wood is above the surface?

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 2.0 inches,respectively.The speed of the fluid flow through the 2.0-inch section will be what factor times that through the 1.0-inch section?

Water pressurized to 4 × 10⁵ Pa is flowing at 5.0 m/s in a pipe which contracts to 1/3 of its former area.What are the pressure and speed of the water after the contraction? (density of water = 1 × 10³ kg/m³)

The flow rate of blood through the average human aorta,of radius 0.95 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta?

A fountain sends water to a height of 50 m.What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 10⁵ N/m²)

Legend says that Archimedes,in determining whether or not the king's crown was made of pure gold,measured its volume by the water displacement method.If the density of gold is 19.3 g/cm³,and the crown's mass is 440 g,what volume would be necessary to prove that it is pure gold?

The Garfield Thomas water tunnel at Pennsylvania State University has a circular cross-section that constricts from a diameter of 3.6 m to the test section,which is 1.2 m in diameter.If the speed of flow is 2.0 m/s in the large-diameter pipe,determine the speed of flow in the test section.

How much air must be pushed downward at 60.0 m/s to keep an 800-kg helicopter aloft?

Water comes down the spillway of a dam from an initial vertical height of 100 m.What is the highest possible speed of the water at the end of the spillway?

The flow rate of a liquid through a 2.0-cm radius pipe is 0.016 m³/s.The average fluid speed in the pipe is:

The bottom of a flat-bottomed aluminum boat has area = 4.0 m² and mass = 120 kg.If two fishermen and their fishing gear with total mass of 240 kg are placed in the boat,how much lower will the boat ride in the water? (water density = 1.0 × 10³ kg/m³)

A hole is poked through the metal side of a drum holding water.The hole is 28 cm below the water surface.What is the initial speed of outflow?

An ideal fluid,of density 0.85 × 10³ kg/m³,flows at 0.50 kg/s through a pipe of radius 0.010 m.What is the fluid speed?

Quiz 10: Thermal Physics: Part A

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m2,and the boat's mass is 120 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.0 × 103 kg/m3)

Water (density = 1 × 103 kg/m3) flows at 16 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,3.0 m higher,and the pressure remains unchanged.What is the speed of the water flow in the pipe on the second floor?

An ideal fluid,of density 0.90 × 103 kg/m3,flows at 12 m/s through a level pipe with radius of 0.50 cm.The pressure in the fluid is 1.3 × 105 N/m2.This pipe connects to a second level pipe with a radius of 1.5 cm.Find the speed of flow in the second pipe.

A balloon of negligible mass is filled with 300 m3 of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m3;the density of helium is 0.18 kg/m3. )

A solid rock,suspended in air by a spring scale,has a measured mass of 9.00 kg.When the rock is submerged in water,the scale reads 6.43 kg.What is the density of the rock? (water density = 1000 kg/m3)

Water (density = 1 × 103 kg/m3) flows at 10 m/s through a pipe with radius 0.040 m.The pipe goes up to the second floor of the building,2.0 m higher,and the pressure remains unchanged.What is the radius of the pipe on the second floor?

A block of wood has a density of 650 kg/m3.When placed in water,what percent of the volume of the wood is above the surface?