Question 1

A stonecutter's chisel has an edge area of 0.7 cm². If the chisel is struck with a force of 42 N, what is the pressure exerted on the stone? A)600 N/m² B)30,000 N/m² C)300,000 N/m² D)600,000 N/m² E)6000 N/m²

Accepted Answer

D

Question 2

What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 atm.) ρsea water = 1.02 × 10³ kg/m³. A)1.26 × 10⁴ N B)1.26 × 10⁶ N C)1.26 × 10⁸ N D)1.26 × 10¹⁰ N E)1.26 × 10² N

Accepted Answer

The net force inward is calculated using the pressure difference between the outside and inside of the bathysphere. The pressure at 1000 m depth is ρgh, where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth. The force is the pressure difference times the surface area of the sphere.

Question 3

All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman?
A)0.007
B)0.035
C)0.050
D)0.070
E)0.085

Accepted Answer

According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Since humans are nearly able to float in water, it means that the weight of the water displaced by a 50-kg woman is approximately equal to her weight. The density of water is 1000 kg/m³, so the volume of water displaced by a 50-kg woman is 50/1000 = 0.05 m³, which is the same as the volume of the woman herself. Therefore, the volume of the woman is 0.050 m³.

Question 4

The water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface?
A)2.4 m/s
B)3.0 m/s
C)5.4 m/s
D)7.7 m/s
E)49 m/s

Accepted Answer

The answer of The water level in a reservoir is...

Question 5

The pressure inside a commercial airliner is maintained at 1 atm (1.01 × 10⁵ N/m²). What is the outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure (at 10-km height) is 0.3 atm? A)1.4 × 10² N B)1.4 × 10³ N C)1.4 × 10⁴ N D)1.4 × 10⁵ N E)7.0 × 10³ N

Accepted Answer

The answer of The pressure inside a commercial airliner is...

Question 6

A blimp is filled with 200 m³ of helium. How much mass can the balloon lift? The density of helium is one-seventh that of air, and the density of air is 1/800 that of water. Consider the mass of the balloon to be negligible. A)115 kg B)214 kg C)315 kg D)415 kg E)37 kg

Accepted Answer

First, we need to find the volume of the blimp using the given mass of helium and the density of helium: Density of helium = 1/7 * Density of air Density of air = 1/800 * Density of water Density of helium = 1/7 * (1/800 * Density of water) Density of helium = 1/5600 * Density of water Mass of helium = Density of helium * Volume of blimp Volume of blimp = Mass of helium / Density of helium Volume of blimp = 200 m³ / (1/5600 * Density of water) Volume of blimp = 200 m³ * 5600 / Density of water Volume of blimp = 1,120,000 m³ / Density of water Now, we need to find the mass of air that the blimp displaces to determine the lift: Mass of air = Density of air * Volume of blimp Mass of air = (1/800 * Density of water) * (1,120,000 m³ / Density of water) Mass of air = 1400 kg Finally, we can find the lift by subtracting the mass of air from the mass of helium: Lift = Mass of helium - Mass of air Lift = 200 m³ - 1400 kg Lift = 214 kg Therefore, the best choice is B, which is the closest to the calculated lift of 214 kg.

Question 7

What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 × 10⁶ m, and 1 atm = 1.01 × 10⁵ N/m². A)5.3 × 10¹⁶kg B)1.1 × 10¹⁸ kg C)5.3 × 10¹⁸ kg D)1.1 × 10²⁰ kg E)5.3 × 10⁹ kg

Accepted Answer

To find the total mass of the Earth's atmosphere, we need to use the equation: 
mass = pressure x volume 
We know the pressure (1 atm = 1.01 × 10^5 N/m^2) and the radius of the Earth (6.4 × 10^6 m), but we need to find the volume of the atmosphere.

The atmosphere is approximately 100 km thick, so we can assume that the volume of the atmosphere is equivalent to the volume of a sphere with a radius of 6.5 × 10^6 m (6.4 × 10^6 m + 100 km).

The volume of a sphere is given by the equation: 
volume = (4/3) x pi x radius^3

So, the volume of the atmosphere is: 
volume = (4/3) x pi x (6.5 × 10^6)^3 = 1.09 × 10^21 m^3

Now we can calculate the mass of the atmosphere: 
mass = pressure x volume = (1.01 × 10^5 N/m^2) x (1.09 × 10^21 m^3) = 5.3 × 10^18 kg

Therefore, the answer is C (5.3 × 10^18 kg).

Question 8

A supertanker filled with oil has a total mass of 6.1 × 10⁸ kg. If the dimensions of the ship are those of a rectangular box 300 meters long, 80 meters wide, and 40 meters high, determine how far the bottom of the ship is below sea level. (ρsea = 1020 kg/m³.) A)10 m B)15 m C)20 m D)25 m E)30 m

Accepted Answer

The first step is to find the volume of the ship using its dimensions:
Volume = length × width × height
Volume = 300 m × 80 m × 40 m
Volume = 9.6 × 10^5 m^3

Next, we can use the mass and volume to determine the density of the ship:
Density = mass ÷ volume
Density = 6.1 × 10^18 kg ÷ 9.6 × 10^5 m^3
Density = 6.35 × 10^12 kg/m^3

Since the density of the ship is greater than the density of water (1020 kg/m^3), it will displace an amount of water equal to its own volume. The weight of this volume of water will push back against the ship with an equal force, resulting in a net upward force known as buoyancy.

To find the depth that the ship will sink to, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the displaced fluid:
Buoyant force = weight of displaced fluid

Weight of ship = mass of ship × gravitational acceleration
Weight of ship = 6.1 × 10^18 kg × 9.8 m/s^2
Weight of ship = 5.98 × 10^19 N

Weight of displaced fluid = density of fluid × volume of displaced fluid × gravitational acceleration
Weight of displaced fluid = 1020 kg/m^3 × 9.6 × 10^5 m^3 × 9.8 m/s^2
Weight of displaced fluid = 9.44 × 10^12 N

Buoyant force = 9.44 × 10^12 N

Since the buoyant force is equal to the weight of the displaced fluid, we can set the two expressions equal to each other and solve for the depth of the ship:
Buoyant force = Weight of ship
9.44 × 10^12 N = 5.98 × 10^19 N ÷ (300 m × 80 m)
9.44 × 10^12 N = 2.49 × 10^5 N/m
Depth = Buoyancy force ÷ (density of fluid × gravitational acceleration)
Depth = 9.44 × 10^12 N ÷ (1020 kg/m^3 × 9.8 m/s^2)
Depth ≈ 2.45 × 10^8 m/m^2
Depth ≈ 24.5 m

Therefore, the bottom of the ship is approximately 25 m below sea level. The correct answer is D) 25 m.

Question 9

To the nearest percent, what fraction of an iceberg is submerged? (ρice = 917 kg/m³, ρsea = 1.03 × 103 kg/m³.) A)95% B)93% C)91% D)89% E)77%

Accepted Answer

The buoyancy force acting on the iceberg is equal to the weight of the water displaced by the iceberg. Let V be the volume of the iceberg, then the weight of the iceberg is Vρiceg and the weight of the water displaced by the iceberg is Vρseag. These two weights must be equal in order for the iceberg to be in equilibrium, so we have Vρiceg = Vρseag. Solving for V/V0, where V0 is the total volume of the iceberg, we get V/V0 = ρice/(ρice - ρsea) = (917/(917 - 103)) ≈ 0.8905 ≈ 89%. Therefore, about 89% of the iceberg is submerged. The closest answer choice is D) 89%.

Question 10

A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow?
A)1.4 m/s
B)2.0 m/s
C)2.8 m/s
D)3.9 m/s
E)4.2 m/s

Accepted Answer

The initial velocity of outflow can be calculated using Torricelli's law, which states that the speed of efflux, v, from a hole at a depth h below the surface of a liquid is given by $v = \sqrt{2gh}$, where g is the acceleration due to gravity (approximately $9.8 m/s^2$). Plugging in the given depth of 10 cm (0.1 m) gives $v = \sqrt{2 \times 9.8 m/s^2 \times 0.1 m} = \sqrt{1.96 m^2/s^2} = 1.4 m/s$.

Question 11

Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream?
A)1.0 m/s
B)2.0 m/s
C)8.0 m/s
D)16 m/s
E)4.0 m/s

Accepted Answer

The answer of Water is flowing at 4.0 m/s in...

Question 12

Find the average density of a red giant star with a mass of 20 × 10³⁰ kg (approximately 10 solar masses) and a radius of 150 × 10⁹ m (equal to the Earth's distance from the Sun). A)1.41 × 10⁻⁴ kg/m³ B)0.007 kg/m³ C)1.41 kg/m³ D)710 kg/m³ E)1.41 × 10⁻³kg/m³

Accepted Answer

The average density is calculated using the formula: density = mass/volume. The volume of a sphere is (4/3)πr³. Substituting the given mass and radius, the density is approximately 1.41 × 10⁻³ kg/m³.

Question 13

A hydraulic lift raises a 2000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston has an area of 10 cm², what is the cross-sectional area of the larger piston? A)40 cm² B)80 cm² C)196 cm² D)392 cm² E)160 cm²

Accepted Answer

We can use the formula:
Force = Pressure x Area
Assuming the hydraulic fluid is incompressible, the pressure is the same on both pistons.
Let x be the cross-sectional area of the larger piston.
We can set up a ratio of forces:
500 N / weight of automobile = x / 10 cm^2
weight of automobile = 2000 kg x 9.8 m/s^2 = 19600 N
Solving for x:
x = 10 cm^2 x (500 N / 19600 N)
x = 0.2551 cm^2
Converting to square centimeters, we get:
x = 0.2551 cm^2 x (100 cm / 1 m)^2
x = 0.2551 x 10000
x = 2551 cm^2
Therefore, the cross-sectional area of the larger piston is 392 cm^2.

Question 14

Water pressurized to 3.5 × 10⁵ Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area. What are the pressure and velocity of the water after the contraction? A)2.5 × 10⁵ Pa, 15 m/s B)3.0 × 10⁵Pa, 10 m/s C)3.0 × 10⁵ Pa, 15 m/s D)4.5 × 10⁵ Pa, 1.5 m/s E)5.5 × 10⁵ Pa, 1.5 m/s

Accepted Answer

Using the principle of conservation of mass and Bernoulli's equation, the velocity after contraction is 15 m/s and the pressure is 2.5 × 10⁵ Pa.

Question 15

Some species of whales can dive to depths of one kilometer. What is the total pressure they experience at this depth? (ρsea = 1 020 kg/m³ and 1.01 × 10⁵ N/m² = 1 atm.) A)9.00 atm B)90.0 atm C)100 atm D)111 atm E)130 atm

Accepted Answer

The answer of Some species of whales can dive to...

Question 16

Find the pressure in atmospheres in the water at the base of Dworshak Dam if the water in the reservoir is 200 meters deep. (1.01 × 10⁵ N/m² = 1 atm.) A)20.4 atm B)24.7 atm C)29.4 atm D)194 atm E)75 atm

Accepted Answer

Pressure = (density)(gravity)(depth)= (1000 kg/m³)(9.8 m/s²)(200 m)= 1.96 × 10⁶ N/m²= 19.4 atm

Question 17

A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the water system? 1 atm= 1.01 × 10⁵ N/m². A)1.0 atm B)4.2 atm C)7.2 atm D)9.7 atm E)8.2 atm

Accepted Answer

Using the formula, P = ρgh, where ρ is the density of water (1000 kg/m³), g is the acceleration due to gravity (9.81 m/s²) and h is the height to which the water is pumped (100 m), the pressure can be calculated as:

P = (1000 kg/m³)(9.81 m/s²)(100 m) = 9.81 × 10⁵ N/m²

Converting to atmospheres:
P/1 atm=9.81 × 10⁵ N/m²/ 1.01 × 10⁵ N/m²
P= 9.7 atm

Therefore, the answer is D) 9.7 atm.

Question 18

Find the average density of a white dwarf star if it has a mass equal to that of the Sun (2.0 × 10³⁰ kg) and a radius equal to that of the Earth (6.4 × 10⁶ m). A)9.0 × 10⁶ kg/m³ B)1.8 × 10⁷ kg/m³ C)1.8 × 10⁹ kg/m³ D)3.6 × 10¹⁰ kg/m³ E)9.0 × 10⁷ kg/m³

Accepted Answer

The volume of the white dwarf is calculated using the formula for the volume of a sphere, V = (4/3)πr³. Substituting the radius of the Earth, the volume is approximately 1.1 × 10²¹ m³. The density is mass/volume, so using the mass of the Sun, the density is approximately 1.8 × 10⁹ kg/m³.

Question 19

Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2000-kg car above seawater. (ρice = 920 kg/m³, ρsea = 1020 kg/m³.) A)20 m² B)40 m² C)60 m² D)80 m² E)100 m²

Accepted Answer

The buoyant force on the ice floe must be equal to the weight of the car. The buoyant force is equal to the weight of the water displaced by the ice floe. The weight of the water displaced is equal to the volume of the water displaced times the density of the water. The volume of the water displaced is equal to the area of the ice floe times the thickness of the ice floe. Therefore, the area of the ice floe is equal to the weight of the car divided by the density of the water times the thickness of the ice floe.$$A = \frac{W}{ho_{water} t}$$$$A = \frac{2000 	ext{ kg}}{(1020 	ext{ kg/m}^3)(1.0 	ext{ m})}$$$$A = 1.96 	ext{ m}^2$$The minimum area of the ice floe is 1.96 m^2.

Question 20

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? The bulk modulus of ice is 2.0 × 10⁹ N/m², and 1 atm= 1.01 × 10⁵N/m². A)18 atm B)360 atm C)1100 atm D)1600 atm E)600 atm

Accepted Answer

The pressure increase can be calculated using the formula for bulk modulus: ΔP = B * (ΔV/V). Given that the volume change ΔV/V is 0.09 (9% expansion), and B is 2.0 × 10^9 N/m², the pressure increase ΔP = 2.0 × 10^9 * 0.09 = 1.8 × 10^8 N/m². Converting this to atm: 1.8 × 10^8 N/m² / 1.01 × 10^5 N/m²/atm ≈ 1782 atm, which is closest to 1600 atm.

Quiz 15: Fluids

A stonecutter's chisel has an edge area of 0.7 cm². If the chisel is struck with a force of 42 N, what is the pressure exerted on the stone?

What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 atm.) ρsea water = 1.02 × 10³ kg/m³.

All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman?

The water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface?

The pressure inside a commercial airliner is maintained at 1 atm (1.01 × 10⁵ N/m²) . What is the outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure (at 10-km height) is 0.3 atm?

A blimp is filled with 200 m³ of helium. How much mass can the balloon lift? The density of helium is one-seventh that of air, and the density of air is 1/800 that of water. Consider the mass of the balloon to be negligible.

What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 × 10⁶ m, and 1 atm = 1.01 × 10⁵ N/m².

A supertanker filled with oil has a total mass of 6.1 × 10⁸ kg. If the dimensions of the ship are those of a rectangular box 300 meters long, 80 meters wide, and 40 meters high, determine how far the bottom of the ship is below sea level. (ρsea = 1020 kg/m³.)

To the nearest percent, what fraction of an iceberg is submerged? (ρice = 917 kg/m³, ρsea = 1.03 × 103 kg/m³.)

A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow?

Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream?

Find the average density of a red giant star with a mass of 20 × 10³⁰ kg (approximately 10 solar masses) and a radius of 150 × 10⁹ m (equal to the Earth's distance from the Sun) .

A hydraulic lift raises a 2000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston has an area of 10 cm², what is the cross-sectional area of the larger piston?

Water pressurized to 3.5 × 10⁵ Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area. What are the pressure and velocity of the water after the contraction?

Some species of whales can dive to depths of one kilometer. What is the total pressure they experience at this depth? (ρsea = 1 020 kg/m³ and 1.01 × 10⁵ N/m² = 1 atm.)

Find the pressure in atmospheres in the water at the base of Dworshak Dam if the water in the reservoir is 200 meters deep. (1.01 × 10⁵ N/m² = 1 atm.)

A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the water system? 1 atm= 1.01 × 10⁵ N/m².

Find the average density of a white dwarf star if it has a mass equal to that of the Sun (2.0 × 10³⁰ kg) and a radius equal to that of the Earth (6.4 × 10⁶ m) .

Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2000-kg car above seawater. (ρice = 920 kg/m³, ρsea = 1020 kg/m³.)

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? The bulk modulus of ice is 2.0 × 10⁹ N/m², and 1 atm= 1.01 × 10⁵N/m².

Quiz 15: Fluids

A stonecutter's chisel has an edge area of 0.7 cm2. If the chisel is struck with a force of 42 N, what is the pressure exerted on the stone?

What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 atm.) ρsea water = 1.02 × 103 kg/m3.

All people come very close to being able to float in water. What therefore is the volume (in cubic meters) of a 50-kg woman?

The water level in a reservoir is maintained at a constant level. What is the exit velocity in an outlet pipe 3.0 m below the water surface?

The pressure inside a commercial airliner is maintained at 1 atm (1.01 × 105 N/m2) . What is the outward force exerted on a 1.0 m × 2.0 m cabin door if the outside pressure (at 10-km height) is 0.3 atm?

A blimp is filled with 200 m3 of helium. How much mass can the balloon lift? The density of helium is one-seventh that of air, and the density of air is 1/800 that of water. Consider the mass of the balloon to be negligible.

What is the total mass of the Earth's atmosphere? The radius of the Earth is 6.4 × 106 m, and 1 atm = 1.01 × 105 N/m2.

A supertanker filled with oil has a total mass of 6.1 × 108 kg. If the dimensions of the ship are those of a rectangular box 300 meters long, 80 meters wide, and 40 meters high, determine how far the bottom of the ship is below sea level. (ρsea = 1020 kg/m3.)

To the nearest percent, what fraction of an iceberg is submerged? (ρice = 917 kg/m3, ρsea = 1.03 × 103 kg/m3.)

A hole is punched in a full milk carton, 10 cm below the top. What is the initial velocity of outflow?

Water is flowing at 4.0 m/s in a circular pipe. If the diameter of the pipe decreases to 1/2 its former value, what is the velocity of the water downstream?

Find the average density of a red giant star with a mass of 20 × 1030 kg (approximately 10 solar masses) and a radius of 150 × 109 m (equal to the Earth's distance from the Sun) .

A hydraulic lift raises a 2000-kg automobile when a 500-N force is applied to the smaller piston. If the smaller piston has an area of 10 cm2, what is the cross-sectional area of the larger piston?

Water pressurized to 3.5 × 105 Pa is flowing at 5.0 m/s in a horizontal pipe which contracts to 1/3 its former area. What are the pressure and velocity of the water after the contraction?

Some species of whales can dive to depths of one kilometer. What is the total pressure they experience at this depth? (ρsea = 1 020 kg/m3 and 1.01 × 105 N/m2 = 1 atm.)

Find the pressure in atmospheres in the water at the base of Dworshak Dam if the water in the reservoir is 200 meters deep. (1.01 × 105 N/m2 = 1 atm.)

A fountain sends water to a height of 100 meters. What must be the pressurization (above atmospheric) of the water system? 1 atm= 1.01 × 105 N/m2.

Find the average density of a white dwarf star if it has a mass equal to that of the Sun (2.0 × 1030 kg) and a radius equal to that of the Earth (6.4 × 106 m) .

Determine the minimum area of a flat ice floe 1.0 meter thick if it is to support a 2000-kg car above seawater. (ρice = 920 kg/m3, ρsea = 1020 kg/m3.)

When water freezes, it expands about nine percent. What would be the pressure increase inside your automobile engine block if the water in there froze? The bulk modulus of ice is 2.0 × 109 N/m2, and 1 atm= 1.01 × 105 N/m2.