Question 1

As ice floats in water,about 10% of the ice floats above the surface of the water.If we float some ice in a glass of water,what will happen to the water level as the ice melts?

Accepted Answer

The water level remains unchanged because the volume of water displaced by the ice is equal to the volume of water the ice turns into when it melts. This is due to the principle of buoyancy and the fact that ice expands to occupy a larger volume than the water it was made from, which compensates for the part of the ice that floats above the water level.

Question 2

How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 10⁵ Pa)

Accepted Answer

The pressure at a certain depth in a liquid depends on the density and height of the liquid column above that depth. Using the equation P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the depth, we can set the pressure at double the surface pressure and solve for h.

2P(surface) = ρgh
2(1.01 × 10^5 Pa) = 1000 kg/m^3 × 9.81 m/s^2 × h
h = 10.3 m

Therefore, the depth at which the pressure is double the surface pressure is 10.3 m. Choice C is the best answer.

Question 3

What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 10³ kg/m³ and water density = 1.0 × 10³ kg/m³)

Accepted Answer

The volume of the cylinder is equal to the volume of water displaced. The density of aluminum is 2.7 × 10³ kg/m³, and the density of water is 1.0 × 10³ kg/m³. Therefore, the volume of water displaced is:V = m/ρ = 2.0 kg / (1.0 × 10³ kg/m³) = 7.4 × 10^-4 m³

Question 4

A U-tube is partially filled with water and then an immiscible liquid is added to the right side.The top of the liquid is a distance h₁ above the level of interface between the liquid and water.On the left side of the tube the top of the water is a distance h₂ above the liquid-water interface on the right side.What is the density of the liquid in terms of the density of water ? Note that h₂ < h₁.

Accepted Answer

According to the U-tube principle, the pressure at points A and B should be equal. At point A: P = atmospheric pressure + ρ_water*g*h1 where ρ_water is the density of water, g is the acceleration due to gravity, and h1 is the height of water above point B. At point B: P = atmospheric pressure + ρ_liquid*g*h2 + ρ_water*g*(h1-h2) where ρ_liquid is the density of the immiscible liquid, and h2 is the height of the liquid above point B. Since the pressure at points A and B are equal: ρ_water*g*h1 = ρ_liquid*g*h2 + ρ_water*g*(h1-h2) ρ_liquid = ρwater * (h1-h2) / h2 Since h₂ < h₁, h2 is smaller than h1-h2, so ρ_liquid should be less than ρ_water. The only choice that satisfies this condition is B.

Question 5

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 600 g,what volume would be necessary to prove that it is pure gold?

Accepted Answer

The answer of Legend says that Archimedes,in determining whether or...

Question 6

A cube of wood of density 0.780 g/cm³ is 11.2 cm on a side.When placed in water,what height of the block will float above the surface? (water density = 1.00 g/cm³)

Accepted Answer

First, we need to determine whether the wood will float or sink in water. If the wood is less dense than water, it will float. If it's more dense, it will sink. We can use the densities given in the problem to determine this:

Density of wood (d1) = 0.780 g/cm³
Density of water (d2) = 1.00 g/cm³

Since the density of wood (0.780 g/cm³) is less than the density of water (1.00 g/cm³), the wood will float in water.

Now, we need to determine how much of the wood will be above the surface of the water. To do this, we can use Archimedes' principle:

The buoyant force (B) on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

In other words, the weight of the wood that is submerged in water will be equal to the weight of the water that the wood displaces. We can set up an equation to solve for the height of the wood that will be above the surface of the water:

Volume of wood (V) = (11.2 cm)³ = 1400.4 cm³
Weight of wood (W1) = Volume x Density = 1400.4 cm³ x 0.780 g/cm³ = 1093.312 g

Weight of displaced water (W2) = Volume x Density = 1400.4 cm³ x 1.00 g/cm³ = 1400.4 g

Buoyant force (B) = Weight of displaced water = 1400.4 g

Since the buoyant force is equal to the weight of the submerged wood, we can set the two weights equal to each other and solve for the height of the wood that is above the surface of the water:

Weight of submerged wood = Weight of displaced water
1093.312 g = (11.2 cm - h)³ x 1.00 g/cm³

Solving for h, we get:
h = 2.46 cm

Therefore, the height of the wood that will float above the surface of the water is 2.46 cm, so the answer is (C) 2.46 cm.

Question 7

Dams at two different locations are needed to form a lake.When the lake is filled,the water level will be at the top of both dams.The Dam #2 is twice as high and twice as wide as Dam #1.How much greater is the force of the water on Dam #2 than the force on Dam #1? (Ignore atmospheric pressure;it is pushing on both sides of the dams. )

Accepted Answer

The force on a dam due to water is proportional to the area of the dam and the square of the height of the water. Since Dam #2 is twice as high and twice as wide as Dam #1, its area is 4 times greater, and the height of the water is twice as high. Therefore, the force on Dam #2 is 4 (area) * 2^2 (height squared) = 16 times greater than the force on Dam #1.

Question 8

A fountain sends water to a height of 113 m.What must be the pressurization (above atmospheric)of the underground water system? (1 atm = 10⁵ N/m²)

Accepted Answer

To find the required pressurization, we can use the formula for pressure due to a column of fluid, $P = \frac{h\rho g}{\rho_{\text{atm}}}$, where $h = 113\,m$ is the height of the water column, $\rho = 1000\,kg/m^3$ is the density of water, $g = 9.8\,m/s^2$ is the acceleration due to gravity, and $\rho_{\text{atm}} = 101,000\,N/m^2$ is the atmospheric pressure. Plugging in the values, we get $P = \frac{113 \times 1000 \times 9.8}{101,000} \approx 11.1\,atm$. This pressure is above atmospheric pressure, so the correct answer is 11.1 atm.

Question 9

The bottom of a flat-bottomed aluminum boat has area = 4.10 m² and mass = 65.0 kg.If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat,how much lower will the boat ride in the water? (H₂O density = 1.0 × 10³ kg/m³)

Accepted Answer

The weight of the boat filled with water (displaced water) is equal to the weight of the boat and its contents. We can use the formula:

(displaced water volume) x (water density) x (gravity) = (boat + contents mass) x (gravity)

Rearranging the formula to solve for the displaced water volume:

displaced water volume = (boat + contents mass) x (gravity) / (water density x gravity)

displaced water volume = (305 kg + 65 kg) / (1000 kg/m^3)

displaced water volume = 0.37 m^3

Since the boat has a flat bottom, the displaced water volume is equal to the volume of water directly under the boat. Therefore, the depth that the boat rides lower in the water is:

depth = displaced water volume / (boat bottom area)

depth = 0.37 m^3 / (4.10 m^2)

depth = 0.0902 m

So the boat rides 0.0902 m lower in the water with the fishermen and their gear on board. The correct answer is C.

Question 10

When lying down,the gauge pressure of the blood at a patient's heart is 13.3 kPa.If the patient suddenly stands up and her body doesn't compensate quickly enough for the pressure changes,what would be the pressure at her head,55.0 cm above her heart? The density of blood is 1 060 kg/m³.

Accepted Answer

The pressure at the patient's head when they stand up can be calculated using the hydrostatic pressure formula: $P = P_0 + \rho gh$, where $P_0$ is the initial pressure (13.3 kPa or 13300 Pa), $\rho$ is the density of blood (1060 kg/m³), $g$ is the acceleration due to gravity (9.8 m/s²), and $h$ is the height difference (0.55 m). The pressure difference due to the height change is $\Delta P = \rho gh = 1060 \times 9.8 \times 0.55$, which calculates to approximately 5703 Pa. Subtracting this from the initial pressure gives the pressure at the head: $13300 - 5703 = 7597$ Pa, or $7.59 \times 10^3$ Pa.

Question 11

A ping-pong ball has an average density of 0.0840 g/cm³ and a diameter of 3.80 cm.What force would be required to keep the ball completely submerged under water?

Accepted Answer

The answer of A ping-pong ball has an average density...

Question 12

The spring of the pressure gauge shown in the figure has a force constant of 900 N/m,and the piston has a radius of 1.5 cm. As the gauge is lowered into water,what change in depth causes the piston to move in by 0.88 cm? The density of water is 1 000 kg/m³.

Accepted Answer

The answer of The spring of the pressure gauge shown...

Question 13

At a pressure of 1 atmosphere a column of mercury in a barometer is supported to the height h = 0.76 m.The density of mercury is 13.6 × 10³ kg/m³.A barometer of similar design filled with water would support a column of water how high at a pressure of 1 atmosphere?

Accepted Answer

The height of the liquid column in a barometer is inversely proportional to the density of the liquid. Since water is much less dense than mercury, a water barometer would support a column of water much higher than the mercury column to exert the same pressure.

Question 14

A U-tube is partially filled with water and then an immiscible liquid is added to the right side.The top of the liquid is a distance h₁ = 2.40 cm above the level of interface between the liquid and water.On the left side of the tube the top of the water is a distance h₂ = 1.48 cm above the liquid-water interface on the right side.What is the density of the liquid in terms of the density of water,1 000 kg/m³?

Accepted Answer

The pressure at the interface must be the same on both sides. Using the hydrostatic pressure formula, ρ_water * g * h2 = ρ_liquid * g * h1. Solving for ρ_liquid gives ρ_liquid = ρ_water * (h2/h1) = 1000 * (1.48/2.40) = 617 kg/m³.

Question 15

The water behind Grand Coulee Dam is 1 000 m wide and 200 m deep.Find the hydrostatic force on the back of the dam.(Hint: the total force = average pressure × area)

Accepted Answer

The answer of The water behind Grand Coulee Dam is...

Question 16

The bottom of a flat-bottomed aluminum boat has an area of 4.20 m² and the boat's mass is 63.0 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.00 × 10³ kg/m³)

Accepted Answer

To find how far below the water surface the boat bottom is, we use the principle of buoyancy, which states that the weight of the displaced water equals the weight of the boat. The weight of the boat is $63.0 \, \text{kg} \times 9.8 \, \text{m/s}^2$. The volume of water displaced equals the weight of the boat divided by the density of water times gravity. Thus, the depth $d$ is given by $d = \frac{\text{Weight of boat}}{\text{Area} \times \text{Density of water} \times g}$. Substituting the given values, we find $d = 0.0150 \, \text{m}$.

Question 17

A reading of a tire gauge tells you that the gauge pressure in a tire is 31 lb/in².What is the absolute pressure in the tire? Assume that atmospheric pressure is 14 lb/in².

Accepted Answer

Absolute pressure is the sum of gauge pressure and atmospheric pressure. Therefore, 31 lb/in² (gauge pressure) + 14 lb/in² (atmospheric pressure) = 45 lb/in² (absolute pressure).

Question 18

A solid rock,suspended in air by a spring scale,has a measured mass of 8.50 kg.When the rock is submerged in water,the scale reads 4.00 kg.What is the density of the rock? (water density = 1 000 kg/m³)

Accepted Answer

The buoyant force equals the weight of the water displaced, which is 8.50 kg - 4.00 kg = 4.50 kg. The volume of the rock is the volume of water displaced, which is 4.50 kg / 1000 kg/m³ = 0.0045 m³. The density of the rock is mass/volume = 8.50 kg / 0.0045 m³ = 1.9E+3 kg/m³.

Question 19

Atmospheric pressure is 1.00 × 10⁵ N/m²,and the density of air is 1.29 kg/m³.If the density of air is constant as you get higher and higher,calculate the height of the atmosphere needed to produce this pressure.

Accepted Answer

The answer of Atmospheric pressure is 1.00 × 10⁵ N/m²,and...

Question 20

Why do vapor bubbles get larger in boiling water as they approach the surface?

Accepted Answer

As the bubble rises, the pressure around it decreases due to the reduction in hydrostatic pressure as the depth decreases. This reduced pressure causes the gas inside the bubble to expand, leading to an increase in its size.

Quiz 9: Fluids and Solids

As ice floats in water,about 10% of the ice floats above the surface of the water.If we float some ice in a glass of water,what will happen to the water level as the ice melts?

How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 10⁵ Pa)

What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 10³ kg/m³ and water density = 1.0 × 10³ kg/m³)

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 600 g,what volume would be necessary to prove that it is pure gold?

A cube of wood of density 0.780 g/cm³ is 11.2 cm on a side.When placed in water,what height of the block will float above the surface? (water density = 1.00 g/cm³)

A fountain sends water to a height of 113 m.What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 10⁵ N/m²)

The bottom of a flat-bottomed aluminum boat has area = 4.10 m² and mass = 65.0 kg.If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat,how much lower will the boat ride in the water? (H₂O density = 1.0 × 10³ kg/m³)

When lying down,the gauge pressure of the blood at a patient's heart is 13.3 kPa.If the patient suddenly stands up and her body doesn't compensate quickly enough for the pressure changes,what would be the pressure at her head,55.0 cm above her heart? The density of blood is 1 060 kg/m³.

A ping-pong ball has an average density of 0.0840 g/cm³ and a diameter of 3.80 cm.What force would be required to keep the ball completely submerged under water?

The spring of the pressure gauge shown in the figure has a force constant of 900 N/m,and the piston has a radius of 1.5 cm. As the gauge is lowered into water,what change in depth causes the piston to move in by 0.88 cm? The density of water is 1 000 kg/m³.

At a pressure of 1 atmosphere a column of mercury in a barometer is supported to the height h = 0.76 m.The density of mercury is 13.6 × 10³ kg/m³.A barometer of similar design filled with water would support a column of water how high at a pressure of 1 atmosphere?

The water behind Grand Coulee Dam is 1 000 m wide and 200 m deep.Find the hydrostatic force on the back of the dam.(Hint: the total force = average pressure × area)

The bottom of a flat-bottomed aluminum boat has an area of 4.20 m² and the boat's mass is 63.0 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.00 × 10³ kg/m³)

A reading of a tire gauge tells you that the gauge pressure in a tire is 31 lb/in².What is the absolute pressure in the tire? Assume that atmospheric pressure is 14 lb/in².

A solid rock,suspended in air by a spring scale,has a measured mass of 8.50 kg.When the rock is submerged in water,the scale reads 4.00 kg.What is the density of the rock? (water density = 1 000 kg/m³)

Atmospheric pressure is 1.00 × 10⁵ N/m²,and the density of air is 1.29 kg/m³.If the density of air is constant as you get higher and higher,calculate the height of the atmosphere needed to produce this pressure.

Why do vapor bubbles get larger in boiling water as they approach the surface?

Quiz 9: Fluids and Solids

As ice floats in water,about 10% of the ice floats above the surface of the water.If we float some ice in a glass of water,what will happen to the water level as the ice melts?

How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 105 Pa)

What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 103 kg/m3 and water density = 1.0 × 103 kg/m3)

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 600 g,what volume would be necessary to prove that it is pure gold?

A cube of wood of density 0.780 g/cm3 is 11.2 cm on a side.When placed in water,what height of the block will float above the surface? (water density = 1.00 g/cm3)

A fountain sends water to a height of 113 m.What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 105 N/m2)

The bottom of a flat-bottomed aluminum boat has area = 4.10 m2 and mass = 65.0 kg.If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat,how much lower will the boat ride in the water? (H2O density = 1.0 × 103 kg/m3)

When lying down,the gauge pressure of the blood at a patient's heart is 13.3 kPa.If the patient suddenly stands up and her body doesn't compensate quickly enough for the pressure changes,what would be the pressure at her head,55.0 cm above her heart? The density of blood is 1 060 kg/m3.

A ping-pong ball has an average density of 0.0840 g/cm3 and a diameter of 3.80 cm.What force would be required to keep the ball completely submerged under water?

The spring of the pressure gauge shown in the figure has a force constant of 900 N/m,and the piston has a radius of 1.5 cm. As the gauge is lowered into water,what change in depth causes the piston to move in by 0.88 cm? The density of water is 1 000 kg/m3.

At a pressure of 1 atmosphere a column of mercury in a barometer is supported to the height h = 0.76 m.The density of mercury is 13.6 × 103 kg/m3.A barometer of similar design filled with water would support a column of water how high at a pressure of 1 atmosphere?

The water behind Grand Coulee Dam is 1 000 m wide and 200 m deep.Find the hydrostatic force on the back of the dam.(Hint: the total force = average pressure × area)

The bottom of a flat-bottomed aluminum boat has an area of 4.20 m2 and the boat's mass is 63.0 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.00 × 103 kg/m3)

A reading of a tire gauge tells you that the gauge pressure in a tire is 31 lb/in2.What is the absolute pressure in the tire? Assume that atmospheric pressure is 14 lb/in2.

A solid rock,suspended in air by a spring scale,has a measured mass of 8.50 kg.When the rock is submerged in water,the scale reads 4.00 kg.What is the density of the rock? (water density = 1 000 kg/m3)

Atmospheric pressure is 1.00 × 105 N/m2,and the density of air is 1.29 kg/m3.If the density of air is constant as you get higher and higher,calculate the height of the atmosphere needed to produce this pressure.

Why do vapor bubbles get larger in boiling water as they approach the surface?

How deep under the surface of a lake would the pressure be double that at the surface? (1 atm = 1.01 × 10⁵ Pa)

What volume of water is displaced by a submerged 2.0-kg cylinder made of solid aluminum? (aluminum density = 2.7 × 10³ kg/m³ and water density = 1.0 × 10³ kg/m³)

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 600 g,what volume would be necessary to prove that it is pure gold?

A cube of wood of density 0.780 g/cm³ is 11.2 cm on a side.When placed in water,what height of the block will float above the surface? (water density = 1.00 g/cm³)

A fountain sends water to a height of 113 m.What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 10⁵ N/m²)

The bottom of a flat-bottomed aluminum boat has area = 4.10 m² and mass = 65.0 kg.If two fishermen and their fishing gear with total mass of 305 kg are placed in the boat,how much lower will the boat ride in the water? (H₂O density = 1.0 × 10³ kg/m³)

When lying down,the gauge pressure of the blood at a patient's heart is 13.3 kPa.If the patient suddenly stands up and her body doesn't compensate quickly enough for the pressure changes,what would be the pressure at her head,55.0 cm above her heart? The density of blood is 1 060 kg/m³.

A ping-pong ball has an average density of 0.0840 g/cm³ and a diameter of 3.80 cm.What force would be required to keep the ball completely submerged under water?

The spring of the pressure gauge shown in the figure has a force constant of 900 N/m,and the piston has a radius of 1.5 cm. As the gauge is lowered into water,what change in depth causes the piston to move in by 0.88 cm? The density of water is 1 000 kg/m³.

At a pressure of 1 atmosphere a column of mercury in a barometer is supported to the height h = 0.76 m.The density of mercury is 13.6 × 10³ kg/m³.A barometer of similar design filled with water would support a column of water how high at a pressure of 1 atmosphere?

The bottom of a flat-bottomed aluminum boat has an area of 4.20 m² and the boat's mass is 63.0 kg.When set afloat in water,how far below the water surface is the boat bottom? (water density = 1.00 × 10³ kg/m³)

A reading of a tire gauge tells you that the gauge pressure in a tire is 31 lb/in².What is the absolute pressure in the tire? Assume that atmospheric pressure is 14 lb/in².

A solid rock,suspended in air by a spring scale,has a measured mass of 8.50 kg.When the rock is submerged in water,the scale reads 4.00 kg.What is the density of the rock? (water density = 1 000 kg/m³)

Atmospheric pressure is 1.00 × 10⁵ N/m²,and the density of air is 1.29 kg/m³.If the density of air is constant as you get higher and higher,calculate the height of the atmosphere needed to produce this pressure.