Question 1

An empty spice bottle has an inner volume of 1.31 × 10⁻⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10⁻⁴ m³ of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water? A)0.69 B)0.81 C)0.85 D)1.00 E)1.46

Accepted Answer

The fraction of the volume submerged is the volume of water displaced divided by the inner volume of the bottle: (1.31 × 10^−4 m^3) / (1.63 × 10^−4 m^3) = 0.69.

Question 2

People can snorkel down to a depth of roughly one meter. This means that the additional pressure on the air in their lungs is roughly A)9800 N. B)9800 Pa. C)9800 ATM. D)19,600 N. E)19,600 N/m².

Accepted Answer

The pressure at a depth of one meter in water is roughly equal to the weight of the water above it, which is 1 atm (or 101,325 Pa) plus the weight of one meter of water. One meter of water has a weight of approximately 9,800 N, which is equal to 9,800 Pa. Therefore, the additional pressure on the air in their lungs is roughly 9,800 Pa or 9.8 kPa.

Question 3

A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt
A)the water level in the pitcher falls.
B)the water level in the pitcher remains the same.
C)water starts to flow out the spout of the pitcher.
D)the pressure on the bottom of the pitcher decreases.
E)the pressure on the bottom of the pitcher increases.

Accepted Answer

When ice melts in water, it converts to liquid water without changing the overall water level in the pitcher. This is because the volume of water produced by the melting ice exactly replaces the volume previously displaced by the ice. The principle of buoyancy dictates that the amount of water displaced by the ice is equal to the weight of the ice. When the ice melts, it turns into the same amount of water it had displaced, keeping the water level constant.

Question 4

Air within the funnel of a large tornado may have a pressure of only 0.2 atm. What is the approximate outward force on a (5 m × 10 m) wall if a tornado suddenly envelops the house? (1 atm = 1.01 × 10⁵ N/m².) A)4 × 10³ N B)4 × 10⁴ N C)4 × 10⁵ N D)4 × 10⁶ N E)7 × 10⁵ N

Accepted Answer

The outward force on the wall is equal to the pressure difference between the inside and outside of the house multiplied by the area of the wall. The pressure difference is (1 atm - 0.2 atm) = 0.8 atm = 8.08 x 10^4 N/m^2. Therefore, the outward force on the wall is (8.08 x 10^4 N/m^2) x (5 m x 10 m) = 4.04 x 10^6 N = 4 x 10^16 N, which is closest to choice D (4 x 10^16 N).

Question 5

An empty spice bottle has an inner volume of 1.31 × 10⁻⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10⁻⁴m³ of water when fully submerged. What volume of mercury (ρHg = 13.6 × 10³ kg/m³) must be added to the empty bottle so that it will just submerge? A)3.75 cm³ B)12.0 cm³ C)101 cm³ D)147 cm³ E)237 cm³

Accepted Answer

The correct answer is A.The mass of the air in the bottle is:$$m_{air} = ho_{air} V_{bottle} = (1.29 	imes 10^{-3} 	ext{ kg/m}^3)(1.31 	imes 10^{-4} 	ext{ m}^3) = 1.69 	imes 10^{-7} 	ext{ kg}$$The mass of the water displaced by the bottle is:$$m_{water} = ho_{water} V_{displaced} = (1000 	ext{ kg/m}^3)(1.63 	imes 10^{-4} 	ext{ m}^3) = 0.163 	ext{ kg}$$The mass of the mercury that must be added to the bottle is:$$m_{mercury} = m_{water} - m_{air} = 0.163 	ext{ kg} - 1.69 	imes 10^{-7} 	ext{ kg} = 0.163 	ext{ kg}$$The volume of the mercury that must be added to the bottle is:$$V_{mercury} = \frac{m_{mercury}}{ho_{mercury}} = \frac{0.163 	ext{ kg}}{13.6 	imes 10^3 	ext{ kg/m}^3} = 1.20 	imes 10^{-5} 	ext{ m}^3 = 12.0 	ext{ cm}^3$$

Question 6

A cube of water ice (ρ = 0.917 × 10³ kg/m³) is placed in mercury (ρ = 13.6 × 10³ kg/m³), which is liquid at 0° Celsius. If we ignore any possible melting of the ice cube and problems with the surface tension of mercury, the fraction of the ice cube that floats above the surface of the mercury is A)0.067 4. B)0.073 5. C)0.926. D)0.933. E)1.00.

Accepted Answer

The answer of A cube of water ice (ρ =...

Question 7

The figure below shows a container filled with water to the height shown. When we compare the pressure at A to the pressure at B, we find that 
A)  .
B)  .
C)pA = pB.
D)pA = 2pB.
E)pA = 4pB.

Accepted Answer

The answer of The figure below shows a container filled...

Question 8

How much power is theoretically available from a mass flow of 1000 kg/s of water when it falls a vertical distance of 100 meters?
A)980 kW
B)98 kW
C)4900 W
D)980 W
E)9600 W

Accepted Answer

The theoretical power available from a mass flow of water falling a distance h is given by P = mgh, where m is the mass flow rate, g is the acceleration due to gravity, and h is the height of the fall.

P = (1000 kg/s) x (9.81 m/s^2) x (100 m) = 981,000 W = 981 kW

Therefore, the best choice is A) 980 kW, which is the closest option to the calculated theoretical power available.

Question 9

A Venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 kg/m³.) A)70 Pa B)85 Pa C)100 Pa D)120 Pa E)81 Pa

Accepted Answer

From the continuity equation, we know that the velocity of the flow through the constricted section is twice the velocity through the wider section. Therefore, the pressure drop in the constricted section is given by:

ΔP = (1/2)ρv² = (1/2)×1.2 kg/m³ × (3.0 m/s)² = 5.4 Pa

However, we must convert the units of diameter from cm to m:

d1 = 2.0 cm = 0.02 m
d2 = 1.0 cm = 0.01 m

Using the formula for the area of a circle, we find that the ratio of areas is:

A2/A1 = (d2/2)² / (d1/2)² = (0.01/0.02)² = 0.25

Therefore, the pressure drop in the constricted section is:

ΔP = ρv² (1 - A2/A1) = (1.2 kg/m³) × (3.0 m/s)² (1 - 0.25) = 81 Pa

The answer is E.

Question 10

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 × 10⁴ N/m and the pressure on the bottom surface is 9.0 × 10⁴ N/m². If the area of the top and bottom surfaces of each wing is 2.0 m², what is the total lift on the model airplane? A)2.0 × 10³ N B)8.0 × 10³ N C)1.6 × 10⁴ N D)3.6 × 10⁴ N E)1.0 × 10³ N

Accepted Answer

The answer of In a wind tunnel the pressure on...

Question 11

The siphon shown is used to transfer liquid from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m. 
A)1.1 m/s
B)2.2 m/s
C)4.4 m/s
D)9.8 m/s
E)6.5 m/s

Accepted Answer

The answer of The siphon shown is used to transfer...

Question 12

A wood block is placed on top of the ice in a large bowl half full of ice. The bowl is then filled to the brim with water, with the wood block riding on top of the ice. As the ice melts,
A)the density of the water decreases.
B)the water level falls below the rim.
C)the water level rises and water spills out of the bowl.
D)the water level does not change.
E)the wood block descends, causing water to spill out of the bowl.

Accepted Answer

Because ice is less dense than water, the displacement of the ice and the wood block will be equal to the weight of the water displaced as the ice melts. Therefore, the water level in the bowl will not change.

Question 13

A thin rectangular piece of wood floats in water. You slowly pour oil with a density equal to that of the wood on the surface of the water until the height of the oil above the water is twice the height of the piece of wood. Which statement is correct?
A)The wood floats on top of the oil, so it sticks up in the air.
B)The wood does not change its position
C)The wood sinks below the surface of the water.
D)The wood is half in the water and half in the oil.
E)The wood floats in the oil just above the water.

Accepted Answer

Since the density of the oil is equal to that of the wood, the wood will float at the interface between the oil and water, not changing its buoyancy significantly but adjusting its position so that it floats in the oil just above the water. This is because objects float at a level where the fluid (or fluids, in this case) can provide enough buoyant force to counteract the object's weight, and since the oil and wood have the same density, the wood will float in the oil layer.

Question 14

Two identical fish, both at sea level, float in two identical aquariums with identical quantities of water. Fish A is in Alaska, so it weighs more than fish B at the equator, since g is larger at sea level in Alaska. Which statement is correct?
A)A comparison is impossible unless they are both floating at the same level.
B)Fish A displaces a greater quantity of water than fish B.
C)Fish B displaces a greater quantity of water than fish A.
D)They both displace the same quantity of water.
E)Fish A has a smaller acceleration than Fish B when equal horizontal forces are applied to each, because Fish A weighs more.

Accepted Answer

The amount of water displaced by an object is solely dependent on the volume of the object, not its weight or location. Since both fish and their aquariums are identical, they displace the same quantity of water, regardless of their location or weight.

Question 15

A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the volume of water delivered per unit time when the clamp is on to the volume of water delivered per unit time without the clamp is
A)  .
B)  .
C)  .
D)  .
E)1.

Accepted Answer

The answer of A hose has been clamped so that...

Question 16

Water is sent from a firehose at 30.0 m/s at an angle of 30.0° above the horizontal. What is the maximum height reached by the water?
A)7.50 m
B)11.5 m
C)15.0 m
D)19.0 m
E)30.0 m

Accepted Answer

The answer of Water is sent from a firehose at...

Question 17

The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains floating ice as well as water. When we weigh the bowls, we find that
A)WA < WB.
B)WA = WB.
C)WA > WB.
D)WB > WA if the volume of the ice cubes is greater than  the volume of the water.
E)WB > WA if the volume of the ice cubes is greater than 9 times the volume of the water.

Accepted Answer

The answer of The water level in identical bowls, A...

Question 18

A Boeing 737 airliner has a mass of 20,000 kg and the total area of both wings (top or bottom) is 100 m². What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude? A)1960 N/m² B)3920 N/m² C)7840 N/m² D)4560 N/m² E)3070 N/m²

Accepted Answer

To keep the airplane at a constant altitude, the lift force must equal the weight of the airplane. The weight of the airplane is the mass (20,000 kg) times the acceleration due to gravity (approximately 9.8 m/s^2), which equals 196,000 N. The pressure difference required to produce this lift force can be found by dividing the lift force by the wing area (100 m^2), resulting in a pressure difference of 1,960 N/m^2.

Question 19

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum power output if 30.0% of the wind's energy can be extracted? ρair = 1.25 kg/m³. A)7.20 kW B)14.7 kW C)21.3 kW D)29.4 kW E)39.6 kW

Accepted Answer

The maximum power output is calculated using the formula P = 0.5 * ρ * A * v^3 * efficiency. Here, A = π * r^2 = π * (5)^2, v = 10 m/s, efficiency = 0.3, and ρ = 1.25 kg/m^3. Plugging in these values gives approximately 14.7 kW.

Question 20

A police crime lab is trying to determine whether someone was murdered or died as a result of an accident. He was struck in the temple by a 4.20-kg sculpture that is alleged to have fallen off a bookcase. The sculpture presumably fell a distance of 1.43 m and the corner that struck him had an area of 0.250 cm². If the time for the sculpture to stop was 1.00 ms, the pressure on his temple, in N/m², was A)8.89 × 10⁴. B)1.65 × 10⁵. C)1.65 × 10⁶. D)8.89 × 10⁸. E)1.65 × 10⁹.

Accepted Answer

The answer of A police crime lab is trying to...

Quiz 15: Fluids

An empty spice bottle has an inner volume of 1.31 × 10−4 m3. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10−4 m3 of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water?

People can snorkel down to a depth of roughly one meter. This means that the additional pressure on the air in their lungs is roughly

A waiter in a restaurant fills a pitcher full of water and ice so that water would spill out if any more were added. As the ice starts to melt

Air within the funnel of a large tornado may have a pressure of only 0.2 atm. What is the approximate outward force on a (5 m × 10 m) wall if a tornado suddenly envelops the house? (1 atm = 1.01 × 105 N/m2.)

An empty spice bottle has an inner volume of 1.31 × 10−4 m3. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10−4m3 of water when fully submerged. What volume of mercury (ρHg = 13.6 × 103 kg/m3) must be added to the empty bottle so that it will just submerge?

The figure below shows a container filled with water to the height shown. When we compare the pressure at A to the pressure at B, we find that

How much power is theoretically available from a mass flow of 1000 kg/s of water when it falls a vertical distance of 100 meters?

A Venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 kg/m3.)

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 × 104 N/m and the pressure on the bottom surface is 9.0 × 104 N/m2. If the area of the top and bottom surfaces of each wing is 2.0 m2, what is the total lift on the model airplane?

The siphon shown is used to transfer liquid from a higher level to a lower level. If the fluid is drawn up and is continuous through the tube, determine the velocity of flow of gasoline if the vertical distance from the liquid surface to the outlet is 1.0 m.

A wood block is placed on top of the ice in a large bowl half full of ice. The bowl is then filled to the brim with water, with the wood block riding on top of the ice. As the ice melts,

A thin rectangular piece of wood floats in water. You slowly pour oil with a density equal to that of the wood on the surface of the water until the height of the oil above the water is twice the height of the piece of wood. Which statement is correct?

Two identical fish, both at sea level, float in two identical aquariums with identical quantities of water. Fish A is in Alaska, so it weighs more than fish B at the equator, since g is larger at sea level in Alaska. Which statement is correct?

A hose has been clamped so that the area at the clamp is only one quarter the area of the rest of the hose. When we ignore the viscosity of water, the ratio of the volume of water delivered per unit time when the clamp is on to the volume of water delivered per unit time without the clamp is

Water is sent from a firehose at 30.0 m/s at an angle of 30.0° above the horizontal. What is the maximum height reached by the water?

The water level in identical bowls, A and B, is exactly the same. A contains only water; B contains floating ice as well as water. When we weigh the bowls, we find that

A Boeing 737 airliner has a mass of 20,000 kg and the total area of both wings (top or bottom) is 100 m2. What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum power output if 30.0% of the wind's energy can be extracted? ρair = 1.25 kg/m3.

An empty spice bottle has an inner volume of 1.31 × 10⁻⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10⁻⁴ m³ of water when fully submerged. What fraction of the total volume of the bottle will be beneath the surface when it is placed in a tank of water?

Air within the funnel of a large tornado may have a pressure of only 0.2 atm. What is the approximate outward force on a (5 m × 10 m) wall if a tornado suddenly envelops the house? (1 atm = 1.01 × 10⁵ N/m².)

An empty spice bottle has an inner volume of 1.31 × 10⁻⁴ m³. It has a mass of 112 g when filled with air, and it displaces 1.63 × 10⁻⁴m³ of water when fully submerged. What volume of mercury (ρHg = 13.6 × 10³ kg/m³) must be added to the empty bottle so that it will just submerge?

A Venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 m/s in the 2.0-cm section? (ρ = 1.2 kg/m³.)

In a wind tunnel the pressure on the top surface of a model airplane wing is 8.8 × 10⁴ N/m and the pressure on the bottom surface is 9.0 × 10⁴ N/m². If the area of the top and bottom surfaces of each wing is 2.0 m², what is the total lift on the model airplane?

A Boeing 737 airliner has a mass of 20,000 kg and the total area of both wings (top or bottom) is 100 m². What is the pressure difference between the top and bottom surface of each wing when the airplane is in flight at a constant altitude?

A wind of velocity 10 m/s is blowing through a wind generator with blade radius 5.00 meters. What is the maximum power output if 30.0% of the wind's energy can be extracted? ρair = 1.25 kg/m³.