Question 1

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 3.30 kg.What is the density of the rock? (water density = 1 000 kg/m³) A)4.55 ´ 10³ kg/m³ B)3.50 ´ 10³ kg/m³ C)1.20 ´ 10³ kg/m³ D)1.58 ´ 10³ kg/m³

Accepted Answer

The buoyant force acting on the rock when submerged in water is equal to the weight of water displaced by the rock. We can use this fact to calculate the volume of the rock:

buoyant force = weight of water displaced
9.00 kg - 3.30 kg = 5.70 kg
5.70 kg = (volume of rock) × (density of water) × (gravitational acceleration)
(volume of rock) = 5.70 kg / (1000 kg/m³) / (9.81 m/s²)
(volume of rock) = 0.000581 m³

Now we can calculate the density of the rock:

density of rock = mass of rock / volume of rock
density of rock = 9.00 kg / 0.000581 m³
density of rock = 15490.19 kg/m³
density of rock ≈ 1.58 × 10⁴ kg/m³

Therefore, the best choice is D.

Question 2

Water (density = 1 ´ 10³ kg/m³)flows at 10 m/s through a pipe with radius 0.030 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)0.046 m B)0.034 m C)0.015 m D)0.012 m

Accepted Answer

We can use Bernoulli's equation:

P1 + ½ρv1^2 + ρgh1 = P2 + ½ρv2^2 + ρgh2

Where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is height.

Since the pressure remains unchanged, we can drop the P1 and P2 terms. Also, since the water is flowing horizontally, we can drop the h1 and h2 terms.

Thus, we are left with:

½ρv1^2 = ½ρv2^2

We can solve for v2:

v2 = v1*(r1/r2)^2

Where r1 is the original radius of the pipe and r2 is the radius of the pipe on the second floor.

Plugging in the given values:

10 = v1*(0.030/r2)^2

Solving for r2:

r2 = 0.034 m

Therefore, the answer is B) 0.034 m.

Question 3

A large stone is resting on the bottom of the swimming pool.The normal force of the bottom of the pool on the stone is equal to the:
A)weight of the stone.
B)weight of the water displaced.
C)sum of the weight of the stone and the weight of the displaced water.
D)difference between the weight of the stone and the weight of the displaced water.

Accepted Answer

The answer of A large stone is resting on the...

Question 4

A heavily loaded boat is floating in a pond.The boat sinks because of a leak.What happens to the surface level of the pond?
A)It stays the same.
B)It goes up.
C)It goes down.
D)More information is needed to reach a conclusion.

Accepted Answer

As the boat sinks, it displaces water and takes up space in the pond. This causes the overall volume of water in the pond to decrease, which leads to a lower surface level.

Question 5

Think of Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe.Imagine that you take measurements along the pipe in the direction of fluid flow.What happens to the sum of the pressure and energy per unit volume?
A)It increases as the pipe diameter increases.
B)It decreases as the pipe diameter increases.
C)It remains constant as the pipe diameter increases.
D)No choices above are valid.

Accepted Answer

According to Bernoulli's equation for horizontal flow, the sum of pressure and energy per unit volume remains constant along the pipe as long as there are no losses due to friction or other factors. Therefore, the sum of pressure and energy per unit volume would remain constant regardless of changes in pipe diameter.

Question 6

A blimp is filled with 400 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)111 kg B)129 kg C)215 kg D)444 kg

Accepted Answer

The answer of A blimp is filled with 400 m³...

Question 7

The flow rate of blood through the average human aorta,of radius 1.0 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 8

A block of wood has specific gravity 0.80.When placed in water,what percent of the volume of the wood is above the surface?
A)0,the block sinks.
B)20%
C)25%
D)80%

Accepted Answer

The specific gravity of 0.80 means the wood is 80% as dense as water. Therefore, 80% of the wood's volume is submerged, and 20% is above the surface.

Question 9

Water comes down the spillway of a dam from an initial vertical height of 170 m.What is the highest possible speed of the water at the end of the spillway?
A)15 m/s
B)25 m/s
C)58 m/s
D)1 370 m/s

Accepted Answer

The highest possible speed of the water can be found using the equation: 
v = sqrt(2gh)
where v is the final velocity, g is the acceleration due to gravity (9.81 m/s^2), and h is the initial height (170 m). 
Plugging in the values, 
v = sqrt(2*9.81*170) 
v = 58.01 m/s which is approximately 58 m/s 
Therefore, the correct choice is C.

Question 10

A heavily loaded boat is floating in a pond.The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water.What happens to the surface level of the pond?
A)It stays the same.
B)It goes up.
C)It goes down.
D)More information is needed to reach a conclusion.

Accepted Answer

The boat is still in the pond and has not been removed, so the displaced water from the boat remains the same. Therefore, the surface level of the pond would stay the same.

Question 11

The flow rate of a liquid through a 2.0-cm-radius pipe is 0.008 0 m³/s.The average fluid speed in the pipe is: A)0.64 m/s. B)2.0 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 12

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?
A)The water level will rise 10% of the volume of the ice that melts.
B)The water level will rise,but not as much as the 10% indicated in answer a.
C)The water level will remain unchanged.
D)The water level will become lower.

Accepted Answer

The water level will remain unchanged because the volume of water displaced by the floating ice is equal to the volume of water that the ice will turn into when it melts.

Question 13

An ideal fluid,of density 0.90 ´ 10³ kg/m³,flows at 6.0 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 radius of 1.5 cm.Find the speed of flow in the second pipe. A)54 m/s B)18 m/s C)0.67 m/s D)0.33 m/s

Accepted Answer

We can use the principle of continuity for ideal fluids which states that the product of the cross-sectional area and the speed of flow is constant throughout the fluid. 
Thus, A1v1 = A2v2 where A1 and A2 are the cross-sectional areas of pipes 1 and 2 respectively, and v1 and v2 are the speeds of flow.
Using this equation and the formula for the cross-sectional area of a pipe (A = πr^2), we can find v2: 
A1 = π(0.005m)^2 = 7.85 ´ 10^-5 m^2 
A2 = π(0.015m)^2 = 7.07 ´ 10^-4 m^2 
v1 = 6.0 m/s

Solving for v2, we get:
v2 = (A1v1)/A2 = (7.85 ´ 10^-5 m^2 × 6.0 m/s)/(7.07 ´ 10^-4 m^2) ≈ 0.67 m/s

Therefore, the best choice is C.

Question 14

A hole is poked through the metal side of a drum holding water.The hole is 18 cm below the water surface.What is the initial speed of outflow?
A)1.9 m/s
B)2.96 m/s
C)3.2 m/s
D)3.5 m/s

Accepted Answer

The answer of A hole is poked through the metal...

Question 15

Water pressurized to 3 ´ 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 ´ 10⁵Pa,10 m/s C)3 ´ 10⁵ Pa,15 m/s D)4 ´ 10⁵Pa,1.5 m/s

Accepted Answer

The speed of the water increases to 15 m/s due to the reduction in area (continuity equation). Using Bernoulli's equation, the pressure decreases to 2 x 10^5 Pa.

Question 16

A fountain sends water to a height of 100 m.What must be the pressurization (above atmospheric)of the underground water system? (1 atm = 10⁵ N/m²) A)1 atm B)4.2 atm C)7.2 atm D)9.8 atm

Accepted Answer

The pressure required to lift water to a height of 100 m can be calculated using the formula:
Pressure = density x gravity x height
Assuming the density of water as 1000 kg/m³ and acceleration due to gravity as 9.8 m/s², we get:
Pressure = 1000 x 9.8 x 100
Pressure = 980,000 N/m²
Converting N/m² to atm, we get:
980,000 N/m² = 980,000/10¹² atm
Pressure = 9.8 atm
Therefore, the pressurization (above atmospheric) of the underground water system must be 9.8 atm. Hence, option D is the correct answer.

Question 17

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 0.100 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)19 m/s D)0.99 m/s

Accepted Answer

The pressure difference between the top of the straw and the liquid in the can needs to be equal to or greater than the weight of the column of liquid that is being lifted, which is:

$\Delta P = ho_{soft\,drink}\cdot g \cdot h$

where $ho_{soft\,drink}$ is the density of the soft drink, $g$ is the acceleration due to gravity, and $h$ is the height of the lifted column of liquid.

The velocity of the air blown across the top of the straw can be calculated using Bernoulli's equation, which relates the pressure, density, and velocity of a fluid:

$P + \frac{1}{2}ho v^2 = 	ext{constant}$

We can assume that the pressure on either side of the straw is approximately atmospheric pressure, so we can set $P$ equal to atmospheric pressure. The velocity of the air needed to lift the liquid half way up the straw can be found by solving for $v$:

$v = \sqrt{\frac{2\cdot \Delta P}{ho_{air}}} = \sqrt{\frac{2\cdot ho_{soft\,drink} \cdot g \cdot h}{ho_{air}}}$

Plugging in the given values, we get:

$v = \sqrt{\frac{2\cdot 1.0	imes10^{3}\,kg/m^3 \cdot 9.81\,m/s^2 \cdot 0.100\,m}{1.3\,kg/m^3}} \approx 26.8\,m/s$

Therefore, the best choice is B) 27 m/s.

Question 18

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 3.0 inches,respectively.The speed of the fluid flow through the 3.0-inch section will be what factor times that through the 1.0-inch section?
A)6.0
B)9.0
C)1/3
D)1/9

Accepted Answer

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

Question 19

Water (density = 1 ´ 10³ kg/m³)flows at 15 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

Bernoulli's equation: P + 1/2 * ρ * v^2 + ρ * g * h = constant. Since the pressure remains unchanged, we have 1/2 * ρ * v1^2 + ρ * g * h1 = 1/2 * ρ * v2^2 + ρ * g * h2. Solving for v2, we get v2 = √(v1^2 + 2 * g * h). Plugging in the given values, we get v2 = √(15^2 + 2 * 9.8 * 3) = 13 m/s.

Question 20

An ideal fluid,of density 0.85 ´ 10³ kg/m³,flows at 0.25 kg/s through a pipe of radius 0.010 m.What is the fluid speed? A)0.85 m/s B)1.3 m/s C)3.0 m/s D)0.94 m/s

Accepted Answer

The correct answer is D because the fluid speed is given by the equation v = Q/(πr^2), where Q is the flow rate, r is the radius of the pipe, and π is the mathematical constant pi. Plugging in the given values, we get v = 0.25 kg/s / (π(0.010 m)^2) = 0.94 m/s.

Quiz 9: Solids and Fluids

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 3.30 kg.What is the density of the rock? (water density = 1 000 kg/m³)

Water (density = 1 ´ 10³ kg/m³) flows at 10 m/s through a pipe with radius 0.030 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 large stone is resting on the bottom of the swimming pool.The normal force of the bottom of the pool on the stone is equal to the:

A heavily loaded boat is floating in a pond.The boat sinks because of a leak.What happens to the surface level of the pond?

Think of Bernoulli's equation as it pertains to an ideal fluid flowing through a horizontal pipe.Imagine that you take measurements along the pipe in the direction of fluid flow.What happens to the sum of the pressure and energy per unit volume?

A blimp is filled with 400 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. )

The flow rate of blood through the average human aorta,of radius 1.0 cm,is about 90 cm³/s.What is the speed of the blood flow through the aorta?

A block of wood has specific gravity 0.80.When placed in water,what percent of the volume of the wood is above the surface?

Water comes down the spillway of a dam from an initial vertical height of 170 m.What is the highest possible speed of the water at the end of the spillway?

A heavily loaded boat is floating in a pond.The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under although it is now deeper in the water.What happens to the surface level of the pond?

The flow rate of a liquid through a 2.0-cm-radius pipe is 0.008 0 m³/s.The average fluid speed in the pipe is:

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?

An ideal fluid,of density 0.90 ´ 10³ kg/m³,flows at 6.0 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 radius of 1.5 cm.Find the speed of flow in the second pipe.

A hole is poked through the metal side of a drum holding water.The hole is 18 cm below the water surface.What is the initial speed of outflow?

Water pressurized to 3 ´ 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 fountain sends water to a height of 100 m.What must be the pressurization (above atmospheric) of the underground water system? (1 atm = 10⁵ N/m²)

An ideal fluid flows through a pipe made of two sections with diameters of 1.0 and 3.0 inches,respectively.The speed of the fluid flow through the 3.0-inch section will be what factor times that through the 1.0-inch section?

Water (density = 1 ´ 10³ kg/m³) flows at 15 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 0.85 ´ 10³ kg/m³,flows at 0.25 kg/s through a pipe of radius 0.010 m.What is the fluid speed?

Quiz 9: Solids and Fluids

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 3.30 kg.What is the density of the rock? (water density = 1 000 kg/m3)

Water (density = 1 ´ 103 kg/m3) flows at 10 m/s through a pipe with radius 0.030 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?