Question 1

A beach ball of radius 30 cm is pushed under water.What force is required to keep the ball submerged?

Accepted Answer

The answer of A beach ball of radius 30 cm...

Question 2

A very large wind turbine is used to extract power from the wind.The turbine has a diameter of 120 meters.What is the maximum power this turbine can extract from the wind.Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

Accepted Answer

The maximum power that can be extracted from the wind by a wind turbine is given by the Betz limit, which states that no more than 59.3% of the kinetic energy in the wind can be captured. The power in the wind can be calculated using the formula: $P = \frac{1}{2} \cdot \rho \cdot A \cdot v^3$, where $P$ is the power in watts, $\rho$ is the air density in kg/m^3, $A$ is the area in square meters through which the wind is passing (the swept area of the turbine blades), and $v$ is the wind speed in m/s. The swept area $A$ can be calculated using the formula for the area of a circle, $A = \pi \cdot r^2$, where $r$ is the radius of the circle.Given:- Diameter of the turbine = 120 meters, so the radius $r = 120/2 = 60$ meters.- Wind speed $v = 10$ m/s.- Density of air $\rho = 1.2$ kg/m^3.First, calculate the swept area $A$:$$A = \pi \cdot r^2 = \pi \cdot (60)^2 = 3600\pi$$Then, calculate the power in the wind:$$P = \frac{1}{2} \cdot 1.2 \cdot 3600\pi \cdot (10)^3$$$$P = 0.5 \cdot 1.2 \cdot 3600 \cdot \pi \cdot 1000$$$$P = 2160000\pi$$To find the maximum power extractable (using the Betz limit of 59.3%):$$P_{max} = 0.593 \cdot 2160000\pi$$$$P_{max} = 1281676.8$$$$P_{max} \approx 4.02 MW$$Therefore, the maximum power this turbine can extract from the wind is approximately 4.02 MW.

Question 3

Which of the following statements is true?

Accepted Answer

If the same object requires a different amount of force to lift it in two different liquids, it means that the buoyant force acting on the object in the two liquids is different. This can only happen if the densities of the two liquids are different. Therefore, B is the correct statement. A is incorrect because it assumes that the density of the object must be less than both liquids, which is not necessarily true. C and D are both incorrect because the pressure on the mask depends on the depth of the dive, not the direction of looking or the distance from the ocean floor. E is incorrect because the density of a material does not change with pressure.

Question 4

The maximum pressure that can be obtained in your local mechanic's hydraulic pump is 2.0 * 10⁵ Pa.The piston has a mass of 1.8 * 10⁴ Kg and a radius R = 1.0 m,what is the largest mass (of a car)for which the pump will work?

Accepted Answer

The answer of The maximum pressure that can be obtained...

Question 5

A wind turbine is used to extract power from the wind.If the diameter of the turbine is doubled,the maximum power extracted from the wind will increase by a factor of

Accepted Answer

The power extracted from the wind is proportional to the area covered by the turbine blades, which is proportional to the square of the diameter. Therefore, if the diameter is doubled, the area (and thus the maximum power extracted) will increase by a factor of 2^2 = 4. So, the correct answer is (B) 4.

Question 6

A glass is initially filled with 155 cm³ water plus 85 cm³ of ice so that the water level is exactly at the rim of the glass,with some of the ice sticking out above the rim.After all of the ice has melted and turned into water,

Accepted Answer

The total volume of water and ice in the glass is 155 + 85 = 240 cm³, which fills the glass up to the rim. When the ice melts, it turns into water and adds an additional 85 cm³ of water to the glass, bringing the total water level to 240 + 85 = 325 cm³. However, since the glass was already filled up to the rim with 240 cm³ of water, there is no additional space for the extra 85 cm³ of water. Therefore, the water level will remain exactly the same, and no water will flow over. Choice C is the correct answer.

Question 7

A wind turbine is used to extract power from the wind.If the speed of the wind is doubled,the maximum power extracted from the wind will increase by a factor of

Accepted Answer

The power extracted from the wind by a wind turbine is proportional to the cube of the wind speed. Therefore, if the wind speed doubles, the power extracted increases by a factor of $2^3 = 8$.

Question 8

Two pistons exert forces F₁ and F₂ on a fluid at points 1 and 2,producing pressures p₁ and p₂ over areas A₁ and A₂.If the pistons do not move under the influence of these forces,it then follows necessarily that

Accepted Answer

The answer of Two pistons exert forces F₁ and F₂...

Question 9

"16 castaways marooned in the South China Sea!" They construct a 50-kg raft made out of Pulau Tiga wood,which Rudy has determined its specific gravity to be 0.047.If each survivor has a mass 100 kg,what is the maximum number of survivors that can ride the raft without sinking? (Rich says that the density of sea water is 1.03 * 10³ kg/m³.)

Accepted Answer

The answer of "16 castaways marooned in the South China...

Question 10

What is the change in volume of a 1.00-m³ block of granite between the surface of the ocean and a 3.00 km depth? (Information that might be useful: The pressure at this depth is about 300 times atmospheric pressure.Atmospheric pressure is 1.013 * 10⁵ Pa.The bulk modulus of granite is 5.0 * 10¹⁰ Pa.)

Accepted Answer

The answer of What is the change in volume of...

Question 11

An object is completely submerged in oil with specific gravity 0.7.Which statement below is correct?

Accepted Answer

The specific gravity of an object compared to the fluid it is submerged in determines its buoyancy. If the specific gravity of the object is less than that of the fluid (0.7 in this case), the object will naturally tend to float, and a downward force would be needed to keep it submerged.

Question 12

A large wind turbine is used to extract power a maximum power of 3.38 MW from the wind.What is the minimum diameter of the turbine which will meet this power requirement? Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

Accepted Answer

The answer of A large wind turbine is used to...

Question 13

A syringe with a plunger of diameter 1.6 cm is attached to a hypodermic needle with a diameter of 2.5 mm.What minimum force must be applied to the plunger to inject into a vein in which the pressure is 2265.9 Pa?

Accepted Answer

We can use the formula for pressure:
Pressure = Force/Area

The area of the plunger is:
Area = πr^2
Area = π(0.8 cm)^2
Area = 2.01 cm^2

Converting to meters:
Area = 2.01 × 10^-4 m^2

The area of the hypodermic needle is:
Area = πr^2
Area = π(1.25 × 10^-3 m)^2
Area = 4.91 × 10^-6 m^2

The total force required is:
Force = Pressure × Area
Force = 2265.9 Pa × (2.01 × 10^-4 m^2 - 4.91 × 10^-6 m^2)
Force = 0.46 N

Therefore, the minimum force required is 0.46 N, which is choice D.

Question 14

What is the buoyant force on a 1.3 m³ helium balloon in air at standard conditions? The density of air is 1.3 kg/m³.

Accepted Answer

The buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. The volume of the helium balloon is $1.3 \, \text{m}^3$, and the density of air is $1.3 \, \text{kg/m}^3$. The mass of air displaced by the balloon is $1.3 \, \text{m}^3 \times 1.3 \, \text{kg/m}^3 = 1.69 \, \text{kg}$. The weight of this air (and thus the buoyant force) is $1.69 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 16.6 \, \text{N}$.

Question 15

A women's high-heeled shoe has an area of 0.5 cm².Assuming that the woman wearing the shoe has a mass of 52 kg,and that all her weight momentarily rests on one heel,what is the pressure that the heel exerts on the floor?

Accepted Answer

The answer of A women's high-heeled shoe has an area...

Question 16

A particular steel cable used in the construction of a suspension bridge experiences a stress which stretches the cable by 0.3% of its manufactured length.Given that Young's modulus for steel is 2.0 * 10¹¹ Pa,find the value of this stress.

Accepted Answer

The answer of A particular steel cable used in the...

Question 17

The Earth's atmosphere is composed (by volume)of 78.08% nitrogen (N₂),20.95% oxygen (O₂),0.93% argon (Ar),0.25% water vapor (H₂O),and traces of other gases,most importantly,carbon dioxide (CO₂).The CO₂ content of the atmosphere is currently around 0.039%.The average mass of a mole of the atmosphere is 28.96 g and the molar mass of carbon dioxide is 44 g.What is the total mass of CO₂ in the Earth's atmosphere?

Accepted Answer

The answer of The Earth's atmosphere is composed (by volume)of...

Question 18

A 3.3-m long wire with a cross sectional area of 4.7 * 10^-5 m² is stretched 8.3 * 10^-4 m by a force of 234 N.What is Young's modulus for this material?

Accepted Answer

Young's modulus (Y) is calculated using the formula Y = (F/A) / (ΔL/L), where F is the force applied, A is the cross-sectional area, ΔL is the change in length, and L is the original length. Substituting the given values: Y = (234 N / (4.7×10^-5 m^2)) / (8.3×10^-4 m / 3.3 m) = 1.98×10^11 N/m^2.

Question 19

The Earth's atmosphere is composed nitrogen (N₂),oxygen (O₂),argon (Ar),water vapor (H₂O),and traces of other gases.There are 6.74·10¹⁶ kg of argon in earth's atmosphere.The average mass of a mole of the atmosphere is 28.96 g and the molar mass of argon is 40 g.What is the percentage,by volume of argon in the Earth's atmosphere?

Accepted Answer

The answer of The Earth's atmosphere is composed nitrogen (N₂),oxygen...

Question 20

Find the pressure difference (in N/m²)between the inside and outside of a window which looks into a swimming pool 12 m below the surface.(The density of water is 1000 kg/m³.)

Accepted Answer

The pressure difference is calculated using the formula: Pressure = density * gravity * height. Here, it is 1000 kg/m³ * 9.8 m/s² * 12 m = 1.176 * 10⁵ N/m², which is approximately 1.17 * 10⁵ N/m².

Quiz 13: Solids and Fluids

A beach ball of radius 30 cm is pushed under water.What force is required to keep the ball submerged?

A very large wind turbine is used to extract power from the wind.The turbine has a diameter of 120 meters.What is the maximum power this turbine can extract from the wind.Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

Which of the following statements is true?

The maximum pressure that can be obtained in your local mechanic's hydraulic pump is 2.0 * 10⁵ Pa.The piston has a mass of 1.8 * 10⁴ Kg and a radius R = 1.0 m,what is the largest mass (of a car) for which the pump will work?

A wind turbine is used to extract power from the wind.If the diameter of the turbine is doubled,the maximum power extracted from the wind will increase by a factor of

A glass is initially filled with 155 cm³ water plus 85 cm³ of ice so that the water level is exactly at the rim of the glass,with some of the ice sticking out above the rim.After all of the ice has melted and turned into water,

A wind turbine is used to extract power from the wind.If the speed of the wind is doubled,the maximum power extracted from the wind will increase by a factor of

Two pistons exert forces F₁ and F₂ on a fluid at points 1 and 2,producing pressures p₁ and p₂ over areas A₁ and A₂.If the pistons do not move under the influence of these forces,it then follows necessarily that

An object is completely submerged in oil with specific gravity 0.7.Which statement below is correct?

A large wind turbine is used to extract power a maximum power of 3.38 MW from the wind.What is the minimum diameter of the turbine which will meet this power requirement? Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

A syringe with a plunger of diameter 1.6 cm is attached to a hypodermic needle with a diameter of 2.5 mm.What minimum force must be applied to the plunger to inject into a vein in which the pressure is 2265.9 Pa?

What is the buoyant force on a 1.3 m³ helium balloon in air at standard conditions? The density of air is 1.3 kg/m³.

A women's high-heeled shoe has an area of 0.5 cm².Assuming that the woman wearing the shoe has a mass of 52 kg,and that all her weight momentarily rests on one heel,what is the pressure that the heel exerts on the floor?

A particular steel cable used in the construction of a suspension bridge experiences a stress which stretches the cable by 0.3% of its manufactured length.Given that Young's modulus for steel is 2.0 * 10¹¹ Pa,find the value of this stress.

A 3.3-m long wire with a cross sectional area of 4.7 * 10^-5 m² is stretched 8.3 * 10^-4 m by a force of 234 N.What is Young's modulus for this material?

Find the pressure difference (in N/m²) between the inside and outside of a window which looks into a swimming pool 12 m below the surface.(The density of water is 1000 kg/m³.)

Quiz 13: Solids and Fluids

A beach ball of radius 30 cm is pushed under water.What force is required to keep the ball submerged?

A very large wind turbine is used to extract power from the wind.The turbine has a diameter of 120 meters.What is the maximum power this turbine can extract from the wind.Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m3.

Which of the following statements is true?

The maximum pressure that can be obtained in your local mechanic's hydraulic pump is 2.0 * 105 Pa.The piston has a mass of 1.8 * 104 Kg and a radius R = 1.0 m,what is the largest mass (of a car) for which the pump will work?

A wind turbine is used to extract power from the wind.If the diameter of the turbine is doubled,the maximum power extracted from the wind will increase by a factor of

A glass is initially filled with 155 cm3 water plus 85 cm3 of ice so that the water level is exactly at the rim of the glass,with some of the ice sticking out above the rim.After all of the ice has melted and turned into water,

A wind turbine is used to extract power from the wind.If the speed of the wind is doubled,the maximum power extracted from the wind will increase by a factor of

Two pistons exert forces F1 and F2 on a fluid at points 1 and 2,producing pressures p1 and p2 over areas A1 and A2.If the pistons do not move under the influence of these forces,it then follows necessarily that

An object is completely submerged in oil with specific gravity 0.7.Which statement below is correct?

A large wind turbine is used to extract power a maximum power of 3.38 MW from the wind.What is the minimum diameter of the turbine which will meet this power requirement? Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m3.

A syringe with a plunger of diameter 1.6 cm is attached to a hypodermic needle with a diameter of 2.5 mm.What minimum force must be applied to the plunger to inject into a vein in which the pressure is 2265.9 Pa?

What is the buoyant force on a 1.3 m3 helium balloon in air at standard conditions? The density of air is 1.3 kg/m3.

A women's high-heeled shoe has an area of 0.5 cm2.Assuming that the woman wearing the shoe has a mass of 52 kg,and that all her weight momentarily rests on one heel,what is the pressure that the heel exerts on the floor?

A particular steel cable used in the construction of a suspension bridge experiences a stress which stretches the cable by 0.3% of its manufactured length.Given that Young's modulus for steel is 2.0 * 1011 Pa,find the value of this stress.

A 3.3-m long wire with a cross sectional area of 4.7 * 10-5 m2 is stretched 8.3 * 10-4 m by a force of 234 N.What is Young's modulus for this material?

Find the pressure difference (in N/m2) between the inside and outside of a window which looks into a swimming pool 12 m below the surface.(The density of water is 1000 kg/m3.)

A very large wind turbine is used to extract power from the wind.The turbine has a diameter of 120 meters.What is the maximum power this turbine can extract from the wind.Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

The maximum pressure that can be obtained in your local mechanic's hydraulic pump is 2.0 * 10⁵ Pa.The piston has a mass of 1.8 * 10⁴ Kg and a radius R = 1.0 m,what is the largest mass (of a car) for which the pump will work?

A glass is initially filled with 155 cm³ water plus 85 cm³ of ice so that the water level is exactly at the rim of the glass,with some of the ice sticking out above the rim.After all of the ice has melted and turned into water,

Two pistons exert forces F₁ and F₂ on a fluid at points 1 and 2,producing pressures p₁ and p₂ over areas A₁ and A₂.If the pistons do not move under the influence of these forces,it then follows necessarily that

A large wind turbine is used to extract power a maximum power of 3.38 MW from the wind.What is the minimum diameter of the turbine which will meet this power requirement? Assume a wind speed of 10 m/s and the density of air is 1.2 kg/m³.

What is the buoyant force on a 1.3 m³ helium balloon in air at standard conditions? The density of air is 1.3 kg/m³.

A women's high-heeled shoe has an area of 0.5 cm².Assuming that the woman wearing the shoe has a mass of 52 kg,and that all her weight momentarily rests on one heel,what is the pressure that the heel exerts on the floor?

A particular steel cable used in the construction of a suspension bridge experiences a stress which stretches the cable by 0.3% of its manufactured length.Given that Young's modulus for steel is 2.0 * 10¹¹ Pa,find the value of this stress.

A 3.3-m long wire with a cross sectional area of 4.7 * 10^-5 m² is stretched 8.3 * 10^-4 m by a force of 234 N.What is Young's modulus for this material?

Find the pressure difference (in N/m²) between the inside and outside of a window which looks into a swimming pool 12 m below the surface.(The density of water is 1000 kg/m³.)