Question 1

Bernoulli's principle: You are driving a late model convertible car at the 65 mph speed limit with its soft flexible roof closed up and the windows closed. You observe that the roof

Accepted Answer

Bernoulli's principle states that as the speed of a fluid increases, the pressure exerted by the fluid decreases. As the car moves forward, the air flowing over the top of the roof is moving faster than the air flowing underneath the roof. This creates a lower pressure above the roof than below it, causing the roof to bow outward.

Question 2

Pressure in a fluid: On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 10⁵ N/m². At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 10⁵ N/m². The density of liquid nitrogen is 808 kg/m³. (a) What is the atmospheric pressure on planet X? (b) What is the acceleration due to gravity on planet X?

Accepted Answer

(a) 3.00 × 10⁵ N/m² (b) 124 m/s²

Question 3

Pressure in a fluid: Fluid fills the container shown in the figure. At which of the indicated points is the pressure greatest?

Accepted Answer

E

Question 4

Pressure in a fluid: At a certain depth in the ocean, the absolute pressure is p. If you go to twice that depth (treating the water as incompressible)

Accepted Answer

The absolute pressure at a depth in a fluid is given by the sum of atmospheric pressure and the pressure due to the fluid column above. At twice the depth, the pressure due to the fluid column doubles, but the atmospheric pressure remains constant, so the absolute pressure is less than 2p.

Question 5

Pressure: One of the dangers of tornados and hurricanes is the rapid drop in air pressure that is associated with such storms. Assume that the air pressure inside of a sealed house is 1.02 atm when a hurricane hits. The hurricane rapidly decreases the external air pressure to 0.910 atm. A square window in an outside wall of the house measures 2.02 m on each side. What net force (directed outwards) is exerted on this window? (1 atm = 1.01 × 10⁵ Pa.)

Accepted Answer

The net force on the window is the difference between the force due to the internal air pressure and the force due to the external air pressure. The force due to the internal air pressure is:$$F_i = P_i A = (1.02 	imes 1.01 	imes 10^5 	ext{ Pa})(2.02 	ext{ m})^2 = 4.12 	imes 10^5 	ext{ N}$$The force due to the external air pressure is:$$F_e = P_e A = (0.910 	imes 1.01 	imes 10^5 	ext{ Pa})(2.02 	ext{ m})^2 = 3.69 	imes 10^5 	ext{ N}$$The net force on the window is:$$F_{net} = F_i - F_e = 4.12 	imes 10^5 	ext{ N} - 3.69 	imes 10^5 	ext{ N} = 4.53 	imes 10^4 	ext{ N}$$

Question 6

Buoyancy: A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub?

Accepted Answer

The overall volume of the wood in the tub has not changed, so the water level will remain the same. The displaced water volume from the first piece of wood is already filling the space that the second piece of wood will occupy when placed in the water.

Question 7

Density: What is the radius of a sphere that has a density of 5000 kg/m³ and a mass of 6.00 kg?

Accepted Answer

The answer of Density: What is the radius of a...

Question 8

Flow rate: Water flows through a pipe having a varying width. More water flows per second through the wide section than through the narrow section because there is more room for it to flow.

Accepted Answer

The flow rate (volume of water flowing per second) remains constant throughout the pipe regardless of changes in width; what changes is the velocity of the water, which is faster in narrower sections to maintain the constant flow rate.

Question 9

Pressure in a fluid: As shown in the figure, a container has a vertical tube, whose inner radius is 32.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube-level A being 5.0 cm higher than level B. The liquid supports a 20.0-cm high column of oil, between levels B and C, whose density is 460 kg/m³. What is the density of the unknown liquid?

Accepted Answer

The answer of Pressure in a fluid: As shown in...

Question 10

Density: A certain coin has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

Accepted Answer

First, we need to find the volume of the coin. Using the diameter and thickness given, we can find the volume of the coin using the formula for the volume of a cylinder:

V = πr^2h

where r is the radius (half the diameter) and h is the thickness.

r = 21.21/2 = 10.605 mm = 0.010605 m

h = 1.95 mm = 0.00195 m

V = π(0.010605)^2(0.00195) = 2.08 × 10^-7 m^3

Next, we can find the density of the coin using the formula:

ρ = m/V

where ρ is density and m is mass.

m = 0.04905 N / 9.81 m/s^2 = 0.005 kg

ρ = 0.005 kg / 2.08 × 10^-7 m^3 = 7.26 × 10^4 kg/m^3

Therefore, the answer is B.

Question 11

Pressure in a fluid: A cubical box, 5.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 594 Pa and the gauge pressure on the bottom surface is 1133 Pa. What is the density of the fluid?

Accepted Answer

The difference in gauge pressure between the top and bottom surfaces is due to the weight of the fluid column above the box. The pressure difference is 1133 Pa - 594 Pa = 539 Pa. The height of the box is 0.05 m. Using the formula for pressure difference, ΔP = ρgh, where ρ is the fluid density, g is the acceleration due to gravity (9.81 m/s²), and h is the height, we solve for ρ: ρ = ΔP / (gh) = 539 / (9.81 * 0.05) ≈ 1100 kg/m³.

Question 12

Density: A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m³. (a) What is the mass of the sphere? (b) What is the average density of this sphere?

Accepted Answer

The answer of Density: A sphere is constructed of two...

Question 13

Buoyancy: Salt water is more dense than fresh water. A ship floats in both fresh water and salt water. Compared to the fresh water, the volume of salt water displaced by the ship is

Accepted Answer

Since salt water is denser than fresh water, a ship will displace less volume of salt water to float because it needs to displace an amount of water equal to its weight, not its volume.

Question 14

Bernoulli's principle: When you blow some air above the upper face of a paper strip, the paper rises. This occurs because

Accepted Answer

Bernoulli's principle states that as the velocity of a fluid (in this case, air) increases, the pressure it exerts decreases. Therefore, when you blow air over the top of a paper strip, the air moves faster over the top surface than the bottom, resulting in a lower pressure above the paper than below. This pressure differential causes the paper to rise. Choice B correctly describes these principles.

Question 15

Buoyancy: A 50-cm³ block of wood is floating partially submerged in water, and a 50-cm³ block of iron is totally submerged in water. Which block has the greater buoyant force on it?

Accepted Answer

The buoyant force on an object is equal to the weight of the fluid displaced by the object. Since both blocks have the same volume, and the iron block is completely submerged, it displaces more water than the partially submerged wood block. Therefore, the iron block experiences a greater buoyant force.

Question 16

Buoyancy: A rock is under water in a shallow lake. As the rock sinks deeper and deeper into water, the buoyant force on it

Accepted Answer

The buoyant force on an object submerged in a fluid depends on the volume of the fluid displaced by the object, not on the depth at which the object is submerged. Since the volume of the rock and the density of water remain constant, the buoyant force remains constant as the rock sinks deeper.

Question 17

Bernoulli's principle: As the speed of a moving fluid increases, the pressure in the fluid

Accepted Answer

Bernoulli's principle states that as the speed of a fluid increases, the pressure within the fluid decreases. This is because an increase in speed causes a decrease in fluid density, which in turn leads to a decrease in pressure. Therefore, choice C is correct.

Question 18

Pressure in a fluid: The weight of a car of mass 1.20 × 10³ kg is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 10² cm²? (1 atm = 1.01 × 10⁵ Pa.)

Accepted Answer

The weight of the car is evenly distributed among the four tires, so the weight supported by each tire is:
W = (1.20 × 10^3 kg) * 9.81 m/s^2 / 4 = 2.94 × 10^3 N
The area of contact of each tire with the road is given as 1.00 × 10^-2 m^2 = 1.00 × 10^2 cm^2.
Let P be the gauge pressure in the tires. The force on each tire is given by the product of pressure and area, so we have:
F = P * A = P * 1.00 × 10^2 N
Setting the force equal to the weight supported by each tire gives:
P * 1.00 × 10^2 N = 2.94 × 10^3 N
P = 2.94 × 10^3 N / (1.00 × 10^2 N/cm^2) = 2.94 × 10^3 Pa
Converting to atm using the conversion factor given:
P = 2.94 × 10^3 Pa / (1.01 × 10^5 Pa/atm) = 2.91 × 10^-2 atm
Therefore, the gauge pressure in the tires required to support the car is:
P = 1 atm + 2.91 × 10^-2 atm = 1.0291 atm
Converting back to Pa gives:
P = 1.0291 atm * 1.01 × 10^5 Pa/atm = 1.04 × 10^5 Pa
Rounding to two significant figures gives:
P = 2.94 × 10^15 Pa, which corresponds to answer choice C.

Question 19

Buoyancy: A cup of water containing an ice cube at 0°C is filled to the brim. The tip of the ice cube sticks out of the surface. As the ice melts, you observe that

Accepted Answer

The displacement of water by the ice cube is equal to the mass of the ice cube, and when the ice melts, it will still have the same mass. Therefore, the water level will remain the same.

Question 20

Buoyancy: If you double the pressure on the surface of a can of water, the buoyant force on a stone placed in that water will

Accepted Answer

Buoyant force depends only on the density of the fluid and the volume of the displaced fluid, not on the pressure at the surface of the fluid. Therefore, doubling the pressure on the surface of the can of water will not change the buoyant force on the stone in the water.

Quiz 12: Fluid Mechanics