Question 1

The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N.
(a) Determine the force that must be applied to the small piston.
(b) Determine the pressure applied to the fluid in the lift.

Accepted Answer

The answer of The small piston of a hydraulic lift...

Question 2

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What net force does the water exert on the lower face of the cylinder?

Accepted Answer

The volume of the cylinder is given by: 
V = πr²h = π((0.620/2)²)(1.20) = 0.904 m³ 
The weight of the cylinder is given by: 
W = mg = ρVg = (1.00 × 10¹³ kg/m³)(9.81 m/s²)(0.904 m³) = 8.82 × 10³ N 
The buoyant force on the cylinder is given by: 
FB = ρVg' = (1.00 × 10¹³ kg/m³)(9.81 m/s²)(0.620/2)² = 712 N 
The net force on the cylinder is given by: 
Fnet = FB - W - P*A = 1120 N downward, where P is the pressure acting on the lower face of the cylinder and A is its area. 
Solving for P, we get: 
P = (FB - W - Fnet)/A = (712 N - 8.82 × 10³ N - 1120 N)/(π(0.620/2)²) = 3.65 × 10¹³ Pa 
The net force that the water exerts on the lower face of the cylinder is given by: 
Fwater = P*A = 4.14 × 10¹⁴ Pa * π(0.620/2)² = 2.61 × 10⁴ N ≈ 4.14 × 10¹⁴ N ≈ 4.14 × 10¹⁴ N (rounded to two significant figures)

Question 3

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

The answer of On planet X, the absolute pressure at...

Question 4

A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

Accepted Answer

The answer of A wooden raft has a mass of...

Question 5

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m³?

Accepted Answer

The answer of A barge is 15.0 m wide and...

Question 6

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What is the weight of the cylinder?

Accepted Answer

The answer of A circular cylinder of height 1.20 m...

Question 7

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 answer of A cubical box, 5.00 cm on each...

Question 8

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/m³, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

Accepted Answer

When the sphere is immersed in the liquid, the buoyant force acting on it is equal to the weight of the liquid displaced by the sphere. The tension in the cord is equal to the weight of the sphere minus the buoyant force. Therefore, the density of the liquid can be calculated as follows:$$density_{liquid} = \frac{weight_{sphere} - tension}{volume_{sphere}}$$$$density_{liquid} = \frac{(6.1 kg)(9.8 m/s^2) - 26 N}{(\frac{4}{3}\pi)(0.1 m)^3}$$$$density_{liquid} = 1500 kg/m^3$$

Question 9

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

Accepted Answer

For the steel ball to barely float, its average density must equal the density of water. The volume of the ball is calculated using the formula for the volume of a sphere, $V = \frac{4}{3}\pi r^3$, where $r$ is the radius of the ball. The mass of the ball can be found by multiplying its volume by the density of steel. To find the thickness of the wall, we consider the volume of steel used, which is the difference between the volume of the outer sphere and the volume of the inner sphere (empty space). By setting the mass of the steel equal to the mass of the water displaced (using the principle of buoyancy), and solving for the thickness, we find that the correct thickness is 6.6 cm.

Question 10

A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock?

Accepted Answer

The answer of A rock is suspended from a scale...

Question 11

A 7.8-kg solid sphere, made of metal whose density is 2500 kg/m³, is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³), what is the tension in the cord?

Accepted Answer

The buoyant force on the sphere is equal to the weight of the water displaced by the sphere. The volume of the sphere is:$$V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi \left(\frac{7.8	ext{ kg}}{2500	ext{ kg/m}^3}ight)^3 = 4.19	imes10^{-3}	ext{ m}^3$$The weight of the water displaced by the sphere is:$$F_b = ho_w g V = (1000	ext{ kg/m}^3)(9.81	ext{ m/s}^2)(4.19	imes10^{-3}	ext{ m}^3) = 41.1	ext{ N}$$The tension in the cord is equal to the weight of the sphere minus the buoyant force:$$T = W - F_b = (7.8	ext{ kg})(9.81	ext{ m/s}^2) - 41.1	ext{ N} = 46.1	ext{ N}$$

Question 12

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Accepted Answer

The answer of The two water reservoirs shown in the...

Question 13

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

Accepted Answer

To solve the problem, we need to compare the weight of the board to the weight of the water it displaces. The weight of the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of the board, density is its density, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of the board can be found using the formula: 
volume = width x thickness x length 
Plugging in the given values, we get: 
volume = 20.0 cm x 5.00 cm x 3.00 m = 3000 cm^3 = 0.003 m^3

The weight of the board is then: 
weight = 0.003 m^3 x 350 kg/m^3 x 9.81 m/s^2 = 10.3 N

The weight of the water displaced by the board can be found using the formula: 
weight = volume x density x gravity 
where volume is the volume of water displaced by the board, density is the density of water, and gravity is the acceleration due to gravity (9.81 m/s^2).

The volume of water displaced by the board is equal to the volume of the submerged part of the board. Let h be the height of the submerged part of the board. Then: 
volume of water = width x h x length 
Plugging in the given values, we get: 
volume of water = 20.0 cm x h x 3.00 m = 0.6 h m^3

The weight of the water displaced by the board is then: 
weight of water = 0.6 h m^3 x 1000 kg/m^3 x 9.81 m/s^2 = 5886 h N

Since the board is floating partially submerged, the weight of the board is equal to the weight of the water displaced by the submerged part of the board. Thus, we have: 
10.3 N = 5886 h N 
Solving for h, we get: 
h = 0.00175 m

Therefore, the fraction of the volume of the board above the surface of the water is: 
fraction = (width x thickness x length - width x h x length) / (width x thickness x length) 
Plugging in the given values, we get: 
fraction = (20.0 cm x 5.00 cm x 3.00 m - 20.0 cm x 0.00175 m x 3.00 m) / (20.0 cm x 5.00 cm x 3.00 m) = 0.65

So, the answer is (B) 0.650.

Question 14

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 each tire supports 1/4 of the weight of the car:
W = mg = (1.20 × 10^3 kg)(9.8 m/s^2) = 1.18 × 10^4 N
Each tire supports W/4 = 2.95 × 10^3 N.
The area of contact of each tire with the road is given as 1.00 × 10^2 cm^2 = 0.01 m^2.
The pressure in each tire can be calculated using the formula P = F/A, where F is the force (2.95 × 10^3 N) and A is the area (0.01 m^2):
P = F/A = (2.95 × 10^3 N)/(0.01 m^2) = 2.95 × 10^5 Pa
This is the absolute pressure, so we need to subtract atmospheric pressure to find the gauge pressure:
P_gauge = P - 1 atm = 2.95 × 10^5 Pa - 1.01 × 10^5 Pa = 1.94 × 10^5 Pa
Converting to scientific notation, we get:
P_gauge = 1.94 × 10^5 Pa = 1.94 × 10^(5-5) Pa = 1.94 × 10^2 kPa = 1.94 × 10^2 × 10^3 Pa = 1.94 × 10^5 Pa
Therefore, the correct answer is C: 2.94 × 10^5 Pa, which is closest to the calculated value of 1.94 × 10^5 Pa.

Question 15

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

Accepted Answer

The answer of A person who weighs 550 N empties...

Question 16

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? (For purposes of this problem, you can neglect the weight of the pistons.)

Accepted Answer

The answer of A 12,000-N car is raised using a...

Question 17

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m³ and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.)

Accepted Answer

First, we need to find the pressure in the system. Since the pistons are at the same level initially, the pressure at the bottom of both sides of the U-tube is atmospheric pressure, 1.013x10^5 N/m^2. Since the oil is incompressible, the pressure at any point in the oil must be the same on both sides of the U-tube. Using Pascal's Law, this means that the pressure at the piston on the larger arm of the U-tube is the same as the pressure at the bottom of the smaller arm.

The pressure at the bottom of the smaller arm can be found using the equation:

P = ρgh

where P is pressure, ρ is density, g is acceleration due to gravity, and h is the height of the oil column above the piston in the smaller arm.

The height of the oil column can be found using the fact that the volume of oil in the U-tube is constant. This means that the product of the area and height of the oil column on each side of the U-tube is the same. Letting h1 and h2 be the heights of the oil column in the larger and smaller arms respectively, we have:

A1h1 = A2h2

where A1 is the area of the larger piston and A2 is the area of the smaller piston. Rearranging this equation, we get:

h2 = (A1/A2)h1

Plugging in the values given, we get:

h2 = (π(0.18^2)/(π(0.05^2))) x 1.20 m = 25.92 m

Now we can use the equation for pressure to find the pressure at the bottom of the smaller arm:

P = ρgh = (800 kg/m^3)(9.81 m/s^2)(25.92 m) = 2.01x10^5 N/m^2

This is the pressure that must be exerted on the oil in the smaller arm in order to lift the car. We can find the force needed to create this pressure using the equation:

F = PA

where F is the force needed, P is the pressure, and A is the area of the smaller piston. Plugging in the values given, we get:

F = (2.01x10^5 N/m^2)(π(0.05^2)) = 1.96 kN

Therefore, the best choice is C.

Question 18

In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 x 10⁴ Pa? The density of the oil is 510 kg/m³.

Accepted Answer

The answer of In the figure, an open tank contains...

Question 19

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Accepted Answer

The answer of The two water reservoirs shown in the...

Question 20

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 As shown in the figure, a container...

Quiz 15: Fluids and Elasticity

The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m³?

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?

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/m³, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock?

A 7.8-kg solid sphere, made of metal whose density is 2500 kg/m³, is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³) , what is the tension in the cord?

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

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.)

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 x 10⁴ Pa? The density of the oil is 510 kg/m³.

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Quiz 15: Fluids and Elasticity

The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m3) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m3?

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?

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/m3, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm3 and that of water is 1000 kg/m3.

A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m3) is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock?

A 7.8-kg solid sphere, made of metal whose density is 2500 kg/m3, is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m3) , what is the tension in the cord?

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible oil with a density of 820 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m3. The board is floating partially submerged in water of density 1000 kg/m3. What fraction of the volume of the board is above the surface of the water?

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.)

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m3) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m3) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 x 104 Pa? The density of the oil is 510 kg/m3.

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m3. The manometer contains incompressible mercury with a density of 13,600 kg/m3. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m³) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?

A barge is 15.0 m wide and 75.0 m long and has vertical sides. The bottom of the hull is 1.20 m below the water surface. What is the weight of the barge and its cargo, if it is floating in fresh water of density 1000 kg/m³?

A 6.1-kg solid sphere, made of metal whose density is 2600 kg/m³, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

A hollow steel ball of diameter 3.0 m barely floats in water. What is the thickness of the wall of the ball? The density of iron is 7.87 g/cm³ and that of water is 1000 kg/m³.

A rock is suspended from a scale reads 20.0 N. A beaker of water (having a density of 1000 kg/m³) is raised up so the rock is totally submerged in the water. The scale now reads 12.5 N. What is the density of the rock?

A 7.8-kg solid sphere, made of metal whose density is 2500 kg/m³, is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³) , what is the tension in the cord?

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density 350 kg/m³. The board is floating partially submerged in water of density 1000 kg/m³. What fraction of the volume of the board is above the surface of the water?

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.)

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 x 10⁴ Pa? The density of the oil is 510 kg/m³.

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?