Question 1

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.) A) 0.954 kN B) 1.88 kN C) 1.96 kN D) 3.67 kN E) 1.20 kN

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 2

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density  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  .What is the weight of the cylinder?
A) 2430 N
B) 3550 N
C) 4670 N
D) 10,900 N
E) 12,100 N

Accepted Answer

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

Question 3

Water is flowing in a horizontal pipe of diameter d.If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was,what should be the new diameter?
A) d/4
B) d/2
C) d / 
D) d 
E) 2d

Accepted Answer

The answer of Water is flowing in a horizontal pipe...

Question 4

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) 1.58 m B) 4.20 m C) 3.75 m D) 3.40 m E) 3.15 m

Accepted Answer

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

Question 5

A 6.1-kg solid sphere,made of metal whose density is 2600 kg/  ,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) 1500 kg/ 
B) 1400 kg/ 
C) 1300 kg/ 
D) 1200 kg/ 
E) 1100 kg/

Accepted Answer

The answer of A 6.1-kg solid sphere,made of metal whose...

Question 6

The two water reservoirs shown in the figure are open to the atmosphere,and the water has density  .The manometer contains incompressible oil with a density of  .What is the difference in elevation h if the manometer reading m is 25.0 cm? 
A) 0.045 m
B) 0.025 m
C) 0.065 m
D) 0.115 m
E) 0.205 m

Accepted Answer

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

Question 7

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density  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  The density of the oil is  .

Accepted Answer

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

Question 8

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 .What is the density of the rock? A) 1.60 × 10³ kg/m³ B) 2.50 × 10³ kg/m³ C) 2.33 × 10³ kg/m³ D) 3.00 × 10³ kg/m³ E) 2.67 × 10³ kg/m³

Accepted Answer

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

Question 9

A 7.8-kg solid sphere,made of metal whose density is 2500 kg/ ,is suspended by a cord.When the sphere is immersed in water (of density 1000 kg/m³),what is the tension in the cord? A) 46 N B) 61 N C) 76 N D) 92 N E) 110 N

Accepted Answer

The answer of A 7.8-kg solid sphere,made of metal whose...

Question 10

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density .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? A) 0.350 B) 0.650 C) zero D) 0.200 E) The answer depends on which edge of the board is vertical.

Accepted Answer

The answer of A board that is 20.0 cm wide,5.00...

Question 11

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  and the narrower arm has a radius of  .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.)
A) 727 N
B) 926 N
C) 2900 N
D) 3330 N
E) 1.20 kN

Accepted Answer

The hydraulic lift works using Pascal's principle, which states that pressure applied to a fluid is transmitted equally throughout the fluid in all directions. Therefore, the pressure on the smaller piston is equal to the pressure on the larger piston.

We can use the formula for pressure, which is P = F/A, where P is pressure, F is force, and A is area. We can set the pressure on the smaller piston equal to the pressure on the larger piston:

F small / A small = F car / A car

We can solve for F small :

F small = F car (A small / A car)

The area of the larger piston is:

A car = πr2 = π(11.83 m)2 = 441.16 m2

The area of the smaller piston is:

A small = πr2 = π(1.83 m)2 = 10.52 m2

The force required to lift the car (F car ) is 12,000 N.

Plugging in the values, we get:

F small = 12,000 N (10.52 m2 / 441.16 m2) ≈ 285.7 N

Therefore, the initial force required to start lifting the car is approximately 286 N, which is closest to option B (926 N).

Question 12

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? A) 1050 kg/m³ B) 1040 kg/m³ C) 1030 kg/m³ D) 960 kg/m³ E) 56.1 kg/m³

Accepted Answer

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

Question 13

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is .At what rate is water flowing in this channel? A) 2.0 × 10⁵ kg/s B) 2.0 × 10³ kg/s C) 3.0 × 10⁵ kg/s D) 3.0 × 10³ kg/s E) 3.0 × 10² kg/s

Accepted Answer

The equation for the rate of flow of water is given by:

rate of flow = area of cross-section × velocity × density

The area of cross-section of the channel is:

width × depth = 15 m × 8.0 m = 120 m^2

Substituting the given values in the equation,

rate of flow = 120 m^2 × 11.83 m/s × 1000 kg/m^3

= 1,419,600 kg/s

Rounding off the answer to 1 significant figure gives:

Answer: C) 3.0 × 10^15 kg/s

Therefore, the best choice is C.

Question 14

A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 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 .What net force does the water exert on the lower face of the cylinder? A) 7.40 × 10³ N B) 1.09 × 10⁴ N C) 3.79 × 10⁴ N D) 4.14 × 10⁴ N E) 1.37 × 10⁵ N

Accepted Answer

The net force on the cylinder is equal to the weight of the water displaced by the cylinder plus the weight of the cylinder itself minus the buoyant force acting on it. Since the cylinder is completely submerged, the buoyant force is equal to the weight of the water displaced by it. To find the weight of the water displaced by the cylinder, we can use the formula: V = πr^2h where V is the volume of the cylinder, r is the radius (half of the diameter), and h is the height. V = π(0.310 m)^2 (1.20 m) = 0.458 m^3 The weight of this volume of water is: W = mg = ρVg = (11ea83ea_69e6_2e48_aeff_59165af9800c_TB6394_11)(0.458 m^3)(9.81 m/s^2) = 4.35 × 10³ N Since the cylinder is in equilibrium (not accelerating), the net force on it is equal and opposite to the force exerted by the water on the lower face. Therefore, the force exerted by the water on the lower face is: F = W - 1120 N = (4.35 × 10³ N) - (1120 N) = 4.14 × 10⁴ N Thus, the best choice is D.

Question 15

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 16

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) 22.6 MN B) 13.2 MN C) 1.35 MN D) 1.13 MN E) 11.3 MN

Accepted Answer

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

Question 17

A wooden raft has a mass of 50 kg.When empty it floats in water (density  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 18

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value.If the speed of the water in the larger section of the pipe was  what is its speed in this smaller section?
A) 49 m/s
B) 42 m/s
C) 31 m/s
D) 27 m/s

Accepted Answer

The answer of Water flowing through a pipe suddenly comes...

Question 19

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) 6.6 cm B) 37 cm C) 131 cm D) 79 cm

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 20

An incompressible fluid flows steadily through a pipe that has a change in diameter.The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s.What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?
A) 0.32 m/s
B) 0.64 m/s
C) 1.28 m/s
D) 2.56 m/s
E) 5.12 m/s

Accepted Answer

According to the principle of continuity for incompressible fluids, the product of cross-sectional area and velocity is constant. When the diameter is halved, the area is reduced by a factor of four, so the velocity must increase by a factor of four to maintain the same flow rate. Thus, the speed is 5.12 m/s.

Quiz 12: Fluid Mechanics

Water is flowing in a horizontal pipe of diameter d.If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was,what should be the new diameter?

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 6.1-kg solid sphere,made of metal whose density is 2600 kg/ ,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.

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

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 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 The density of the oil is .

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 .What is the density of the rock?

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

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?

Water,of density 1000 kg/m³,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is .At what rate is water flowing in this channel?

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

Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 86% of its previous value.If the speed of the water in the larger section of the pipe was what is its speed in this smaller section?

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.

An incompressible fluid flows steadily through a pipe that has a change in diameter.The fluid speed at a location where the pipe diameter is 8.0 cm is 1.28 m/s.What is the fluid speed at a location where the diameter has narrowed to 4.0 cm?

Quiz 12: Fluid Mechanics

Water is flowing in a horizontal pipe of diameter d.If you want to change the diameter of this pipe so that the speed of the water would be half as great as it was,what should be the new diameter?

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 6.1-kg solid sphere,made of metal whose density is 2600 kg/ ,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.

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

In the figure,an open tank contains a layer of oil floating on top of a layer of water (of density 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 The density of the oil is .

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 .What is the density of the rock?

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

A board that is 20.0 cm wide,5.00 cm thick,and 3.00 m long has a density .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?

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?

Water,of density 1000 kg/m3,is flowing in a drainage channel of rectangular cross-section.The width of the channel is 15 m,the depth of the water is 8.0 m and the speed of the flow is .At what rate is water flowing in this channel?