Question 1

A large cylindrical water tank is mounted on a platform with its central axis vertical. The water level is 3.75 m above the base of the tank, and base is 6.50 m above the ground. A small hole 2.22 mm in diameter has formed in the base of the tank. Both the hole and the top of the tank are open to the air. We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m³. (a) How many cubic meters of water per second is this tank losing? (b) How fast is the water from the hole moving just as it reaches the ground?

Accepted Answer

The answer of A large cylindrical water tank is mounted...

Question 2

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

A)  46 N 
B)  61 N 
C)  76 N 
D)  92 N 
E)  110 N

Question 3

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

A)  0.350 
B)  0.650 
C)  zero 
D)  0.200 
E)  The answer depends on which edge of the board is vertical.

Question 4

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?

Accepted Answer

A)  d/4 
B)  d/2 
C)  d /  
D)  d  
E)  2d

Question 5

Water flows in the horizontal pipe shown in the figure. At point A the area is 25.0 cm2 and the speed of the water is 2.00 m/s. At B the area is 16.0 cm2. The fluid in the manometer is mercury, which has a density of 13,600 kg/m3. We can treat water as an ideal fluid having a density of 1000 kg/m3. What is the manometer reading h?

Accepted Answer

A)  0.546 cm 
B)  1.31 cm 
C)  2.81 cm 
D)  2.16 cm 
E)  3.36 cm

Question 6

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

A)  1500 kg/m3 
B)  1400 kg/m3 
C)  1300 kg/m3 
D)  1200 kg/m3 
E)  1100 kg/m3

Question 7

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 8

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

Accepted Answer

A)  2.0 mL 
B)  2.4 mL 
C)  2.8 mL 
D)  3.2 mL 
E)  3.6 mL

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

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

Question 10

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 36 m/s, what is its speed in this smaller section?

Accepted Answer

A)  49 m/s 
B)  42 m/s 
C)  31 m/s 
D)  27 m/s

Question 11

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

A)  29.1 × 103 kg/m3 
B)  7.26 × 103 kg/m3 
C)  9.25 × 103 kg/m3 
D)  2.31 × 103 kg/m3 
E)  71.2 × 103 kg/m3

Question 12

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 107 N/m2). By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2.

Accepted Answer

A)  2.3 × 10-3 m3 
B)  3.3 × 10-3 m3 
C)  4.3 × 10-3 m3 
D)  5.3 × 10-3 m3 
E)  6.3 × 10-3 m3

Question 13

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

Accepted Answer

A)  1.2 MN/m2 
B)  1.4 MN/m2 
C)  1.6 MN/m2 
D)  1.8 MN/m2 
E)  2.0 MN/m2

Question 14

The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m2. What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

Accepted Answer

A)  64 kN 
B)  9.0 kN 
C)  42 kN 
D)  85 kN 
E)  21 kN

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

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

Question 16

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m3?

Accepted Answer

A)  4.00 kPa 
B)  7.50 kPa 
C)  5.82 kPa 
D)  6.42 kPa 
E)  4.61 kPa

Question 17

A very light 1.00-m wire consists of two segments of equal length, one of steel (Young's modulus is 2.00 × 1011 N/m2) and one of brass (Young's modulus is 9.0 × 1010 N/m2). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight w is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. Find the weight w.

Accepted Answer

A)  190 N 
B)  390 N 
C)  780 N 
D)  1000 N 
E)  3100 N

Question 18

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

A)  2430 N 
B)  3550 N 
C)  4670 N 
D)  10,900 N 
E)  12,100 N

Question 19

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

Accepted Answer

A)  4.98 cm 
B)  1.27 cm 
C)  6.59 cm 
D)  1.56 cm 
E)  7.22 cm

Question 20

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...

Exam 15: Fluids and Elasticity

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?

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?

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 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.

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.

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

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.

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 36 m/s, what is its speed in this smaller section?

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?

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

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 a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

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

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.

Exam 15: Fluids and Elasticity

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?

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?

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 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.

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.

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

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.

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 36 m/s, what is its speed in this smaller section?

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?

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 107 N/m2) . By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2.

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m2. What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

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 a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m3?

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

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 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?

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?

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.

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.

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

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.

At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 10⁷N/m²) . By how much has 1.0 m³ of water been compressed by this pressure? The bulk modulus of water is 2.3 × 10⁹ N/m².

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

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 a section of horizontal pipe with a diameter of 3.00 cm the pressure is 5.21 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.50 cm. What is the pressure in the narrower region if water behaves like an ideal fluid of density 1000 kg/m³?

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