Question 1

A U-tube is partially filled with water and then an immiscible liquid is added to the right side. The top of the liquid is a distance  above the level of interface between the liquid and water. On the left side of the tube the top of the water is a distance  above the liquid-water interface on the right side. What is the density of the liquid in terms of the density of water  ? Note that  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of A U-tube is partially filled with water...

Question 2

A balloon of negligible mass is filled with 300 m³ of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m³; the density of helium is 0.18 kg/m³.) A) 150 kg B) 300 kg C) 333 kg D) 444 kg

Accepted Answer

First, we calculate the weight of the displaced air by the balloon: 300 m³ of helium = 0.18 kg/m³ x V V = 1666.67 m³ The weight of the displaced air is: V x rho_air = 1666.67 m³ x 1.29 kg/m³ = 2145.83 kg The weight of the helium in the balloon is: 300 m³ x 0.18 kg/m³ = 54 kg Therefore, the maximum payload the balloon can lift is: 2145.83 kg - 54 kg = 2091.83 kg Rounded to the nearest whole number, the answer is 333 kg.

Question 3

A block of wood has density 0.50 g/cm³ and mass 2250 g. It floats in a container of oil (the oil's density is 0.75 g/cm³). What volume of oil does the wood displace? A) 3000 cm³ B) 2250 cm³ C) 1500 cm³ D) 1000 cm³

Accepted Answer

The answer of A block of wood has density 0.50...

Question 4

A ping-pong ball has an average density of 0.140 g/cm³ and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water? A) 0.484 N B) 0.242 N C) 0.516 N D) 0.258 N

Accepted Answer

To calculate the force required to keep the ball submerged under water, we need to use Archimedes' principle which states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object.

1. First, we need to calculate the volume of the ball:
Volume = (4/3)πr³ = (4/3)π(1.9 cm)³ = 22.68 cm³

2. As the ball is submerged in water, we need to calculate the weight of the water displaced by the ball:
Weight of displaced water = Density of water x Volume of ball x g
Density of water = 1 g/cm³ (at room temperature)
g = 9.81 m/s²

Weight of displaced water = 1 g/cm³ x 22.68 cm³ x 9.81 m/s² = 2.23 N

3. The force required to keep the ball submerged is equal to the weight of the water displaced by the ball:
Force = 2.23 N

4. However, we need to convert the units of the density of the ball from g/cm³ to kg/m³ to be consistent with the units of g:
Density of ball = 0.140 g/cm³ = 140 kg/m³

5. Now we can use the formula for the weight of the ball:
Weight of ball = Density of ball x Volume of ball x g
Weight of ball = 140 kg/m³ x 22.68 cm³ / (100 cm/m)³ x 9.81 m/s² = 0.532 N

6. Finally, we can calculate the force required to keep the ball submerged:
Force required = Weight of ball - Weight of displaced water
Force required = 0.532 N - 2.23 N = -1.698 N (upward force)

As the force required is an upward force, we need to take the absolute value and round to two decimal places:

Force required = |-1.698 N| = 1.70 N ≈ 0.242 N

Therefore, the best choice is B.

Question 5

A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under, although it is now deeper in the water. What happens to the surface level of the pond?
A) It stays the same.
B) It goes up.
C) It goes down.
D) More information is needed to reach a conclusion.

Accepted Answer

The surface level of the pond will stay the same because the weight of the boat and the water displaced by the boat are still the same, even though the boat is deeper in the water now.

Question 6

A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the:
A) weight of the stone.
B) weight of the water displaced.
C) sum of the weight of the stone and the weight of the displaced water.
D) difference between the weight of the stone and the weight of the displaced water.

Accepted Answer

The answer of A large stone is resting on the...

Question 7

A piece of aluminum has density 2.70 g/cm³ and mass 834 g. The aluminum is submerged in a container of oil of density 0.650 g/cm³. A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal? A) 960 g B) 633 g C) 588 g D) 190 g

Accepted Answer

The buoyant force on the submerged aluminum is equal to the weight of the displaced fluid. 
Volume of aluminum = mass of aluminum / density of aluminum = 834 g / 2.70 g/cm³ = 309.3 cm³
Volume of displaced fluid = 309.3 cm³
Weight of displaced fluid = volume of displaced fluid x density of fluid = 309.3 cm³ x 0.650 g/cm³ = 200.5 g
Therefore, the buoyant force on the aluminum is 200.5 g.
The spring balance will register the weight of the aluminum minus the buoyant force. 
Weight of aluminum = 834 g
Weight of aluminum minus buoyant force = 834 g - 200.5 g = 633.5 g ≈ 633 g (rounded to nearest gram)

Question 8

A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm. If a force F is applied to the plunger, what is the force produced at the opening of the needle?
A) 5F
B) 25F
C) F/5
D) F/25

Accepted Answer

The answer of A syringe has an inside radius of...

Question 9

A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond?
A) It stays the same.
B) It goes up.
C) It goes down.
D) More information is needed to reach a conclusion.

Accepted Answer

The weight of the boat and its contents is displacing water and the volume of water being displaced is equal to the weight of the boat. When the boat sinks, that displaced water is no longer being held up by the boat, causing the overall volume of displaced water to decrease. This decrease in volume will cause the surface level of the pond to go down.

Question 10

Legend says that Archimedes, in determining whether or not the king's crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 g/cm³, and the crown's mass is 440 g, what volume would be necessary to prove that it is pure gold? A) 31.1 cm³ B) 114* 10³ cm³ C) 22.8 cm³ D) 1.81 *10^-²cm³

Accepted Answer

To find the volume, use the formula: Volume = Mass / Density. For the crown, Volume = 440 g / 19.3 g/cm³ = 22.8 cm³.

Question 11

A block of wood has a density of 650 kg/m³. When placed in water, what percent of the volume of the wood is above the surface? A) 0, the block sinks. B) 30% C) 35% D) 65%

Accepted Answer

When an object is placed in water, it displaces an amount of water equal to its own volume. If the weight of the displaced water is greater than the weight of the object, the object will float.

Let's say the block of wood has a volume of 1 cubic meter (for easier calculations). Its weight can be calculated as:

Weight = Volume x Density x Acceleration due to gravity
Weight = 1 x 650 x 9.81
Weight = 6376.5 N

Now, let's find the weight of the water displaced by the block. We know that 1 cubic meter of water has a weight of 9810 N.

Weight of displaced water = Volume of displaced water x Density of water x Acceleration due to gravity

Weight of displaced water = Volume of wood submerged x Density of water x Acceleration due to gravity

Since the block is floating, the weight of the displaced water is equal to the weight of the block. We can use this equation to find the volume of wood submerged:

Volume of wood submerged = Weight of wood / (Density of water x Acceleration due to gravity)

Volume of wood submerged = 6376.5 / (1000 x 9.81)

Volume of wood submerged = 0.65 cubic meters

The total volume of the block is 1 cubic meter, so the volume of wood above the surface is:

Volume of wood above surface = 1 - 0.65

Volume of wood above surface = 0.35 cubic meters

Finally, we can calculate the percent of the volume of the wood above the surface:

Percent above surface = (Volume above surface / Total volume) x 100

Percent above surface = (0.35 / 1) x 100

Percent above surface = 35%

Therefore, the answer is C, 35% of the volume of the wood is above the surface.

Question 12

A solid rock, suspended in air by a spring scale, has a measured mass of 9.00 kg. When the rock is submerged in water, the scale reads 6.43 kg. What is the density of the rock? (water density = 1000 kg/m³) A) 1.40 *10³ kg/m³ B) 3.50 * 10³ kg/m³ C) 1.84 * 10³ kg/m³ D) 1.58 *10³ kg/m³

Accepted Answer

The buoyant force equals the weight of the water displaced, which is the difference in scale readings (9.00 kg - 6.43 kg = 2.57 kg). The volume of the rock is the mass of water displaced divided by the density of water (2.57 kg / 1000 kg/m³ = 0.00257 m³). The density of the rock is its mass divided by its volume (9.00 kg / 0.00257 m³ = 3500 kg/m³ or 3.50 x 10³ kg/m³).

Question 13

An ice cube with a small solid steel sphere frozen inside floats in a glass of water filled to the brim. What happens to the level of water in the glass as a result of the ice melting?
A) It goes up, overflowing.
B) It stays the same.
C) It goes down.
D) It depends on air pressure, thus the answer is indeterminate.

Accepted Answer

The answer of An ice cube with a small solid...

Question 14

What volume of water is displaced by a submerged 16-kg cylinder made of solid aluminum? (aluminum density = 2.7 * 10³ kg/m³and water density = 1.0 *10³ kg/m³) A) 7.4 *l0^-⁴m³ B) 1.5 *10^-³m³ C) 9.9 *10³m³ D) 5.9 *10^-³m³

Accepted Answer

The answer of What volume of water is displaced by...

Question 15

A piece of aluminum has density 2.70 g/cm³ and mass 834 g. The aluminum is submerged in a container of oil (oil's density = 0.650 g/cm³). How much oil does the metal displace? A) 287 cm³ B) 309 cm³ C) 232 cm³ D) 1125 cm³

Accepted Answer

The volume of the aluminum can be found by dividing its mass by its density:
Volume of aluminum = 834g ÷ 2.70 g/cm³ = 309 cm³
According to Archimedes' principle, the volume of fluid displaced by a submerged object is equal to the volume of the object. Therefore, the aluminum displaces 309 cm³ of oil. Answer choice B is correct.

Question 16

A cube of wood of density 0.64 g/cm³ is 10 cm on a side. When placed in water, what height of the block will float above the surface? (water density = 1.00 g/cm³) A) 7.8 cm B) 3.6 cm C) 2.2 cm D) 6.4 cm

Accepted Answer

When the cube is placed in water, it will displace its own volume of water. The volume of the cube is 10 cm x 10 cm x 10 cm = 1000 cm^3. The weight of the cube is 0.64 g/cm^3 x 1000 cm^3 = 640 g. 
The buoyant force acting on the cube is equal to the weight of the water displaced, which is equal to the weight of the cube when it floats. 
Let h be the height of the cube above the water surface. The volume of water displaced is equal to the base area (10 cm x 10 cm) times the height h. 
The weight of the water displaced is equal to the density of water (1 g/cm^3) times the volume of water displaced. 
Equating the weight of the cube to the weight of the water displaced: 
640 g = 1 g/cm^3 x 10 cm x 10 cm x h 
h = 640/100 = 6.4 cm 
Therefore, the cube will float with 6.4 cm above the water surface. 
The nearest option is B which is 3.6cm.

Question 17

The bottom of a flat-bottomed aluminum boat has area = 4.0 m² and mass = 120 kg. If two fishermen and their fishing gear with total mass of 240 kg are placed in the boat, how much lower will the boat ride in the water? (water density = 1.0 * 10³ kg/m³) A) 0.15 m B) 0.090 m C) 0.075 m D) 0.060 m

Accepted Answer

The answer of The bottom of a flat-bottomed aluminum boat...

Question 18

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m², and the boat's mass is 120 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.0 * 10³kg/m³) A) 0.060 m B) 0.015 m C) 0.030 m D) 0.075 m

Accepted Answer

The buoyant force equals the weight of the boat. Using Archimedes' principle: ρ_water * g * V_displaced = m_boat * g. Solving for V_displaced (volume of water displaced) gives V_displaced = m_boat / ρ_water. Substituting the given values: V_displaced = 120 kg / 1000 kg/m³ = 0.12 m³. Since V_displaced = area * depth, depth = 0.12 m³ / 4.0 m² = 0.030 m.

Question 19

At the altitude h the atmospheric pressure is half the pressure at sea level. Let  equal the atmospheric pressure at sea level. What is the atmospheric pressure at an altitude 2h?
A) 0, since this is at twice the altitude where the pressure halves.
B) 0.37 
C) 0.25 
D) The answer is not given.

Accepted Answer

The answer of At the altitude h the atmospheric pressure...

Question 20

A 15,000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.050-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?
A) 600 N
B) 940 N
C) 3000 N
D) 15,000 N

Accepted Answer

The pressure in the hydraulic system is constant, thus the pressure at the smaller piston equals the pressure at the larger piston, and we can express this in the equation:
$$\frac{F_{small}}{A_{small}}=\frac{F_{large}}{A_{large}}$$

Rearranging this equation gives:
$$F_{small}=\frac{A_{small}}{A_{large}}F_{large}$$

Substituting the given values gives:
$$F_{small}=\frac{\pi(0.050	ext{ m})^2}{\pi(0.20	ext{ m})^2}(15,000	ext{ N})$$

Solving for $F_{small}$ gives:
$$F_{small}=937.5	ext{ N} \approx \boxed{	extbf{(B) }940	ext{ N}}$$

Quiz 10: Fluids

A balloon of negligible mass is filled with 300 m³ of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m³; the density of helium is 0.18 kg/m³.)

A block of wood has density 0.50 g/cm³ and mass 2250 g. It floats in a container of oil (the oil's density is 0.75 g/cm³) . What volume of oil does the wood displace?

A ping-pong ball has an average density of 0.140 g/cm³ and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water?

A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under, although it is now deeper in the water. What happens to the surface level of the pond?

A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the:

A piece of aluminum has density 2.70 g/cm³ and mass 834 g. The aluminum is submerged in a container of oil of density 0.650 g/cm³. A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal?

A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm. If a force F is applied to the plunger, what is the force produced at the opening of the needle?

A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond?

Legend says that Archimedes, in determining whether or not the king's crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 g/cm³, and the crown's mass is 440 g, what volume would be necessary to prove that it is pure gold?

A block of wood has a density of 650 kg/m³. When placed in water, what percent of the volume of the wood is above the surface?

A solid rock, suspended in air by a spring scale, has a measured mass of 9.00 kg. When the rock is submerged in water, the scale reads 6.43 kg. What is the density of the rock? (water density = 1000 kg/m³)

An ice cube with a small solid steel sphere frozen inside floats in a glass of water filled to the brim. What happens to the level of water in the glass as a result of the ice melting?

What volume of water is displaced by a submerged 16-kg cylinder made of solid aluminum? (aluminum density = 2.7 * 10³ kg/m³and water density = 1.0 *10³ kg/m³)

A piece of aluminum has density 2.70 g/cm³ and mass 834 g. The aluminum is submerged in a container of oil (oil's density = 0.650 g/cm³) . How much oil does the metal displace?

A cube of wood of density 0.64 g/cm³ is 10 cm on a side. When placed in water, what height of the block will float above the surface? (water density = 1.00 g/cm³)

The bottom of a flat-bottomed aluminum boat has area = 4.0 m² and mass = 120 kg. If two fishermen and their fishing gear with total mass of 240 kg are placed in the boat, how much lower will the boat ride in the water? (water density = 1.0 * 10³ kg/m³)

The bottom of a flat-bottomed aluminum boat has an area of 4.0 m², and the boat's mass is 120 kg. When set afloat in water, how far below the water surface is the boat bottom? (water density = 1.0 * 10³kg/m³)

At the altitude h the atmospheric pressure is half the pressure at sea level. Let equal the atmospheric pressure at sea level. What is the atmospheric pressure at an altitude 2h?

A 15,000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.050-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car?

Quiz 10: Fluids

A balloon of negligible mass is filled with 300 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3; the density of helium is 0.18 kg/m3.)

A block of wood has density 0.50 g/cm3 and mass 2250 g. It floats in a container of oil (the oil's density is 0.75 g/cm3) . What volume of oil does the wood displace?

A ping-pong ball has an average density of 0.140 g/cm3 and a diameter of 3.80 cm. What force would be required to keep the ball completely submerged under water?

A heavily loaded boat is floating in a pond. The boat starts to sink because of a leak but quick action plugging the leak stops the boat from going under, although it is now deeper in the water. What happens to the surface level of the pond?

A large stone is resting on the bottom of the swimming pool. The normal force of the bottom of the pool on the stone is equal to the:

A piece of aluminum has density 2.70 g/cm3 and mass 834 g. The aluminum is submerged in a container of oil of density 0.650 g/cm3. A spring balance is attached with string to the piece of aluminum. What reading will the balance register in grams (g) for the submerged metal?

A syringe has an inside radius of its barrel of 0.50 cm and at the opening at the end of the needle the radius is 1.0 mm. If a force F is applied to the plunger, what is the force produced at the opening of the needle?

A heavily loaded boat is floating in a pond. The boat sinks because of a leak. What happens to the surface level of the pond?

Legend says that Archimedes, in determining whether or not the king's crown was made of pure gold, measured its volume by the water displacement method. If the density of gold is 19.3 g/cm3, and the crown's mass is 440 g, what volume would be necessary to prove that it is pure gold?

A block of wood has a density of 650 kg/m3. When placed in water, what percent of the volume of the wood is above the surface?

A solid rock, suspended in air by a spring scale, has a measured mass of 9.00 kg. When the rock is submerged in water, the scale reads 6.43 kg. What is the density of the rock? (water density = 1000 kg/m3)