Buoyancy and Archimedes' Principle

21 questions

All types21 Multiple choice12 Numeric3 Ordering6

Four identical airtight containers, each with a total volume of $1 \text{ m}^3$ , are placed in different situations. Arrange these situations in order from the GREATEST buoyant force acting on the container to the LEAST buoyant force.

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Answer

The correct order from greatest to least buoyant force is: fully submerged in saltwater, fully submerged in freshwater, half-submerged in freshwater, and sitting on dry land.

Buoyant force is determined by the weight of the displaced fluid. A fully submerged object in saltwater displaces the heaviest amount of fluid. A fully submerged object in freshwater displaces slightly less weight because freshwater is less dense. A half-submerged object displaces only half the volume of water, yielding an even smaller force. An object on dry land displaces no water, experiencing zero buoyant force.

Step-by-Step Solution

Recall Archimedes' Principle.

The buoyant force is equal to the weight of the displaced fluid (

F_b = \text{fluid density} \times \text{volume displaced} \times \text{gravity}

This formula identifies the two main variables that affect buoyant force: the density of the fluid and the volume of fluid displaced.

Compare the volume of fluid displaced in each scenario.

Both completely submerged scenarios displace the full

1 \text{ m}^3

volume. The half-submerged floating scenario displaces

0.5 \text{ m}^3

. The dry land scenario displaces

0 \text{ m}^3

Volume displaced is the primary factor in determining the magnitude of buoyant force.

Compare the fluid densities for the fully submerged scenarios.

Saltwater has a higher density than standard freshwater. Therefore,

1 \text{ m}^3

of saltwater weighs more than

1 \text{ m}^3

of freshwater.

When displaced volumes are equal, the fluid with the higher density exerts a greater buoyant force.

Order the scenarios based on the weight of the displaced fluid.

Submerged in Saltwater > Submerged in Freshwater > Half-submerged in Freshwater > Dry land.

This sequence correctly ranks the situations from greatest to least buoyant force.

Key Concept

According to Archimedes' Principle, buoyant force is directly proportional to both the volume of fluid displaced and the density of that fluid.

Question 2Question →

A solid metal sphere is suspended from a digital spring scale and lowered completely into four different storage tanks, each containing a different liquid. The true weight of the sphere in the air remains constant.

The liquids and their approximate densities are:
- Gasoline: $0.75 \text{ g/cm}^3$
- Glycerin: $1.26 \text{ g/cm}^3$
- Freshwater: $1.00 \text{ g/cm}^3$
- Ocean water: $1.03 \text{ g/cm}^3$

Arrange the liquids in order based on the apparent weight shown on the spring scale when the sphere is completely submerged, from the GREATEST apparent weight to the LEAST apparent weight.

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Answer

Gasoline, Freshwater, Ocean water, Glycerin

The correct order follows the fluid densities from lowest to highest. A fluid with a lower density displaces less mass for a given volume, exerting a smaller upward buoyant force. Because Apparent Weight = True Weight - Buoyant Force, the smallest buoyant force results in the largest apparent weight. Therefore, gasoline (lowest density) yields the greatest apparent weight, and glycerin (highest density) yields the least apparent weight.

Step-by-Step Solution

Identify the relationship between true weight, apparent weight, and buoyant force.

Apparent Weight = True Weight - Buoyant Force

A submerged object experiences an upward buoyant force that opposes gravity, reducing the measured weight on the scale.

Determine how the buoyant force relates to the different liquids.

Buoyant Force is directly proportional to the density of the liquid.

According to Archimedes' principle, buoyant force equals the weight of the displaced fluid. Since the same sphere is completely submerged every time, the displaced volume is constant, making buoyant force depend entirely on fluid density.

Correlate fluid density with apparent weight.

Lower fluid density produces a smaller buoyant force, resulting in a greater apparent weight.

Since apparent weight is calculated by subtracting the buoyant force from the constant true weight, subtracting a smaller value leaves a larger apparent weight.

Order the liquids from lowest density to highest density.

Gasoline (0.75), Freshwater (1.00), Ocean water (1.03), Glycerin (1.26).

This sequence represents the progression from the smallest buoyant force (greatest apparent weight) to the largest buoyant force (least apparent weight).

Key Concept

The apparent weight of a submerged object is its true weight minus the buoyant force. For a constant volume, a lower density fluid exerts a smaller buoyant force, resulting in a greater apparent weight.

Estimated Time:1m 0s

Question 3Question →

A maintenance barge is floating in a closed canal lock filled with water. The barge carries a heavy load of solid steel beams. If the crew unloads the steel beams directly into the water, causing them to sink to the bottom of the lock, what happens to the overall water level in the lock, and why?

The water level rises, because the submerged steel now displaces a volume of water equal to its heavy weight.

The water level remains the same, because the total mass of the barge, steel, and water in the lock system has not changed.

The water level falls, because the sunken steel displaces less water than it did when its weight was supported by the floating barge.

The water level rises, because the steel beams displace more water when resting on the bottom than when sitting on the barge.

Show answer & explanation

Answer: The water level falls, because the sunken steel displaces less water than it did when its weight was supported by the floating barge.

Answer

The water level falls, because the sunken steel displaces less water than it did when its weight was supported by the floating barge.

When the steel beams are on the barge, they must displace a volume of water equal to their weight in order to float. Because steel is denser than water, this displaced volume of water is larger than the actual physical volume of the steel beams. When the beams are thrown overboard and sink, they only displace a volume of water equal to their own physical volume. Since they are now displacing a smaller volume of water than before, the overall water level in the lock falls.

Step-by-Step Solution

Determine the volume of water displaced by the steel beams when they are floating on the barge.

The steel beams are part of a floating system, so they displace a weight of water equal to their own weight.

According to Archimedes' principle, a floating object displaces a volume of fluid whose weight equals the object's weight. The displaced volume is

V_{floating} = \frac{W_{steel}}{d_{water}}

where

d

is density.

Determine the volume of water displaced by the steel beams when they sink to the bottom of the lock.

The steel beams are completely submerged, so they displace a volume of water equal to their own geometric volume.

A completely submerged object displaces a volume of fluid exactly equal to its own volume, so

V_{submerged} = V_{steel}

Compare the two displaced volumes.

Since steel is denser than water (

d_{steel} > d_{water}

), the volume of the steel itself is much less than the volume of water that has the same weight. Therefore,

V_{submerged} < V_{floating}

Density is mass divided by volume. For a given mass (or weight), a material with a higher density occupies a smaller geometric volume.

Determine the effect on the overall water level in the lock.

Because the total volume of water displaced by the system decreases when the steel is dropped to the bottom, the overall water level falls.

The water level in a closed system depends directly on the total volume of water being displaced by objects in the water.

Key Concept

Flotation equilibrium vs. Submerged volume

Question 4Question →

A solid machine part is suspended from a spring scale. In the air, the scale reads $60 \text{ N}$ . When the part is completely submerged in water, the scale reads $40 \text{ N}$ . The part is then removed, dried, and completely submerged in a vat of unknown oil, where the scale reads $45 \text{ N}$ . Based on these readings, what is the density of the oil compared to the density of water?

0.75 times the density of water

1.33 times the density of water

0.25 times the density of water

1.13 times the density of water

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Answer: 0.75 times the density of water

Answer

The oil is 0.75 times the density of water.

According to Archimedes' principle, buoyant force equals the weight of the displaced fluid (

F_b = \rho \cdot V \cdot g

). The buoyant force in water is

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

. The buoyant force in the oil is

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

. Because the part is fully submerged in both instances, the displaced volume (

V

) is identical. Therefore, the buoyant forces are directly proportional to the fluid densities. The ratio of the oil's density to the water's density is the ratio of their buoyant forces:

15 \text{ N} / 20 \text{ N} = 0.75

Step-by-Step Solution

Calculate the buoyant force exerted by the water.

60 \text{ N} - 40 \text{ N} = 20 \text{ N}

The buoyant force is equal to the object's true weight in air minus its apparent weight when submerged.

Calculate the buoyant force exerted by the oil.

60 \text{ N} - 45 \text{ N} = 15 \text{ N}

To compare the lifting effect of the two fluids, we need to know the specific buoyant force each exerts on the identical volume.

Calculate the ratio of the oil's density to the water's density.

15 \text{ N} / 20 \text{ N} = 0.75

Because the same object is completely submerged in both fluids, the displaced volume is constant. Therefore, the buoyant forces are directly proportional to the densities of the fluids.

Key Concept

Apparent weight and Archimedes' Principle

Question 5Question →

A marine engineering lab is evaluating four solid wooden cubes of identical dimensions for a flotation device. The cubes are set adrift in a freshwater basin (density = $1.00 \text{ g/cm}^3$ ) and allowed to reach floating equilibrium. Based on the material densities provided, arrange the wood types in order of the percentage of their volume that remains ABOVE the water line, starting from the SMALLEST percentage exposed and ending with the LARGEST percentage exposed.

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Answer

The correct order from smallest to largest percentage above water is: Oak wood, Teak wood, Pine wood, and Balsa wood.

The fraction of a floating object submerged is equal to its density divided by the fluid's density. Because fresh water has a density of

1.00 \text{ g/cm}^3

, a wood block's submerged percentage directly matches its density value as a percentage. The Oak block (

0.75 \text{ g/cm}^3

) is

75\%

submerged, leaving the smallest amount (

25\%

) exposed above water. Conversely, the Balsa block (

0.20 \text{ g/cm}^3

) is only

20\%

submerged, leaving the largest amount (

80\%

) exposed.

Step-by-Step Solution

Determine the relationship between material density and submerged volume for a floating object.

For a floating object, the fraction of its volume that is submerged is equal to the ratio of the object's density to the fluid's density (

V_{sub}/V_{total} = \rho_{obj}/\rho_{fluid}

This relationship is derived directly from Archimedes' principle, where the upward buoyant force equals the downward weight of the floating object.

Calculate the percentage of volume submerged for each type of wood.

Since the water density is

1.00 \text{ g/cm}^3

, the submerged fraction is simply the wood's density divided by 1. Oak is

75\%

submerged, Teak is

65\%

submerged, Pine is

40\%

submerged, and Balsa is

20\%

submerged.

This establishes exactly how much of each block is sitting below the water level.

Calculate the percentage of volume above water (exposed) for each type of wood.

The exposed percentage is calculated as

100\% - \text{submerged percentage}

. Oak =

25\%

, Teak =

35\%

, Pine =

60\%

, Balsa =

80\%

The question specifically asks for the percentage that remains ABOVE the water surface, requiring an inversion of the submerged values.

Arrange the wood types from smallest to largest exposed percentage.

Smallest to largest exposed percentage: Oak (

25\%

), Teak (

35\%

), Pine (

60\%

), Balsa (

80\%

This directly answers the prompt's final ordering requirement.

Key Concept

For an object floating in equilibrium, the fraction of its volume that is submerged equals the ratio of its density to the fluid's density. A higher density object will sit lower in the fluid, exposing less of its volume above the surface.

Question 6Question →

Two solid metal blocks, one made of aluminum and one made of lead, have the exact same size and shape. Both blocks are completely submerged in a tank of freshwater. Which of the following statements about the upward buoyant force acting on the blocks is true?

The buoyant force is the same for both blocks because they displace the same volume of water.

The buoyant force is greater on the lead block because it has a greater mass.

The buoyant force is greater on the aluminum block because it has less mass.

The buoyant force acting on each block is exactly equal to its respective weight.

Show answer & explanation

Answer: The buoyant force is the same for both blocks because they displace the same volume of water.

Answer

The buoyant force is the same for both blocks because they displace the same volume of water.

According to Archimedes' Principle, buoyant force is determined entirely by the weight of the displaced fluid. Since both blocks have the exact same physical dimensions and are completely submerged in the same fluid, they displace the exact same volume of water. Therefore, they experience the exact same upward buoyant force, regardless of their individual weights or material compositions.

Step-by-Step Solution

Recall Archimedes' Principle.

The upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces.

This is the fundamental rule governing buoyancy.

Determine the displaced volume for each block.

Since both blocks have the exact same physical dimensions (size and shape) and are both completely submerged, they displace the exact same volume of water.

Displaced volume depends solely on the submerged volume of the object.

Compare the resulting buoyant forces.

Because they displace the same volume of the same fluid, the weight of the displaced fluid is identical for both blocks. Therefore, they experience the exact same buoyant force.

Buoyant force is independent of the object's mass, density, or weight, as long as the displaced volume is the same.

Key Concept

Archimedes' Principle (Volume vs. Mass)

Question 7Question →

An overflow container is filled to the brim with a specialized drilling mud that weighs $15 \text{ N}$ per liter. A solid geological core sample weighing $75 \text{ N}$ in the air is completely submerged in the mud, causing exactly $2$ liters of mud to spill into a measuring basin. Based on Archimedes' principle, what is the apparent weight of the core sample while it is fully suspended in the mud?

45 \text{ N}

30 \text{ N}

60 \text{ N}

105 \text{ N}

Show answer & explanation

Answer: $45 \text{ N}$

Answer

The apparent weight of the core sample is

45 \text{ N}

Archimedes' principle dictates that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Because the core sample displaces

2

liters of mud (which weighs

15 \text{ N}

per liter), the upward buoyant force is

30 \text{ N}

. The apparent weight is the actual downward weight (

75 \text{ N}

) minus this upward buoyant force (

30 \text{ N}

), resulting in a net apparent weight of

45 \text{ N}

Step-by-Step Solution

Calculate the weight of the displaced drilling mud.

2 \text{ liters} \times 15 \text{ N/liter} = 30 \text{ N}

According to Archimedes' principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces.

Calculate the apparent weight of the submerged core sample.

75 \text{ N} - 30 \text{ N} = 45 \text{ N}

The apparent weight is determined by subtracting the upward buoyant force from the actual downward weight of the object.

Key Concept

Apparent weight and Archimedes' principle

Question 8Question →

A small metal anchor weighs $120 \text{ N}$ in the air. When the anchor is completely submerged in water, the tension on its lifting cable is measured to be $85 \text{ N}$ . What is the magnitude of the buoyant force acting on the submerged anchor?

Show answer & explanation

Answer: 35

Answer

According to Archimedes' principle, the upward buoyant force exerted on a submerged object reduces its apparent weight. The buoyant force is equal to the difference between its true weight in the air and its apparent weight in the fluid. Subtracting the apparent weight (85 N) from the true weight (120 N) gives a buoyant force of 35 N.

Step-by-Step Solution

Identify the actual weight and the apparent weight.

Actual weight = 120 N, Apparent weight = 85 N

These values represent the downward force of gravity and the net downward force when submerged, respectively.

Calculate the buoyant force.

120 N - 85 N = 35 N

The buoyant force is the upward force that accounts for the reduction in weight. It is found by subtracting the apparent weight from the actual weight.

Key Concept

Apparent Weight and Buoyant Force

Question 9Question →

A deep-sea recovery team locates a lost concrete mooring block resting on the ocean floor. The solid concrete block has a physical volume of $2 \text{ m}^3$ and a total downward weight of $45,000 \text{ N}$ . The surrounding seawater has a weight density of $10,000 \text{ N/m}^3$ . According to Archimedes' principle, what is the magnitude of the upward buoyant force acting on the completely submerged block?

45,000 \text{ N}

20,000 \text{ N}

25,000 \text{ N}

65,000 \text{ N}

Show answer & explanation

Answer: $20,000 \text{ N}$

Answer

The correct answer is

20,000 \text{ N}

, which is found by multiplying the block's volume by the weight density of the seawater.

According to Archimedes' Principle, the buoyant force exerted on an object is exactly equal to the weight of the fluid that the object displaces. Because the block is completely submerged, it displaces a volume of water equal to its own volume (

2 \text{ m}^3

). Multiplying this volume by the water's weight density (

10,000 \text{ N/m}^3

) yields an upward buoyant force of

20,000 \text{ N}

. The actual weight of the concrete block is irrelevant to calculating the buoyant force.

Step-by-Step Solution

Identify the formula for buoyant force based on Archimedes' Principle.

Buoyant Force = Volume of displaced fluid × Weight density of the fluid.

To establish that buoyancy depends exclusively on fluid properties and displaced volume, rather than the object's own weight.

Extract the necessary physical values from the problem description.

The displaced volume is equal to the block's volume (

2 \text{ m}^3

), and the fluid's weight density is

10,000 \text{ N/m}^3

To separate the relevant variables needed for the calculation from the distractor information (the block's

45,000 \text{ N}

weight).

Calculate the magnitude of the upward buoyant force.

2 \text{ m}^3 \times 10,000 \text{ N/m}^3 = 20,000 \text{ N}

To determine the final upward thrust exerted by the seawater.

Key Concept

Archimedes' Principle states that the buoyant force on a completely submerged object equals the weight of the fluid it displaces, independent of the object's own downward weight.

Question 10Question →

Four different objects are completely submerged in a tank of fresh water. The mass of each object and the volume of water it displaces are recorded below. Arrange the objects in order of the buoyant force exerted on them by the water, from LEAST buoyant force to GREATEST buoyant force.

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Answer

The correct sequence from least to greatest buoyant force is: Iron weight, Lead brick, Aluminum gear, Wooden block.

According to Archimedes' principle, the buoyant force acting on an object is equal to the weight of the fluid it displaces. Because all the objects are in the same fresh water, the buoyant force is directly proportional to the displaced volume. By ordering the displaced volumes from smallest to largest (

0.2 \text{ L}

0.5 \text{ L}

1.0 \text{ L}

2.0 \text{ L}

), we accurately order the buoyant forces from least to greatest.

Step-by-Step Solution

Recall the definition of Archimedes' principle.

The buoyant force acting on a submerged object is equal to the weight of the fluid that the object displaces.

This principle establishes that when objects are submerged in the same fluid, the buoyant force depends entirely on the volume of fluid displaced, not the mass of the objects themselves.

Extract the relevant data for each object.

Iron =

0.2 \text{ L}

, Lead =

0.5 \text{ L}

, Aluminum =

1.0 \text{ L}

, Wood =

2.0 \text{ L}

The mass values provided (

0.5 \text{ kg}

3.0 \text{ kg}

) are distractor information and should be ignored for calculating buoyant force.

Rank the objects based on their displaced volumes from least to greatest.

Iron (

0.2 \text{ L}

) < Lead (

0.5 \text{ L}

) < Aluminum (

1.0 \text{ L}

) < Wood (

2.0 \text{ L}

Since greater displaced volume equals greater buoyant force, this is the final correct order.

Key Concept

According to Archimedes' Principle, the buoyant force on a submerged object depends only on the density of the fluid and the volume of the fluid displaced, completely independent of the object's mass or weight.

Estimated Time:45s

Question 11Question →

A solid steel engine block with a true weight of $2,000 \text{ N}$ is completely submerged in a freshwater lake. The block displaces a volume of water that weighs $250 \text{ N}$ . According to Archimedes' principle, what is the magnitude of the upward buoyant force acting on the engine block?

2,000 \text{ N}

1,750 \text{ N}

2,250 \text{ N}

250 \text{ N}

Show answer & explanation

Answer: $250 \text{ N}$

Answer

250 \text{ N}

According to Archimedes' principle, the upward buoyant force on an object submerged in a fluid is exactly equal to the weight of the fluid it displaces. Since the engine block displaces water weighing

250 \text{ N}

, the buoyant force acting upon it is exactly

250 \text{ N}

Step-by-Step Solution

Identify the values provided in the scenario.

The true weight of the block is

2,000 \text{ N}

and the weight of the displaced water is

250 \text{ N}

Extracting given values clarifies which numbers represent which physical properties.

Apply Archimedes' principle to determine the buoyant force.

Archimedes' principle states that the upward buoyant force is equal to the weight of the displaced fluid.

This principle directly links the volume of fluid displaced to the upward force exerted by the fluid.

Select the value that represents the weight of the displaced fluid.

The weight of the displaced water is

250 \text{ N}

, therefore the buoyant force is

250 \text{ N}

The object's own weight does not determine the buoyant force; only the displaced fluid's weight matters.

Key Concept

Archimedes' Principle and Buoyant Force

Question 12Question →

A marine salvage team is recovering two solid objects resting on the ocean floor: a 100-pound lead weight and a 100-pound concrete block. Lead has a significantly higher density than concrete. While both objects are completely submerged, which of the following statements is correct regarding the buoyant forces acting on them?

Both objects experience the same buoyant force because they have identical weights.

The concrete block experiences a greater buoyant force because it displaces a larger volume of water.

The lead weight experiences a greater buoyant force because its higher density creates a stronger downward reaction.

The lead weight experiences a greater buoyant force because its concentrated mass exerts more pressure on the water.

Show answer & explanation

Answer: The concrete block experiences a greater buoyant force because it displaces a larger volume of water.

Answer

The concrete block experiences a greater buoyant force because it displaces a larger volume of water.

According to Archimedes' Principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces. Because both objects weigh 100 pounds but concrete is less dense than lead, the concrete block must take up more space (larger volume). When completely submerged, the larger volume of the concrete block displaces a larger volume of water, resulting in a significantly greater upward buoyant force compared to the smaller, denser lead weight.

Step-by-Step Solution

Analyze the relationship between weight, density, and volume for both objects.

Both weigh 100 pounds, but lead is denser than concrete. Therefore, the 100-pound concrete block must have a larger physical volume than the 100-pound lead weight.

Density is mass per unit volume. For objects of equal mass, the less dense material takes up more space.

Apply Archimedes' Principle to completely submerged objects.

The buoyant force is equal to the weight of the displaced fluid. The volume of displaced fluid equals the volume of the submerged object.

Archimedes' Principle states that an object fully or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid that it displaces.

Compare the displaced fluid volumes and resulting buoyant forces.

Because the concrete block has a larger volume, it displaces more water than the lead weight. Consequently, the concrete block experiences a greater upward buoyant force.

Greater displaced volume directly results in a proportionally greater buoyant force, regardless of the object's interior weight.

Key Concept

Buoyancy and Archimedes' Principle

Question 13Question →

A rigid, sealed cylindrical pontoon is pushed completely underwater in a testing pool, where it displaces $200 \text{ liters}$ of water. The empty pontoon weighs $400 \text{ N}$ . A technician then pulls the pontoon out, places $150 \text{ N}$ of solid lead weights inside it, seals it, and forces it completely back under the water. Which of the following best describes the change in the upward buoyant force acting on the completely submerged pontoon?

It remains exactly the same because the exterior volume of the pontoon displacing the water has not changed.

It increases by

150 \text{ N}

to directly counteract the additional weight of the lead inside.

It decreases because the overall density of the pontoon assembly has become significantly greater.

It increases due to the heavier pontoon creating a stronger downward force, which produces a larger upward reaction from the water.

Show answer & explanation

Answer: It remains exactly the same because the exterior volume of the pontoon displacing the water has not changed.

Answer

The upward buoyant force remains exactly the same because the rigid exterior volume displacing the water does not change.

Archimedes' principle states that the buoyant force on a completely submerged object is equal to the weight of the fluid it displaces. Because the pontoon is rigid, its exterior volume does not change when lead weights are added inside. Since it displaces the exact same volume of water when forced completely underwater in both scenarios, the upward buoyant force acting on it remains perfectly constant, regardless of its increased internal weight.

Step-by-Step Solution

Identify the factors that determine buoyant force according to Archimedes' Principle.

Buoyant force depends only on the density of the fluid and the volume of the fluid displaced by the object (

F_b = \rho \cdot V \cdot g

This establishes the fundamental physics rule needed to solve the problem.

Analyze what changes between the first and second scenario.

The total weight of the pontoon increases from

400 \text{ N}

550 \text{ N}

To see if any variables in the buoyant force equation have been affected.

Determine if the volume of displaced fluid changes.

Because the pontoon is rigid, its exterior dimensions do not expand or shrink. Since it is completely submerged in both cases, the displaced volume remains exactly

200 \text{ liters}

To calculate the final impact on the buoyant force.

Evaluate the final state of the buoyant force.

Since both the fluid (water) and the displaced volume (

200 \text{ liters}

) remain constant, the buoyant force remains identical.

To arrive at the final conceptual conclusion.

Key Concept

Archimedes' Principle states that buoyant force is equal to the weight of the fluid displaced, meaning it depends on the object's volume, not its mass.

Question 14Question →

Four solid machine parts are completely submerged in a deep vat of hydraulic fluid. Their respective masses and physical volumes are listed below. Arrange the machine parts in order from the LEAST buoyant force experienced to the GREATEST buoyant force experienced.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from least to greatest buoyant force is based entirely on the objects' volumes: Machine Part 3, Machine Part 1, Machine Part 4, and Machine Part 2.

Archimedes' Principle states that the buoyant force on an object equals the weight of the fluid it displaces. Because all the machine parts are entirely submerged in the exact same hydraulic fluid, the buoyant force is determined exclusively by their physical volumes. Therefore, ordering them from least to greatest buoyant force simply requires ordering them from smallest to largest volume:

4 \text{ L}

6 \text{ L}

8 \text{ L}

, and

12 \text{ L}

Step-by-Step Solution

Identify the relevant variable for determining buoyant force on fully submerged objects.

Buoyant force depends solely on the volume of displaced fluid, not the mass of the object.

According to Archimedes' Principle, the buoyant force equals the weight of the displaced fluid. Since all parts are submerged in the same fluid, displaced volume is the only variable.

Compare the volumes of all four machine parts.

The volumes are: Part 3 (

4 \text{ L}

), Part 1 (

6 \text{ L}

), Part 4 (

8 \text{ L}

), and Part 2 (

12 \text{ L}

Extracting the volume metric from each item allows for direct comparison.

Arrange the parts in ascending order based on their volume.

The correct order is Part 3, Part 1, Part 4, Part 2.

A smaller physical volume displaces less fluid, resulting in a proportionally smaller upward buoyant force.

Key Concept

For fully submerged objects, the buoyant force is directly proportional to the object's volume (which dictates the volume of fluid displaced), completely independent of the object's mass.

Question 15Question →

A technician drops two completely sealed metal canisters into a large vat of testing fluid. Canister A is completely hollow. Canister B has the exact same exterior dimensions and shape as Canister A, but is filled completely with solid lead weights. Both canisters are pushed down and held completely stationary underwater. Which of the following statements is true regarding the upward buoyant force acting on the canisters?

The buoyant forces acting on both canisters are exactly equal because they displace the same volume of fluid.

The buoyant force on Canister B is greater because its higher mass interacts more strongly with the surrounding fluid.

The buoyant force on Canister A is greater because its lower weight provides less resistance to the upward push of the fluid.

Canister B experiences no buoyant force because its total weight overcomes the lifting capacity of the fluid.

Show answer & explanation

Answer: The buoyant forces acting on both canisters are exactly equal because they displace the same volume of fluid.

Answer

The buoyant forces acting on both canisters are exactly equal because they displace the same volume of fluid.

According to Archimedes' principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Since both canisters are perfectly sealed, completely submerged, and have identical exterior dimensions, they displace the exact same volume of testing fluid. Therefore, the fluid exerts the exact same upward force on both, despite the fact that Canister B is much heavier.

Step-by-Step Solution

Identify the physics principle governing the situation.

Archimedes' principle states that the upward buoyant force is equal to the weight of the fluid displaced by the object.

To determine what variables influence buoyant force.

Determine the factors that affect the volume of fluid displaced.

The displaced volume depends strictly on the exterior dimensions of the completely submerged object.

The formula for buoyant force is

F_B = \rho \cdot V \cdot g

, where

V

is the displaced volume.

Compare the exterior volumes of Canister A and Canister B.

The problem states both canisters have the exact same exterior dimensions and shape, meaning they displace the exact same volume of fluid.

To establish the relationship between the two displaced volumes.

Evaluate the buoyant force based on the displaced volumes.

Because the displaced volumes are equal, the upward buoyant forces exerted by the fluid must also be equal, regardless of the internal mass.

To reach the final conclusion regarding the buoyant forces.

Key Concept

Buoyancy and Archimedes' Principle

Question 16Question →

A salvage crane is lifting a solid brass propeller from the bottom of a freshwater lake. The propeller has a true weight of $1,200 \text{ N}$ in the air. When it is completely submerged in the water, it displaces $35 \text{ liters}$ of water.

If $1 \text{ liter}$ of water weighs exactly $10 \text{ N}$ , what is the apparent weight of the propeller, in Newtons, while it is still completely underwater?

Show answer & explanation

Answer: 850

Answer

850

The propeller experiences an upward buoyant force equal to the weight of the water it displaces. Since it displaces

35 \text{ liters}

and each liter weighs

10 \text{ N}

, the buoyant force is

350 \text{ N}

. The apparent weight is the true weight (

1,200 \text{ N}

) minus this buoyant force (

350 \text{ N}

), resulting in

850 \text{ N}

Step-by-Step Solution

Calculate the weight of the displaced water to find the buoyant force.

Buoyant force =

350 \text{ N}

According to Archimedes' Principle, the buoyant force on an object is equal to the weight of the fluid it displaces. Here,

35 \text{ liters} \times 10 \text{ N/liter} = 350 \text{ N}

Subtract the buoyant force from the true weight to find the apparent weight.

Apparent weight =

850 \text{ N}

The apparent weight of a submerged object is its actual weight in air minus the upward buoyant force exerted by the fluid (

1,200 \text{ N} - 350 \text{ N} = 850 \text{ N}

Key Concept

Archimedes' principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object. The apparent weight of a submerged object is its true weight minus the buoyant force.

Estimated Time:1m 0s

Question 17Question →

A heavy steel transport barge leaves the salty water of an ocean bay and enters a freshwater river. The total weight of the barge and its cargo remains exactly the same. Given that saltwater has a significantly higher density than freshwater, how will the depth that the barge sinks into the water (its draft) change, and why?

It will sink deeper into the water, because it must displace a larger volume of the less-dense freshwater to equal its own weight.

Its draft will remain exactly the same, because the required buoyant force depends entirely on the barge's total weight, which has not changed.

It will float higher in the water, because the lighter freshwater pushes upward against the hull with a greater pressure.

It will sink deeper into the water, because the lack of salt in the river water causes the barge's overall mass to increase.

Show answer & explanation

Answer: It will sink deeper into the water, because it must displace a larger volume of the less-dense freshwater to equal its own weight.

Answer

The barge will sink deeper into the water because it must displace a larger volume of the less-dense freshwater to equal its own weight.

According to Archimedes' principle, a floating object displaces a weight of fluid equal to its own true weight. Because the barge's weight is constant, it must displace the exact same *weight* of water in both locations to stay afloat. Since freshwater is less dense (weighs less per unit of volume) than saltwater, a larger physical *volume* of freshwater must be displaced to equal the barge's massive weight. To displace more volume, the barge must sink deeper into the water, increasing its draft.

Step-by-Step Solution

Identify the conditions for a floating object.

A floating object is in equilibrium, meaning the upward buoyant force (

F_b

) must exactly equal the object's downward true weight (

W

This is the fundamental principle of flotation derived from Archimedes' principle.

Relate the buoyant force to fluid density and displaced volume.

Buoyant force equals the weight of the displaced fluid, expressed as

F_b = \rho \times V \times g

, where

\rho

is fluid density,

V

is displaced volume, and

g

is gravity.

This formula shows how fluid properties generate the upward force.

Apply the relationship to the barge moving from saltwater to freshwater.

Since

F_b

must remain constant (because the barge's weight is constant), and the fluid density (

\rho

) decreases in freshwater, the displaced volume (

V

) must increase to compensate.

Displacing a larger volume of water means the hull of the barge must sink deeper (increasing its draft).

Key Concept

Buoyancy and floating equilibrium (Archimedes' Principle)

Estimated Time:1m 0s

Question 18Question →

During a hydro-engineering project, a completely sealed hollow steel sphere is used as an underwater sensor housing. The sphere has an external volume of $2.5 \text{ m}^3$ and a dry weight of $35,000 \text{ N}$ in the air. When completely submerged in a testing pool where the water's weight density is $10,000 \text{ N/m}^3$ , what is the net downward force (apparent weight) of the housing in Newtons?

Show answer & explanation

Answer: 10000

Answer

10000

The net downward force, or apparent weight, is found by subtracting the upward buoyant force from the object's true dry weight. Since the object displaces

2.5 \text{ m}^3

of water with a weight density of

10,000 \text{ N/m}^3

, the buoyant force is

25,000 \text{ N}

. Subtracting this upward force from the

35,000 \text{ N}

downward dry weight leaves a net downward force of

10,000 \text{ N}

Step-by-Step Solution

Calculate the buoyant force acting on the submerged housing.

25,000 N

According to Archimedes' principle, the buoyant force equals the weight of the fluid displaced by the object's external volume (

2.5 \text{ m}^3 \times 10,000 \text{ N/m}^3 = 25,000 \text{ N}

Calculate the apparent weight (net downward force).

10,000 N

The apparent weight is the actual weight in air minus the upward buoyant force (

35,000 \text{ N} - 25,000 \text{ N} = 10,000 \text{ N}

Key Concept

Archimedes' Principle and Apparent Weight

Question 19Question →

Two solid machine components, Component X and Component Y, have the exact same volume but are cast from different metals. Component X weighs $15 \text{ N}$ in air, and Component Y weighs $45 \text{ N}$ in air.

Both components are separately lowered into identical displacement tanks filled to the brim with water. When Component X is completely submerged, exactly $5 \text{ N}$ of water spills out of the tank. When Component Y is completely submerged, what is the weight of the water that spills out?

5 \text{ N}

15 \text{ N}

40 \text{ N}

45 \text{ N}

Show answer & explanation

Answer: $5 \text{ N}$

Answer

The weight of the water that spills out is

5 \text{ N}

The correct answer is

5 \text{ N}

. When an object is fully submerged in a fluid, it displaces a volume of fluid equal to its own volume. According to Archimedes' Principle, the buoyant force acting on the object is equal to the weight of this displaced fluid. Because Component Y has the exact same volume as Component X, it must displace the exact same amount of water, meaning the weight of the overflowing water remains

5 \text{ N}

. The object's weight in air does not affect how much fluid it displaces once it is completely submerged.

Step-by-Step Solution

Identify the relationship between the two components.

Both Component X and Component Y share the exact same volume, despite having different weights in air.

The physical volume of an object dictates how much fluid it can displace when fully submerged.

Apply Archimedes' principle of displacement.

Because both components have identical volumes, completely submerging either one will displace the exact same volume of water.

A fully submerged object always displaces a volume of fluid equal to its own total volume, regardless of its density or mass.

Determine the weight of the displaced water for Component Y.

Since Component X displaced

5 \text{ N}

of water, Component Y must also displace

5 \text{ N}

of water.

Equal volumes of the same fluid (water) will naturally have the same weight.

Key Concept

Buoyancy and Archimedes' Principle

Estimated Time:1m 0s

Question 20Question →

A naval submarine uses internal ballast tanks to take in or pump out seawater, allowing it to change its overall weight while its total external volume remains exactly the same. Arrange the following operational states of the submarine in order of the submarine's OVERALL AVERAGE DENSITY, from LEAST dense to MOST dense.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from least dense to most dense is: Floating on the surface, followed by Hovering motionless, and finally Resting on the ocean floor.

Density directly dictates buoyancy states. An object with a density lower than seawater will float on the surface. An object with a density equal to seawater will hover neutrally. An object with a density greater than seawater will sink to the bottom. Therefore, the order from least to most dense is: floating, hovering, sinking.

Step-by-Step Solution

Analyze the condition required for an object to float.

The state of 'Floating on the surface' represents the lowest density.

According to Archimedes' principle, an object floats (positive buoyancy) when its overall density is less than the density of the fluid it is in.

Analyze the condition required for an object to hover underwater.

The state of 'Hovering motionless' represents a medium density.

An object achieves neutral buoyancy and hovers when its weight perfectly matches the buoyant force of the fully displaced fluid, meaning its density is exactly equal to the fluid's density.

Analyze the condition required for an object to sink.

The state of 'Resting on the solid ocean floor' represents the highest density.

An object sinks (negative buoyancy) when its weight exceeds the maximum possible buoyant force, meaning its overall density is greater than the fluid's density.

Key Concept

Buoyancy and Density Relationships (Positive, Neutral, and Negative Buoyancy)

Estimated Time:45s

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