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Archimedes' Principle

2.5 Archimedes' Principle
PHYSICS • Form 5 • Chapter 2: Pressure

2.5 Archimedes' Principle

Archimedes' principle explains why heavy steel ships float while a small lump of solid plasticine sinks in water. When an object is placed in a fluid, the difference in fluid pressure between the bottom surface and the top surface creates an upward resultant force known as buoyant force.

Learning Objectives

  • Explain buoyant force as an upward resultant force caused by the pressure difference between the upper and lower surfaces of an immersed object.
  • State Archimedes' principle and relate buoyant force to the weight of fluid displaced.
  • Explain the relationship between the equilibrium of forces and the state of floatation of an object in a fluid.
  • Describe daily applications of Archimedes' principle, including hydrometers, ships and Plimsoll lines, submarines, and hot air balloons.
  • Solve numerical problems involving buoyant force and Archimedes' principle using the formula \(F_B = \rho V g\).

Derivation of Buoyant Force on a Submerged Cylinder and States of Floatation

See how pressure difference at depths \(h_1\) and \(h_2\) creates a net upward buoyant force, and compare the three states of floatation.

Pressure Difference Creates Buoyant Force

Liquid Pressure increases with depth: \(P = h\rho g\) Cylinder Area, \(A\) \(F_1 = P_1 A\) downward \(F_2 = P_2 A\) upward \(F_B = F_2 - F_1 = \rho V g\)

Three States of Floatation

\(W = F_B\) \(W\) \(F_B\) Floats / stationary \(W > F_B\) \(W\) \(F_B\) Sinks \(W < F_B\) \(W\) \(F_B\) Rises

Short Explanation

What is Buoyant Force?

Buoyant force is the force acting upwards on an object immersed in a liquid when there is a pressure difference between the lower surface and upper surface of the object.

Origin of Buoyant Force

Liquid pressure increases with depth according to \(P = h\rho g\). The bottom of a submerged object experiences higher pressure than the top, producing a greater upward force on the bottom than downward force on the top.

Archimedes' Principle

An object which is partially or fully immersed in a fluid will experience a buoyant force equal to the weight of fluid displaced.

Apparent Loss in Weight

Apparent loss in weight equals the buoyant force: \(F_B = W_A - W_W\).

Buoyant Force Formula

\(F_B = \rho V g\)

where \(\rho\) = density of fluid (kg m⁻³), \(V\) = volume of fluid displaced = volume of submerged part of object (m³), and \(g\) = gravitational acceleration (m s⁻²).

Floatation State Forces Resultant Force Motion
\(W = F_B\) Balanced forces Zero Stationary / floats in equilibrium
\(W > F_B\) Unbalanced forces Downwards Accelerates downwards and sinks
\(W < F_B\) Unbalanced forces Upwards Accelerates upwards and rises

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What causes buoyant force on an object submerged in a liquid?

Check Answer
Answer: The pressure difference between the lower surface and upper surface of the object, where the upward pressure at the bottom is greater than the downward pressure at the top.
2

An object weighing 15 N in air has an apparent weight of 11 N when fully immersed in water. What is the buoyant force acting on the object?

Check Answer
Answer: Buoyant force = Apparent loss in weight = \(15\ \mathrm{N} - 11\ \mathrm{N} = 4\ \mathrm{N}\).
3

Why does a hydrometer float higher in a high-density liquid compared to a low-density liquid?

Check Answer
Answer: In a high-density liquid, a smaller volume of liquid needs to be displaced to produce a buoyant force equal to the weight of the hydrometer.

Common Mistakes

  • !Confusing the volume of the object with the volume of fluid displaced: \(V\) in \(F_B = \rho V g\) refers strictly to the volume of the submerged part of the object.
  • !Using the density of the submerged object instead of the density of the fluid (\(\rho\)) in the buoyant force formula.
  • !Thinking that heavy objects cannot float: floatation depends on average density and displaced volume.

Concept Misunderstandings

Misunderstanding

Archimedes' principle applies only to liquids.

Correct Concept

Archimedes' principle applies to all fluids, including gases like air, for example in hot air balloons.

Misunderstanding

The hydrometer scale has zero at the top.

Correct Concept

A hydrometer scale does not start from zero because no liquid has zero density; the smallest density value is at the top because less dense liquids cause deeper submersion.

Misunderstanding

Buoyant force increases the deeper an object is submerged.

Correct Concept

Once an object is fully submerged, the volume of displaced water remains constant, so buoyant force does not increase with further depth if fluid density is uniform.

Summary

  • Buoyant force is the upward resultant force arising from the difference in liquid pressure between the top and bottom of an immersed object: \(F_B = F_2 - F_1 = \rho V g\).
  • Archimedes' principle: Buoyant force equals the weight of fluid displaced: \(F_B = W_D =\) apparent loss in weight.
  • Floating condition: Resultant force is zero when \(W = F_B\); the weight of a floating object equals the weight of fluid displaced.
  • Practical devices using this principle include hydrometers, ships and Plimsoll lines, submarines, and hot air balloons.

Short Activity

Objective: Test your understanding of buoyant force, Archimedes' principle and its applications.

A. Objective Quiz

1 A solid metal block weighs 50 N in air. When fully immersed in water, it displaces water weighing 18 N. What is the reading of the spring balance supporting the block in water?

2 Which of the following explains why a submarine dives deeper into the sea?

B. Fill in the Blanks

3 Archimedes' principle states that an object partially or fully immersed in a fluid experiences a buoyant force equal to the of fluid displaced.

4 In the buoyant force formula \(F_B = \rho V g\), the symbol \(V\) represents the volume of displaced.

C. Matching / Drag and Drop

Drag each application or concept to the correct working principle or description. If using a phone, tap the answer first, then tap the matching box.

Application / Concept
Hydrometer
Submarine ballast tank
Hot air balloon
Floating ship
Working Principle / Description
Sinks deeper in less dense liquids and has smaller density markings at the topCorrect ✓Try againEmpty
Floods with water to increase total weight when submerging and uses compressed air to blow out water when surfacingCorrect ✓Try againEmpty
Uses a burner to heat air and decrease density so that buoyant force exceeds total weightCorrect ✓Try againEmpty
Achieves equilibrium where its total weight is exactly equal to the weight of water displacedCorrect ✓Try againEmpty
 

Keywords

Buoyant force Archimedes' principle Apparent loss in weight Fluid Hydrometer Plimsoll line Ballast tank
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Archimedes' Principle

2.5 Archimedes' Principle
PHYSICS • Form 5 • Chapter 2: Pressure

2.5 Archimedes' Principle

Archimedes' principle explains why heavy steel ships float while a small lump of solid plasticine sinks in water. When an object is placed in a fluid, the difference in fluid pressure between the bottom surface and the top surface creates an upward resultant force known as buoyant force.

Learning Objectives

  • Explain buoyant force as an upward resultant force caused by the pressure difference between the upper and lower surfaces of an immersed object.
  • State Archimedes' principle and relate buoyant force to the weight of fluid displaced.
  • Explain the relationship between the equilibrium of forces and the state of floatation of an object in a fluid.
  • Describe daily applications of Archimedes' principle, including hydrometers, ships and Plimsoll lines, submarines, and hot air balloons.
  • Solve numerical problems involving buoyant force and Archimedes' principle using the formula \(F_B = \rho V g\).

Derivation of Buoyant Force on a Submerged Cylinder and States of Floatation

See how pressure difference at depths \(h_1\) and \(h_2\) creates a net upward buoyant force, and compare the three states of floatation.

Pressure Difference Creates Buoyant Force

Liquid Pressure increases with depth: \(P = h\rho g\) Cylinder Area, \(A\) \(F_1 = P_1 A\) downward \(F_2 = P_2 A\) upward \(F_B = F_2 - F_1 = \rho V g\)

Three States of Floatation

\(W = F_B\) \(W\) \(F_B\) Floats / stationary \(W > F_B\) \(W\) \(F_B\) Sinks \(W < F_B\) \(W\) \(F_B\) Rises

Short Explanation

What is Buoyant Force?

Buoyant force is the force acting upwards on an object immersed in a liquid when there is a pressure difference between the lower surface and upper surface of the object.

Origin of Buoyant Force

Liquid pressure increases with depth according to \(P = h\rho g\). The bottom of a submerged object experiences higher pressure than the top, producing a greater upward force on the bottom than downward force on the top.

Archimedes' Principle

An object which is partially or fully immersed in a fluid will experience a buoyant force equal to the weight of fluid displaced.

Apparent Loss in Weight

Apparent loss in weight equals the buoyant force: \(F_B = W_A - W_W\).

Buoyant Force Formula

\(F_B = \rho V g\)

where \(\rho\) = density of fluid (kg m⁻³), \(V\) = volume of fluid displaced = volume of submerged part of object (m³), and \(g\) = gravitational acceleration (m s⁻²).

Floatation State Forces Resultant Force Motion
\(W = F_B\) Balanced forces Zero Stationary / floats in equilibrium
\(W > F_B\) Unbalanced forces Downwards Accelerates downwards and sinks
\(W < F_B\) Unbalanced forces Upwards Accelerates upwards and rises

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What causes buoyant force on an object submerged in a liquid?

Check Answer
Answer: The pressure difference between the lower surface and upper surface of the object, where the upward pressure at the bottom is greater than the downward pressure at the top.
2

An object weighing 15 N in air has an apparent weight of 11 N when fully immersed in water. What is the buoyant force acting on the object?

Check Answer
Answer: Buoyant force = Apparent loss in weight = \(15\ \mathrm{N} - 11\ \mathrm{N} = 4\ \mathrm{N}\).
3

Why does a hydrometer float higher in a high-density liquid compared to a low-density liquid?

Check Answer
Answer: In a high-density liquid, a smaller volume of liquid needs to be displaced to produce a buoyant force equal to the weight of the hydrometer.

Common Mistakes

  • !Confusing the volume of the object with the volume of fluid displaced: \(V\) in \(F_B = \rho V g\) refers strictly to the volume of the submerged part of the object.
  • !Using the density of the submerged object instead of the density of the fluid (\(\rho\)) in the buoyant force formula.
  • !Thinking that heavy objects cannot float: floatation depends on average density and displaced volume.

Concept Misunderstandings

Misunderstanding

Archimedes' principle applies only to liquids.

Correct Concept

Archimedes' principle applies to all fluids, including gases like air, for example in hot air balloons.

Misunderstanding

The hydrometer scale has zero at the top.

Correct Concept

A hydrometer scale does not start from zero because no liquid has zero density; the smallest density value is at the top because less dense liquids cause deeper submersion.

Misunderstanding

Buoyant force increases the deeper an object is submerged.

Correct Concept

Once an object is fully submerged, the volume of displaced water remains constant, so buoyant force does not increase with further depth if fluid density is uniform.

Summary

  • Buoyant force is the upward resultant force arising from the difference in liquid pressure between the top and bottom of an immersed object: \(F_B = F_2 - F_1 = \rho V g\).
  • Archimedes' principle: Buoyant force equals the weight of fluid displaced: \(F_B = W_D =\) apparent loss in weight.
  • Floating condition: Resultant force is zero when \(W = F_B\); the weight of a floating object equals the weight of fluid displaced.
  • Practical devices using this principle include hydrometers, ships and Plimsoll lines, submarines, and hot air balloons.

Short Activity

Objective: Test your understanding of buoyant force, Archimedes' principle and its applications.

A. Objective Quiz

1 A solid metal block weighs 50 N in air. When fully immersed in water, it displaces water weighing 18 N. What is the reading of the spring balance supporting the block in water?

2 Which of the following explains why a submarine dives deeper into the sea?

B. Fill in the Blanks

3 Archimedes' principle states that an object partially or fully immersed in a fluid experiences a buoyant force equal to the of fluid displaced.

4 In the buoyant force formula \(F_B = \rho V g\), the symbol \(V\) represents the volume of displaced.

C. Matching / Drag and Drop

Drag each application or concept to the correct working principle or description. If using a phone, tap the answer first, then tap the matching box.

Application / Concept
Hydrometer
Submarine ballast tank
Hot air balloon
Floating ship
Working Principle / Description
Sinks deeper in less dense liquids and has smaller density markings at the topCorrect ✓Try againEmpty
Floods with water to increase total weight when submerging and uses compressed air to blow out water when surfacingCorrect ✓Try againEmpty
Uses a burner to heat air and decrease density so that buoyant force exceeds total weightCorrect ✓Try againEmpty
Achieves equilibrium where its total weight is exactly equal to the weight of water displacedCorrect ✓Try againEmpty
 

Keywords

Buoyant force Archimedes' principle Apparent loss in weight Fluid Hydrometer Plimsoll line Ballast tank
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Pressure
Topic : Archimedes Principle
Form 5 Physics
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