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
Three States of Floatation
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”.
What causes buoyant force on an object submerged in a liquid?
Check Answer
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
Why does a hydrometer float higher in a high-density liquid compared to a low-density liquid?
Check Answer
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
Archimedes' principle applies only to liquids.
Archimedes' principle applies to all fluids, including gases like air, for example in hot air balloons.
The hydrometer scale has zero at the top.
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.
Buoyant force increases the deeper an object is submerged.
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.
