Archimedes’ Principle Formula, Derivation & Everyday Applications
Archimedes’ Principle is a fundamental concept in Physics that explains how and why objects float or sink in fluids. It is a physical law related to buoyancy, describing the force that fluids exert on objects placed in them.
The statement of Archimedes’ Principle is: Any body completely or partially submerged in a fluid (liquid or gas) at rest is acted upon by an upward, or buoyant, force. The size of this force is equal to the weight of the fluid displaced by the body.
Understanding Buoyant Force
When you place an object in a fluid, the fluid pushes upward against the object. This upward push is called the buoyant force. If the buoyant force is greater than the object’s weight, it will float. If not, it will sink. This concept is essential in understanding the behavior of objects in liquids and gases.
The magnitude of the buoyant force does not depend on the type of material of the object, but only on the amount of fluid displaced and the density of that fluid.
Archimedes’ Principle Formula
The buoyant force (FB) experienced by an object in a fluid is given by:
Where:
- ρ (rho) = Density of the fluid
- g = Acceleration due to gravity
- V = Volume of fluid displaced by the object
Step-by-Step: Solving Archimedes’ Principle Problems
| Step | What To Do | Example |
|---|---|---|
| 1 | Identify the object’s volume and the fluid’s density. | Iron block (mass 2 kg, density 8000 kg/m³) in water (density 1000 kg/m³) |
| 2 | Calculate the object’s volume (V = mass/density). | V = 2 / 8000 = 0.00025 m³ |
| 3 | Compute buoyant force (FB = ρ × g × V). | FB = 1000 × 9.8 × 0.00025 = 2.45 N |
| 4 | Compare FB to the object’s weight (W = mass × g). | W = 2 × 9.8 = 19.6 N. The object sinks, as weight > buoyant force. |
Key Applications and Examples
Archimedes’ Principle has a wide range of applications in science and daily life. Below are some important areas where this principle is essential.
- Design and floating of ships and boats
- Functioning of submarines
- Operation of hot air balloons
- Measurement of fluid densities using hydrometers
- Icebergs floating on water
Summary Table: Archimedes’ Principle in Action
| Situation | Buoyant Force vs. Weight | Result |
|---|---|---|
| If FB = W | Equal | Object floats, fully or partially submerged |
| If FB < W | Less than | Object sinks |
| If FB > W | Greater than | Object rises until equilibrium is achieved |
Practical Example
Suppose a piece of wood is placed in water. The wood displaces water equal to its own volume. If the buoyant force due to displaced water equals the wood’s weight, it floats. If not, it will sink.
Thus, by comparing the weight of fluid displaced and the object’s actual weight, you can always determine whether it will sink or float.
Common Applications
| Application Area | Role of Archimedes’ Principle |
|---|---|
| Ships and Boats | Allows heavy vessels to float by displacing large amounts of water. |
| Submarines | Control floatation and depth using water intake in ballast tanks. |
| Hot Air Balloons | Buoyancy in air causes balloons to rise. |
| Hydrometers | Measures fluid density based on amount displaced. |
Key Takeaways and Next Steps
Understanding Archimedes’ Principle helps you analyze everyday phenomena, from floating objects to engineering problems involving fluids. Keep practicing with different examples to strengthen your grasp on buoyancy and its significance.
To explore this topic further and tackle practice questions, visit Vedantu’s dedicated Physics resource page:
Applying Archimedes’ Principle lays the foundation for fields such as engineering, hydrodynamics, and other real-world sciences.
FAQs on Archimedes’ Principle Explained for Students
1. What is Archimedes’ Principle in simple words?
Archimedes’ Principle states that any object, wholly or partly immersed in a fluid, experiences an upward buoyant force equal to the weight of fluid displaced by the object. Simply put, if something is in water (or any fluid), the fluid pushes up on it with a force equal to what the fluid itself would weigh if it filled the same space.
2. State Archimedes’ Principle.
Archimedes’ Principle: When a body is completely or partially immersed in a fluid, it experiences an upward force (buoyant force) equal to the weight of the fluid displaced by the body. This principle helps explain why objects float or sink in water.
3. What is the formula for buoyant force?
The buoyant force (FB) can be calculated using:
FB = ρ × g × V
where:
- ρ = density of fluid (kg/m³)
- g = acceleration due to gravity (m/s²)
- V = volume of fluid displaced (m³)
4. What are some applications of Archimedes’ Principle?
Common applications of Archimedes’ Principle include:
- Designing ships and submarines to ensure floating
- Lactometers and hydrometers to measure density of liquids
- Hot air balloons rising in air
- Life jackets to keep people afloat
- Measurement of body fat by water displacement
5. Why do ships made of iron float, but a solid iron ball sinks?
Ships are hollow and displace more water overall, making the buoyant force greater than the ship’s weight, so they float. An iron ball of the same mass has much less volume, so it displaces less water, resulting in a smaller upthrust than its weight, and it sinks.
6. How do you calculate whether an object will float or sink?
An object will float if the buoyant force is equal to or greater than its weight. It will sink if its weight is greater than the upthrust. Use these steps:
- Calculate volume: V = mass/density of object
- Find buoyant force: FB = ρfluid × g × V
- Compare with object’s weight: Weight = mass × g
7. Does Archimedes’ Principle apply to gases?
Yes, Archimedes’ Principle applies to gases as well as liquids. For example, hot air balloons rise because the balloon displaces heavier (colder) air, experiencing an upward buoyant force.
8. What is the difference between Archimedes’ Principle and Bernoulli’s Principle?
Archimedes’ Principle explains floating or sinking by buoyant force in a fluid, while Bernoulli’s Principle relates to fluid flow and pressure, explaining phenomena like airplane lift through differences in pressure and velocity. Both are key fluid mechanics concepts but describe different behaviors.
9. Can you state some daily life examples of Archimedes’ Principle?
Examples of Archimedes’ Principle in daily life:
- Floating of icebergs in ocean
- A person swimming
- Hydrometers measuring liquid purity
- Hot air balloons taking off
- Life jackets keeping people afloat
10. How is Archimedes’ Principle derived?
Archimedes’ Principle is derived as follows:
When an object is immersed in a fluid, pressure at the bottom is greater than at the top. The difference in pressure creates an upward force (upthrust), equal to the weight of the fluid displaced by the object. This is proven using the formulas for fluid pressure (P = hρg) and area calculations.
11. What are the important terms related to Archimedes’ Principle?
Key terms include:
- Buoyant Force – Upward force from displaced fluid
- Upthrust – Synonym for buoyant force
- Density – Mass per unit volume of a substance
- Displacement – Volume of fluid pushed away by object
12. What is upthrust and how is it measured?
Upthrust is the upward force exerted by a fluid on an object placed in it. It is measured as:
Upthrust = Weight of fluid displaced = ρfluid × g × Vobject submerged
It determines whether an object will float or sink.
