NCERT Class 9 Science Chapter 9: Floatation, Thrust, and Archimedes' Principle - Master Study Guide

Introduction to Floatation, Thrust, and Pressure

Have you ever wondered why a heavy iron ship floats on water, whereas a tiny iron nail sinks immediately? Why does a wooden block rise to the surface when pushed underwater? Why do wide straps feel more comfortable when carrying heavy school bags? The answers to all these fascinating physical phenomena lie in the principles of Thrust, Pressure, Buoyancy, and Floatation.

In the CBSE NCERT Class 9 Science curriculum, the study of fluids—liquids and gases—and their mechanics forms a vital part of physics. Fluids exert forces on objects placed within them, and understanding how force is distributed across surface area helps us explain natural events and engineer advanced technology, from submarines to hydrometers. This comprehensive guide breaks down each topic section by section to provide you with a master study resource.

Thrust and Pressure

To understand why objects exert force differently depending on how they are positioned, we must first define two fundamental physical quantities: thrust and pressure.

Understanding Thrust

When an object is placed on a surface, it exerts a force due to its weight. When this force acts perpendicular (at an angle of 90 degrees) to the surface, it is specifically called Thrust.

• Definition: Thrust is the total force acting perpendicularly on a surface.
• Nature: It is a vector quantity, having both magnitude and direction.
• SI Unit: Since thrust is a force, its SI unit is the Newton (N).
• Example: Standing on loose sand. The total weight of your body acts perpendicularly downward onto the sand surface.

Understanding Pressure

The effect of thrust depends on the total area over which it is applied. Pressure is the mathematical representation of how thrust is distributed across a surface area.

• Definition: Pressure is defined as the force or thrust acting per unit area of a surface.
• Formula: Pressure = Thrust / Area  ⇒  P = F / A
• SI Unit: The SI unit of pressure is Newton per square metre (N/m²) or Pascal (Pa), named in honour of scientist Blaise Pascal. (1 Pa = 1 N/m²).

Factors Affecting Pressure

From the equation P = F / A, it is clear that pressure depends on two primary factors:

• Magnitude of Force (Thrust): Pressure is directly proportional to the applied force. Increasing the force increases the pressure if the area remains constant.
• Surface Area: Pressure is inversely proportional to the area of contact. Keeping force constant, a smaller area results in higher pressure, while a larger area results in lower pressure.

Real-World Applications of Pressure:

• Sharp Knives: The cutting edge of a knife has a very small surface area. Applying a modest force generates huge pressure, allowing it to cut effortlessly through vegetables.
• Building Foundations: Buildings have wide foundations to increase the contact area with the ground, reducing pressure and preventing the structure from sinking.
• Wide Straps on Bags: School bags are equipped with broad straps so that the heavy weight of books is spread over a larger shoulder area, minimizing painful pressure.
• Tractors and Tanks: Heavy tractors use wide tires, and army tanks use caterpillar tracks to distribute weight over a vast area, enabling movement across soft mud without sinking.

Pressure in Fluids

All liquids and gases are classified as fluids because they can flow. Unlike solids, which exert pressure only downward on the surface beneath them, fluids exert pressure in all directions—downward, upward, and laterally against the walls of their container.

Fluid pressure increases with depth because the deeper layers of fluid support the weight of all the fluid layers sitting above them.

Buoyancy and Upthrust

When you immerse an object in water, it feels lighter than it does in air. A bucket full of water feels significantly lighter while inside a well than when pulled out into the air. This phenomenon is caused by fluid buoyancy.

The Concept of Buoyancy

When an object is placed or immersed in a fluid, the fluid exerts an upward force on the object. This upward force exerted by a fluid on an immersed body is called the Buoyant Force or Upthrust.

The tendency of a fluid to exert this upward force on an immersed body is known as Buoyancy.

• Direction of Buoyant Force: Always directed vertically upward, opposing the force of gravity.
• Unit: Measured in Newtons (N).

Factors Affecting Buoyant Force

The magnitude of the buoyant force depends on two critical parameters:

• Volume of the Immersed Object: As more of an object's volume is submerged in fluid, the buoyant force increases until the object is completely submerged. Once completely submerged, further depth does not change the buoyant force.
• Density of the Fluid: A fluid with higher density exerts a greater upward buoyant force on an object. For instance, dense saltwater exerts a greater buoyant force than pure freshwater.

Why Objects Sink or Float in a Liquid

Whether an object sinks or floats when placed in a liquid depends on the balance between two opposing forces: the downward gravitational force (weight of the object) and the upward buoyant force exerted by the liquid.

Archimedes' Principle

The quantitative measure of buoyant force was first discovered by the ancient Greek mathematician and inventor Archimedes.

Statement of Archimedes' Principle

Archimedes' Principle states that: "When a body is immersed fully or partially in a fluid, it experiences an upward force (buoyant force) that is equal to the weight of the fluid displaced by it."

Mathematical Formulation:

Buoyant Force (F_b) = Weight of Displaced Fluid (W_fluid) = m_fluid × g = ρ_fluid × V_displaced × g

Where:

• ρ_fluid = Density of the fluid
• V_displaced = Volume of the displaced fluid (equal to submerged volume of the object)
• g = Acceleration due to gravity

Experimental Verification

To demonstrate Archimedes' Principle in a laboratory:

1. Suspend a heavy metal block from a spring balance and note its weight in air (e.g., 5 N).
2. Fill an Eureka vessel (overflow can) with water up to its spout level and place a measuring cylinder below the spout.
3. Gently lower the metal block into the water while keeping it attached to the spring balance.
4. Note the reduced reading on the spring balance (e.g., 3 N). Apparent loss in weight = 5 N - 3 N = 2 N.
5. Measure the volume of water overflowed into the measuring cylinder and calculate its weight. The weight of displaced water will equal exactly 2 N.

This confirms that the loss of weight in fluid = Buoyant Force = Weight of displaced fluid.

Applications of Archimedes' Principle

Archimedes' Principle has crucial practical engineering applications:

• Designing Ships and Submarines: Steel ships float because their hollow structure encloses large volumes of air, creating a huge average volume that displaces an equal weight of water before the ship fully submerges. Submarines use ballast tanks filled with water or air to alter overall density and sink or surface at will.
• Hydrometers: Instruments used to determine the specific gravity or density of liquids.
• Lactometers: Specialized hydrometers used to test the purity of milk samples.
• Hot Air Balloons: Rise because the hot air inside the balloon is less dense than the surrounding cold atmospheric air, generating an upward buoyant force greater than the balloon's total weight.

Density and Relative Density

To predict how materials behave in different fluids, physical scientists rely on the concepts of density and relative density.

Density of a Substance

Density is an intrinsic property of matter that describes how tightly mass is packed into a given volume.

• Definition: Mass per unit volume of a substance.
• Formula: Density (ρ) = Mass (m) / Volume (V)
• SI Unit: Kilogram per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³).
• Conversion: 1 g/cm³ = 1000 kg/m³. Density of pure water at 4°C is 1000 kg/m³ or 1 g/cm³.

Relative Density and Its Calculation

Comparing the density of various substances to a standard substance (pure water) gives us Relative Density.

• Definition: The ratio of the density of a substance to the density of water at 4°C.
• Formula: Relative Density = (Density of Substance) / (Density of Water)
• Dimensionless Quantity: Because relative density is a ratio of two identical physical quantities, it has no units.
• Interpretation: If a substance has a relative density less than 1, it will float in pure water. If its relative density is greater than 1, it will sink in water.

Comparison Table: Density vs Relative Density

Important Questions and Answers

Question 1: Why is it easier to swim in sea water than in river water?

Answer: Sea water contains dissolved salts, which significantly increases its density compared to fresh river water. According to Archimedes' Principle, a fluid with a higher density exerts a greater buoyant force on an immersed body. Because sea water exerts a higher buoyant force, a swimmer's body experiences greater upward support, making it easier to float and swim in sea water.

Question 2: A block of wood of mass 6 kg and dimensions 40 cm × 20 cm × 10 cm is placed on a tabletop. Calculate the pressure exerted by the wooden block if it is placed on the table with its sides of dimensions: (a) 20 cm × 10 cm, and (b) 40 cm × 20 cm. (Take g = 10 m/s²)

Answer:

Given:

• Mass of block (m) = 6 kg
• Weight/Thrust (F) = m × g = 6 kg × 10 m/s² = 60 N

Case (a): Surface area in contact (A₁) = 20 cm × 10 cm = 0.2 m × 0.1 m = 0.02 m²

Pressure (P₁) = Thrust / Area = 60 N / 0.02 m² = 3000 Pa (N/m²)

Case (b): Surface area in contact (A₂) = 40 cm × 20 cm = 0.4 m × 0.2 m = 0.08 m²

Pressure (P₂) = Thrust / Area = 60 N / 0.08 m² = 750 Pa (N/m²)

Conclusion: Smaller contact area produces significantly higher pressure.

Question 3: Relative density of silver is 10.8. The density of water is 10³ kg/m³. What is the density of silver in SI units?

Answer:

Given:

• Relative Density of silver = 10.8
• Density of water = 10³ kg/m³ = 1000 kg/m³

Using the formula:

Relative Density = Density of Silver / Density of Water

10.8 = Density of Silver / 1000 kg/m³

Density of Silver = 10.8 × 1000 kg/m³ = 10.8 × 10³ kg/m³ (or 10800 kg/m³).

Question 4: Why does a plastic block released underwater come up to the surface of water?

Answer: Plastic has a density lower than that of water. When submerged underwater, the weight of water displaced by the plastic block (the upward buoyant force) is greater than the downward gravitational weight of the plastic block itself. Due to this net upward force, the plastic block accelerates upward and floats on the surface of water.

Question 5: State Archimedes' principle and mention two practical applications derived from it.

Answer:

Archimedes' Principle: When a body is partially or fully immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by it.

Applications:

• Designing ocean-going ships and submarines.
• Designing lactometers to test the purity of milk and hydrometers to measure liquid density.

Chapter Summary

• Thrust: The perpendicular force acting on a surface. Unit: Newton (N).
• Pressure: Thrust acting per unit area (P = F / A). Unit: Pascal (Pa) or N/m².
• Pressure increases with smaller surface area and decreases with larger surface area.
• Fluids (liquids and gases) exert pressure in all directions on container walls.
• Buoyancy: The tendency of a fluid to exert an upward buoyant force on an immersed object.
• An object floats if its density is less than or equal to the fluid density; it sinks if its density is greater than the fluid density.
• Archimedes' Principle: Upward buoyant force = Weight of fluid displaced by the immersed object.
• Density: Mass per unit volume (ρ = m / V) measured in kg/m³.
• Relative Density: Ratio of substance density to pure water density; it is a unitless ratio.