Class 9 Physics – Chapter 6: Mechanical Properties of Matter

Introduction to Mechanical Properties of Matter

The mechanical properties of matter describe how materials respond to external forces, including their elasticity, strength, and behavior under pressure.

When we stretch a rubber band, compress a spring, or dive deep into water, we're experiencing the mechanical properties of matter. This chapter explores how materials deform under forces, the relationship between force and deformation, and how pressure acts in fluids and gases.

Key Concepts Covered

Deforming force and elasticity
Hooke's law and spring constant
Density and its measurement
Pressure and its dependence on area
Pressure in liquids and its calculation
Atmospheric pressure and its measurement
Pascal's law and its applications
Hydraulic systems and force multiplication

Important Definitions

Deforming Force: An external force applied on an object that can change its size or shape.

Elasticity: The property of solids by which they return to their original shape when the deforming force ceases to act.

Elastic Limit: The maximum extent to which a solid may be stretched without permanent alteration of size or shape.

Inelastic Materials: Materials that do not return to their original shape after the removal of the deforming force.

Spring Constant: A measure of a spring's stiffness, defined as the force required to produce unit extension.

Density: The mass per unit volume of a substance.

Pressure: The force exerted normally on a unit area of an object.

Atmospheric Pressure: The pressure exerted by the weight of the atmosphere on the Earth's surface.

Pascal's Law: When pressure is applied at one point in an enclosed fluid, it is transmitted equally to all parts of the fluid without loss.

Key Formulas

Hooke's Law

\[F = kx\]

Where \( F \) is force, \( k \) is spring constant, and \( x \) is extension

Spring Constant

\[k = \frac{F}{x}\]

Where \( k \) is spring constant, \( F \) is force, and \( x \) is extension

Density

\[\rho = \frac{m}{V}\]

Where \( \rho \) is density, \( m \) is mass, and \( V \) is volume

Pressure

\[P = \frac{F}{A}\]

Where \( P \) is pressure, \( F \) is force, and \( A \) is area

Pressure in Liquids

\[P = \rho g h\]

Where \( P \) is pressure, \( \rho \) is density, \( g \) is gravity, and \( h \) is depth

Hydraulic Force Multiplication

\[F_2 = F_1 \times \left( \frac{A_2}{A_1} \right)\]

Where \( F_1 \) and \( F_2 \) are forces, \( A_1 \) and \( A_2 \) are areas

Detailed Chapter Content

1. Elasticity and Deforming Force

When an external force is applied to an object, it may change the object's size or shape. Such a force is called a deforming force.

If an object returns to its original shape and size after the deforming force is removed, it is said to be elastic. This property is called elasticity.

Examples include springs, rubber bands, and tennis balls that regain their shape after deformation.

2. Hooke's Law and Spring Constant

Within the elastic limit of a helical spring, the extension or compression is directly proportional to the applied force. This is known as Hooke's law.

The spring constant \( k \) is a measure of the stiffness of a spring. A higher spring constant means a stiffer spring.

Force-Extension Graph: A graph of force against extension is a straight line passing through the origin within the elastic limit. The gradient of this graph gives the spring constant.

3. Applications of Hooke's Law

Spring scales: Use the extension or compression of a spring to determine weight
Balance wheel of mechanical clocks: Uses spring to control back and forth motion
Galvanometer: Uses a tiny spring called hair spring for electrical connections and restoring the pointer
Suspension systems in vehicles: Use springs to absorb shocks

4. Density and Its Measurement

Density is defined as mass per unit volume. The SI unit of density is kilogram per cubic meter (\(kgm^{-3}\)).

Density can be determined by measuring mass and volume:

For regular solids: Measure dimensions and calculate volume
For irregular solids: Use displacement method

5. Pressure and Its Dependence on Area

Pressure is defined as force per unit area. It is a scalar quantity measured in pascals (Pa).

Pressure depends on the area over which force is distributed:

Small area → High pressure (e.g., sharp knife, thumb pin)
Large area → Low pressure (e.g., elephant feet, snowshoes)

6. Pressure in Liquids

Liquids exert pressure in all directions, and this pressure increases with depth according to the formula:

\[P = \rho g h\]

Pressure always acts perpendicular (normal) to a surface. This is why liquid jets out at right angles to container walls.

7. Atmospheric Pressure

The atmosphere exerts pressure on the Earth's surface due to the weight of air above. At sea level, standard atmospheric pressure is \(1.013 \times 10^5 Pa\).

We don't feel this enormous pressure because the pressure inside our bodies balances the external atmospheric pressure.

8. Measurement of Atmospheric Pressure

Atmospheric pressure is measured using a barometer. A simple mercury barometer consists of a glass tube filled with mercury and inverted in a dish of mercury.

At sea level, the height of the mercury column is about 760 mm, which corresponds to standard atmospheric pressure.

9. Pascal's Law and Hydraulic Systems

Pascal's law states that when pressure is applied at one point in an enclosed fluid, it is transmitted equally to all parts of the fluid without loss.

Applications of Pascal's law include:

Hydraulic press: Used to compress materials like cotton bales
Hydraulic brakes: Used in vehicles to apply braking force
Hydraulic jacks: Used to lift heavy objects like cars

10. Force Multiplication in Hydraulic Systems

Hydraulic systems can multiply force using Pascal's law. A small force applied to a small piston can produce a large force on a larger piston:

\[F_2 = F_1 \times \left( \frac{A_2}{A_1} \right)\]

Since \( A_2 > A_1 \), therefore \( F_2 > F_1 \), making the system a force multiplier.

Daily Life Applications

        Pressure and Area Relationship
        Sharp blades: Small area creates high pressure for easy cutting
Thumb pins: Sharp end with small area creates high pressure for piercing
Elephant feet: Large area reduces pressure to prevent sinking
Walking on pebbles: Small contact area increases pressure, causing pain
Racing animals: Small foot area increases pressure for better grip

      

        Atmospheric Pressure
        Drinking with a straw: Atmospheric pressure pushes liquid up when we suck air out
Syringe operation: Atmospheric pressure pushes liquid into the syringe
Tin can experiment: Demonstrates crushing force of atmospheric pressure
Weather forecasting: Changes in atmospheric pressure indicate weather changes

      

Comparison Tables

Force vs Pressure

Force Pressure Force is a push or pull acting on an object Pressure is the force applied per unit area Measured in newtons (N) Measured in pascals (Pa) Formula: \( F = ma \) Formula: \( P = \frac{F}{A} \)

Elastic vs Inelastic Materials

Elastic Materials Inelastic Materials Return to original shape after force removal Do not return to original shape after force removal Examples: Spring, rubber band, tennis ball Examples: Clay dough, plasticine Follow Hooke's law within elastic limit Do not follow Hooke's law

Sample Problems

Problem 1: Spring Constant Calculation

Given:

A force of 10 N stretches a spring by 5 cm. Calculate the spring constant.

Solution:

Using Hooke's law: \( F = kx \)

\( k = \frac{F}{x} = \frac{10}{0.05} = 200 \, Nm^{-1} \)

The spring constant is 200 N/m.

Problem 2: Pressure Calculation

Given:

A force of 500 N is applied on an area of 2 m². Calculate the pressure.

Solution:

Using pressure formula: \( P = \frac{F}{A} \)

\( P = \frac{500}{2} = 250 \, Pa \)

The pressure is 250 pascals.