Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Properties of matter → Elasticity ↓


Hooke's law


Hooke's Law is a fundamental principle in physics, particularly in the study of elasticity and the properties of matter. It is named after the 17th-century British scientist Robert Hooke. The law describes the behavior of elastic materials, such as springs, when a force is applied to them. Understanding the principles behind Hooke's Law helps explain how materials stretch and contract, which is important in a variety of fields ranging from engineering to everyday applications.

The basic concept of Hooke's law

Hooke's law states that the amount of extension or compression of an elastic material is directly proportional to the force applied to it, as long as the material is not stretched or compressed beyond its elastic limit. In simple terms, if you pull or push a spring, it will stretch or compress. The amount it stretches or compresses is proportional to the amount of force you use.

The mathematical expression of Hooke's law is:

        F = k * x

Where:

  • F is the force applied to the spring (measured in Newtons, N).
  • k is the spring constant (measured in newtons per meter, N/m). It is a measure of the stiffness of the spring.
  • x is the displacement or change in length from the rest position (measured in meters).

Visual example of Hooke's law

Imagine a simple metal spring. When this spring is in its natural state, there is no force acting on it, and its length is in equilibrium. If you apply a force to stretch the spring, it will stretch. Conversely, if you apply a compression force, it will shorten.

Length of rest

In the visual example above, the line represents the spring at its original, undeformed length. The blue and red circles represent the position of the spring's boundaries before and after the force is applied, respectively.

Elastic limit and proportionality

Hooke's law is true only when the material is within its elastic limit. The elastic limit is the maximum extent to which the material can be stretched or compressed without permanent deformation. Beyond this point, the material will not return to its original shape and size when the force is removed, and Hooke's law no longer applies.

Real-world example: Waterfalls in everyday life

Consider the spring in a pen. When you click the pen, you compress the spring. The force you apply is proportional to the amount you compress the spring. As you release the force, the spring stretches and pushes the nib of the pen back to its original position.

Finding the spring constant k

spring constant (k) is a measure of the stiffness of a spring. A large value of k indicates a stiff spring that does not stretch or compress easily. Conversely, a small value of k indicates a spring that deforms easily under force.

For example, a car suspension spring is designed with a large k to support the weight of the vehicle, while a lighter, softer spring in a toy may have a smaller k.

Energy stored in a stretched or compressed spring

The energy stored in a spring when it is stretched or compressed is known as potential energy, specifically elastic potential energy. The formula for calculating elastic potential energy in a spring is:

        u = 0.5 * k * x²

Where:

  • U is the elastic potential energy (measured in joules, J).
  • k is the spring constant (measured in N/m).
  • x is the displacement (measured in meters).

Example of calculation using Hooke's law

Let's consider a practical example. Suppose you have a spring with k = 300 N/m, and you apply a force of 9 N to stretch it. How far will the spring stretch?

Using Hooke's law formula:

        F = k * x

Rearrange to solve for x :

        x = f / k

Substitute the given values:

        x = 9 N / 300 N/m = 0.03 m

Thus, the spring will extend by 0.03 m, which is 3 cm.

Practical applications of Hooke's law

  • Construction and mechanical engineering: Engineers use Hooke's law to design springs for cars, machines, and buildings, ensuring they effectively absorb shocks and vibrations.
  • Sports equipment: Hooke's law is applied in designing athletic gear such as trampolines and diving boards to provide the optimal amount of buoyancy and flexibility.
  • Everyday objects: Pens, mattresses, and watches use the principles of Hooke's law for functionality and comfort.

Modeling of simple harmonic motion

Hooke's law is the basis for understanding simple harmonic motion, the type of oscillation seen in systems such as pendulums and springs. When a spring obeys Hooke's law, it is often seen as oscillating back and forth at a specific natural frequency.

Conclusion

In conclusion, Hooke's Law is a simple but powerful tool for understanding how materials expand and contract under force. By learning how to apply this law, you gain information about the physical properties of materials and their limits, which is important in a variety of scientific and engineering applications. Whether you are analyzing the mechanism in a simple spring toy or designing complex machinery, Hooke's Law provides a foundational understanding of elasticity and mechanical behavior.


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Hooke's law

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