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 → Mechanics → Work, Energy and Power ↓


Work–energy theorem


The work-energy theorem is a principle that connects the concepts of work and energy. In simple terms, it tells us that the work done by all the forces acting on an object is equal to the change in its kinetic energy. This theorem is a fundamental concept in physics and it helps us understand how energy is transferred and transformed.

Understanding work and energy

Before getting into the work-energy theorem, let us briefly understand what we mean by work and energy in physics.

Work

In physics, work is done when a force moves an object a distance. However, not all forces do work. Only the component of the force that acts in the direction of displacement does work.

The formula for work W is given as:

W = F × d × cos(θ)

Where:

  • F is the applied force.
  • d is the displacement of the object.
  • θ is the angle between the direction of force and displacement.

Example: Imagine you are pushing a heavy box across the floor. If you apply a force of 10 Newtons and the box moves 5 meters in the same direction, the work done is:

W = 10 N × 5 m × cos(0°) = 50 Joules

Since the force is in the direction of displacement, the angle is 0 degrees, and cos(0°) is 1.

Force(F) displacement (d)

Energy

Energy is the capacity to do work. It comes in various forms, such as kinetic energy, potential energy, thermal energy, etc.

Kinetic energy

Kinetic energy is the energy an object has due to its motion. It is given by the formula:

KE = 0.5 × m × v²

Where:

  • m is the mass of the object.
  • v is the velocity of the object.

Example: A car with a mass of 1000 kg moving at a speed of 20 m/s has the kinetic energy:

KE = 0.5 × 1000 kg × (20 m/s)² = 200,000 Joules
moving car Velocity (v)

Work–energy theorem

According to the work-energy theorem, the total work done by all forces acting on an object is equal to the change in its kinetic energy. Mathematically it is expressed as:

W_total = ΔKE = KE_final - KE_initial

Where:

  • W_total is the total work done.
  • ΔKE is the change in kinetic energy.
  • KE_initial is the initial kinetic energy.
  • KE_final is the final kinetic energy.

Application of the work-energy theorem

Let us see how we can apply the work-energy theorem to different scenarios:

Example 1: Stopping the car

Imagine that a car stops due to the force of friction. The work done by friction is equal to the change in the kinetic energy of the car.

Landscape:

A car of mass 1000 kg is moving at a speed of 30 m/s. The driver applies the brake and the car stops. Calculate the work done by the brake.

Solution:

KE_initial = 0.5 × 1000 kg × (30 m/s)² = 450,000 Joules
KE_final = 0 (since the car stops)
W_total = KE_final - KE_initial = 0 - 450,000 Joules = -450,000 Joules

The negative sign indicates that the work done by the brake is opposite to the motion of the car.

braking car clash

Example 2: Roller coaster

Consider a roller coaster at the top of a hill. As it descends, its potential energy is converted into kinetic energy.

Landscape:

A roller coaster with a mass of 500 kg is at rest at the top of a hill 10 m high. Calculate the speed of the coaster at the bottom of the hill.

Solution:

Potential energy at the top of the hill:

PE_initial = m × g × h = 500 kg × 9.8 m/s² × 10 m = 49,000 Joules

Since the coaster is stationary at the top, KE_initial is 0. At the bottom, all the potential energy is converted to kinetic energy:

KE_final = PE_initial = 49,000 Joules

Now use the kinetic energy formula to find the speed:

49,000 Joules = 0.5 × 500 kg × v²
v² = 49,000 / 250
v = √(196) ≈ 14 m/s
Roller Coaster Top (PE_High) lower(KE_high)

Example 3: Lifting a body

The work done while lifting a body is stored as potential energy. If it is dropped, the potential energy is converted back into kinetic energy when it falls.

Landscape:

A mass of 50 kg is raised to a height of 5 m. Calculate its speed just before the mass is dropped to the ground.

Solution:

Potential energy at 5 m:

PE_initial = m × g × h = 50 kg × 9.8 m/s² × 5 m = 2,450 Joules

Below, just before hitting the ground, all of this is converted into kinetic energy:

KE_final = PE_initial = 2,450 Joules

Using the kinetic energy formula:

2,450 Joules = 0.5 × 50 kg × v²
v² = 2,450 / 25
v = √(98) ≈ 9.9 m/s
Mass Top (PE_High) lower(KE_High)

Conclusion

The work-energy theorem provides a powerful way to analyze forces and motion in a variety of physical situations. Whether it's braking a vehicle, the thrilling descent of a roller coaster, or lifting and dropping an object, understanding how work and energy interact helps us describe and predict motion efficiently.

By understanding these fundamental principles, we not only solve theoretical problems, but also gain valuable insight into real-world mechanics. The work-energy theorem encapsulates this understanding by linking forces to changes in energy, making it an essential concept in the study of physics.


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Work–energy theorem

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