Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Mechanics → Work, Energy and Power ↓


Work–energy theorem


The work-energy theorem is a very important concept in physics, especially when studying mechanics. It describes the relationship between the work done on an object and the change in its kinetic energy. By understanding this theorem, you will gain insight into how forces affect the motion of objects.

Understanding work, energy, and power

Before we dive into the work-energy theorem, let's understand some key terms: work, energy, and power.

What is the work?

Work can mean many things in everyday language, but in physics work has a specific meaning. Work is done when a force causes an object to move in the direction of the force. It can be calculated using the formula:

Work (W) = Force (F) × Distance (d) × cos(θ)

Here, θ is the angle between the force and the direction of motion.

For example, imagine you are pushing a box on the floor. If you apply a force of 10 Newtons to push the box 5 meters in the direction of the force, the work done is:

W = F × d × cos(θ) = 10 N × 5 m × cos(0°) = 50 Joules

This is because the force and velocity are in the same direction (angle 0°), and cos(0°) is 1.

What is energy?

Energy is the capacity to do work. It exists in various forms, such as kinetic energy, potential energy, thermal energy, and more. In the context of the work-energy theorem, we are mostly concerned with kinetic energy.

Kinetic energy

Kinetic energy is the energy produced by an object due to its motion. It depends on the mass and velocity of the object and is calculated using the following formula:

Kinetic Energy (KE) = 0.5 × Mass (m) × Velocity (v)^2

For example, if a 2-kg object is moving at a velocity of 3 m/s, its kinetic energy is:

KE = 0.5 × 2 kg × (3 m/s)^2 = 9 Joules

What is power?

Power is the rate at which work is done or energy is transferred. It is measured in watts (W) and can be calculated using the formula:

Power (P) = Work (W) / Time (t)

For example, if 100 joules of work is done in 5 seconds, the power is:

P = 100 Joules / 5 s = 20 Watts

Explanation of the work-energy theorem

According to the work-energy theorem, the work done by the net force applied on an object is equal to the change in its kinetic energy. In simple words, when work is done on an object, it changes the energy of the object.

Mathematical expression

This theorem can be expressed mathematically as follows:

Work Done (W) = Change in Kinetic Energy (ΔKE)

This can be further written as:

W = KE_final - KE_initial

Where:

  • KE_final is the kinetic energy at the final state.
  • KE_initial is the kinetic energy at the initial state.

Visual example

Consider an example where a ball is rolling on a flat surface. It starts with an initial velocity, and then a force is applied to speed it up.

Initial During Final

In this illustration:

  • The left ball represents the initial kinetic state.
  • The middle ball represents the ball in motion, as work is being done on it.
  • The right ball represents the final state, where the kinetic energy has increased.

Textual examples

Let's look at a practical example where the work-energy theorem applies:

Imagine you are riding your bicycle. In the beginning, you start from rest and begin to pedal. After some time, you reach a speed of 5 m/s. The kinetic energy of the bicycle increases due to the work done by the force you apply to the pedal. We can express this scenario in equations:

Suppose the total mass of you and the bicycle is 70 kg. The initial kinetic energy when the bike is at rest is:

KE_initial = 0.5 × 70 kg × (0 m/s)^2 = 0 Joules

The final kinetic energy after reaching the speed is:

KE_final = 0.5 × 70 kg × (5 m/s)^2 = 875 Joules

So, the work done on the cycle is:

Work Done (W) = KE_final - KE_initial = 875 Joules - 0 Joules = 875 Joules

Applications of the work-energy theorem

The work–energy theorem is a fundamental principle used in a variety of applications:

In engineering

Engineers use the work-energy principle to design machines and vehicles. For example, understanding how work is converted into energy helps design more efficient engines, elevators, and moving systems.

Athletics and sports

In sports, athletes use this concept to improve their performance. For example, sprinters apply more force to increase their kinetic energy, resulting in faster speeds.

In our daily life

We unconsciously apply the work-energy theorem in our daily activities without even realizing what it is. Pushing a shopping cart, riding a bicycle to school, or even lifting books all involve work, which leads to a change in kinetic energy.

Space probes

The theorem's application also extends to space exploration, where it helps calculate fuel requirements to change a spacecraft's velocity.

Conclusion

The work-energy theorem provides an important relationship between applied force and changes in momentum. Its implications extend from everyday phenomena to complex engineering designs. By understanding how work affects energy, you can better understand motion and the mechanics that underpin the world around us.

With this knowledge, you are now equipped to study topics in physics in more depth, and lay a solid foundation for how energy and work interact to produce motion and do work.


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Work–energy theorem

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