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 done by constant and variable force


In the world of physics, the concepts of work, energy, and power help us understand how and why things move. These ideas are fundamental to explaining the natural world, from the motion of planets to the flip of a simple switch. Let's delve deeper into the topic of work, focusing specifically on the work done by constant and variable forces.

Understanding the work

In everyday language, "work" can mean any task that we have to complete. However, in physics, work has a specific definition. Work is done when a force causes an object to move. The formula to calculate work is:

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

Here:

  • Work (W) is the work done which is measured in Joules (J).
  • Force (F) is the force applied which is measured in Newtons (N).
  • Distance (d) is the distance moved in the direction of the force, measured in meters (m).
  • θ is the angle between the force and the direction of motion.

Visual example

F D θ

In this figure, a force F is applied at an angle θ to move an object a distance d.

Work done by a constant force

When the force acting on an object remains constant in both magnitude and direction while the object is moving, the formula for work becomes simple. Let's assume that the direction of force and speed are the same, which means θ = 0 degrees. Then we have:

Work (W) = Force (F) × Distance (d)

This position typically involves straightforward scenarios, such as pushing a cart, pulling a box, or lifting an object at a steady speed.
For example, if you push a trolley a distance of 5 m with a force of 20 N, the work done will be 100 J.

Example

Imagine you are pushing a box on a level floor:

  • Force (F): 10N
  • Distance (d): 5 meters

Calculate the work done using the formula:

Work = 10 N × 5 m = 50 J

Thus, you have done 50 joules of work in lifting the box up.

Work done by a variable force

Most real-world scenarios involve forces that change in magnitude and/or direction as the object moves. This is where the concept of work done by a changing force comes into play.

Imagine a force F graphed against a distance d. The area under the force-distance graph represents the work done by a variable force.

Visual concept

Distance (d) Force(F)

This graph shows that the force also changes with the speed of the object, making calculating work more complicated.

Brief summary

To calculate the work done by a variable force:

  • Divide the distance into smaller intervals where the force can be considered constant.
  • Calculate the work done in each interval.
  • Add up all the small tasks performed to find the total work.

In mathematical terms, this process is known as integration. For a variable force, the work done is given by the integral:

Work (W) = ∫ F(x) dx

where F(x) is the force as a function of position x.

Example

Suppose a force acts on an object as follows:
F(x) = 3x + 2, from x = 0 to x = 4.

To find the work done:

Work (W) = ∫ from 0 to 4 (3x + 2) dx = [1.5x² + 2x] from 0 to 4 = (1.5(4)² + 2(4)) - (1.5(0)² + 2(0)) = (24 + 8) - 0 = 32 J

Thus, the work done by the variable force is 32 joules.

Applications in real life

Understanding work, whether it is constant or variable, is important in designing mechanisms and structures that use energy efficiently. Beyond the physics classroom:

  • Car engines have to convert fuel into work to run the vehicles.
  • Roller coasters rely on the work done by gravity and resistance forces.
  • Cranes and elevators use working principles to safely lift goods and people.

Conclusion

The concept of work, especially differentiating between constant and variable forces, helps to understand energy transfer in different systems. Whether it is pushing a box or calculating force at different inclinations, mastering these concepts will lead to a deeper understanding of the physical world around us.


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Work done by constant and variable force

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