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 → Simple machines ↓


Machine efficiency


When we talk about machines in physics, we are essentially dealing with devices that help us do work more easily. Machines have been a vital part of human progress because they enable us to perform tasks that would otherwise be very difficult, if not impossible. Think of things like pulleys, levers, and inclined planes. These simple machines allow us to multiply force and overcome resistance, making our daily tasks more manageable.

What is efficiency?

The term "efficiency" in the context of machines means how well the machine converts input energy into useful output energy. When we feed energy to a machine, not all of that energy is converted into useful work. Some of it is often lost as heat due to friction. Efficiency is a way of measuring this conversion process and tells us how much of the input energy is actually used for the intended purpose.

Mathematically, efficiency is expressed as:

Efficiency (%) = (Useful Output Energy / Input Energy) * 100

If a machine has high efficiency, it means that most of the input energy is being converted into output work, and very little energy is being wasted. Conversely, if the machine is less efficient, a large portion of the input energy is being wasted.

Expressing efficiency with force and work

In the case of machines such as levers or inclined planes, efficiency can be expressed in terms of force and distance:

Efficiency (%) = (Work Output / Work Input) * 100

In terms of mechanics, work is the product of force and distance:

Work = Force x Distance

This means that for any given machine:

Work Input = Input Force x Input Distance
Work Output = Output Force x Output Distance

Example: efficiency of a lever

Let's consider a lever, which is a simple machine. Imagine you have a lever to lift a heavy stone.

Input ForceBaseOutput Force

In this scenario, the input work is provided by the person pulling down on one end of the lever. The output work is the lifting of the stone at the other end. We can calculate the efficiency of the lever by comparing these two work quantities.

Suppose you apply an input force of 10 N at a distance of 5 meters. The work input can be calculated as:

Work Input = 10 N * 5 m = 50 Joules

Now, suppose the lever lifts the stone with an output force of 25 N, but only lifts it 1 meter. The work output is:

Work Output = 25 N * 1 m = 25 Joules

Thus, the efficiency of the lever is:

Efficiency = (25/50) * 100 = 50%

This means that only half of the input energy is utilised in lifting the stone while the remaining energy is lost due to friction and other resistances.

Another example: efficiency of an inclined plane

Consider an inclined plane, a simple machine that enables you to raise an object to a greater height with less effort than lifting it vertically.

inclined planeHeight

Suppose you are trying to push a box weighing 20 N up a height of 2 meters. The force required to push the box all the way up is 10 N, and the length of the slope is 5 meters.

The task input is:

Work Input = 10 N * 5 m = 50 Joules

The work required to lift the box vertically is:

Work Output = 20 N * 2 m = 40 Joules

The efficiency of using the inclined plane is:

Efficiency = (40/50) * 100 = 80%

This means that 80% of your effort goes into lifting the box, and the rest of the effort is wasted mainly due to friction on the slope.

Why are machines never 100% efficient?

Even the best-designed machines lose some energy during operation. This is mainly due to friction, which converts a portion of the energy into heat. The smoother the contact surface, the less friction, but it can never be completely eliminated.

In real-world applications, factors such as air resistance, deformation of materials, and sound emissions also contribute to energy losses. This is why no mechanical system can achieve 100% efficiency. Engineers and designers constantly work to reduce these losses to improve the efficiency of machines.

Increasing the efficiency of the machine

Though it is impossible to achieve perfect efficiency, steps can be taken to improve the efficiency of a machine:

  • Reducing friction through lubrication.
  • Using light and stiff materials to minimise distortion.
  • Improving aerodynamic design to reduce air resistance.

Conclusion

Efficiency is an important concept in understanding how machines work and how they can be improved. Even though simple machines such as levers and inclined planes are not perfectly efficient due to energy losses, they still play an essential role in making tasks easier by reducing the amount of human effort required. By understanding and improving efficiency, we can better design and use machines to do work more effectively.


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Machine efficiency

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