Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics → Work, Energy and Power ↓


Efficiency of machines


Machines are a fundamental part of our everyday lives, helping us to do work more efficiently. In physics, particularly in the study of work, energy, and power, it is important to understand the efficiency of machines. Efficiency generally tells us how well a machine is converting the energy put into it into useful work or output energy.

Efficiency is defined as the ratio of useful work output to total work input, usually expressed as a percentage:

Efficiency (%) = (Useful Work Output / Total Work Input) × 100

Understanding work in machines

In physics, work is done when a force is applied to an object, and the object moves in the direction of the force. The formula for work is:

Work = Force × Distance × cos(θ)

Where:

  • Force is the force applied to the object (in Newtons).
  • Distance is the distance the object moves (in meters).
  • θ is the angle between the force and the direction of motion.

For machines, work input is the work done on the machine, while work output is the work done by the machine. Efficiency can help us determine how much energy is typically wasted due to friction and heat.

Energy and power in machines

Energy is the capacity to do work. Machines convert energy from one form to another. For example, an engine can convert chemical energy (from fuel) into mechanical energy (motion).

Power is the rate at which work is done or energy is transferred. It is defined as:

Power = Work / Time

Where power is measured in watts (W), work is measured in joules (J), and time is measured in seconds (s). For machines, improving efficiency means more power output for the same power input, or conversely, less power input for the same power output.

To understand efficiency better, let's look at some examples and illustrations.

Example 1: Lever efficiency

Consider a simple lever, one of the basic machines. Levers allow a person to lift heavy loads with little effort. Suppose you use a lever to lift a 200 N weight a distance of 1 m. The effort force applied over a distance of 4 m is 50 N.

Total Work Input:

Work Input = Effort Force × Effort Distance = 50 N × 4 m = 200 J

Useful work output (equal to work done on the load):

Work Output = Load Force × Load Distance = 200 N × 1 m = 200 J

Now, let us calculate the efficiency:

Efficiency (%) = (Work Output / Work Input) × 100 = (200 J / 200 J) × 100 = 100%

This idealized calculation assumes a frictionless environment. In real-life scenarios, the efficiency will be low due to friction and other resistive forces causing energy to be lost as heat.

Effort (50N) Load (200N)

Example 2: Inclined plane efficiency

Consider using an inclined plane to load a heavy object onto a truck. The load weighs 500 N, and the incline is 5 m long by 1 m high. By applying force parallel to the incline, you can move the load with less force.

Without inclination, lifting straight up would require 500 N (500 J) per 1 m. Let's calculate the work required using an inclined plane.

Suppose you apply a force of 125 N to the plane:

Total Work Input:

Work Input = Force × Distance = 125 N × 5 m = 625 J

Useful work output (work done on the load):

Work Output = Load × Vertical Distance = 500 N × 1 m = 500 J

Calculate the efficiency:

Efficiency (%) = (Work Output / Work Input) × 100 = (500 J / 625 J) × 100 = 80%

20% of the inefficiency is produced by the friction between the object and the inclined plane.

125N 1m 5m

Energy loss and real world efficiency

Perfect machines do not exist. In the real world, various factors contribute to low efficiency, such as friction, air resistance, electrical resistance, heat dissipation, etc. Understanding these losses helps in designing better machines that attempt to minimize energy loss.

Consider an automobile engine. It converts fuel (chemical energy) into mechanical energy to drive the car. Some energy is also lost to heat, sound, and friction. Engineers analyze these energy transformations to improve the engine's efficiency.

Example 3: Efficiency of an automobile engine

Suppose an automobile engine has a thermal energy input of 1000 joules (J) of fuel energy. However, only 250 joules are converted into mechanical work. The efficiency of the engine is calculated as:

Efficiency (%) = (250 J / 1000 J) × 100 = 25%

This means that 75% of the energy is lost primarily as heat. Engineers work to reduce these losses to improve vehicle fuel efficiency, leading to innovations such as hybrid and electric powertrains.

Efficiency in electrical machines

Electrical machines also deal with efficiency issues. Consider electric motors. They convert electrical energy into mechanical work. Losses include electrical resistance in wires and friction in moving parts, among other things.

When you plug in an electric device such as a motor, you are supplying electricity to it. How efficiently the motor converts this electricity determines its practicality in real life.

Example 4: Electric motor efficiency

Suppose an electric motor receives 500 W of electrical power and delivers 450 W of mechanical power. Let's determine its efficiency.

Efficiency (%) = (450 W / 500 W) × 100 = 90%

This means that 10% of the power is not used for work, but is possibly lost due to resistance and friction in the circuit.

Visual conclusion on efficiency

Efficiency is vital in designing and using machines. It defines how effectively a machine does the work it is designed to do. In examples such as our lever and inclined plane diagrams, we see that machines can change the force distribution and reduce the effort required to do work, but this can result in energy losses.

By understanding efficiency, scientists and engineers improve the quality of life through more efficient engines, motors, and other machines, saving both energy and resources, which is vital to sustainable development.

As you explore this concept in your physics studies, keep in mind everyday applications where efficiency plays a critical role, from household appliances to large industrial systems.


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Efficiency of machines

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