Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Work and Energy ↓


Power and efficiency


In classical mechanics, the concepts of work, power, and efficiency are fundamental in understanding how forces interact with objects and how energy is transferred or transformed. Let us delve deeper into the intricacies of power and efficiency, discussing their definitions, examples, and real-world applications in detail.

Work in physics

Before we discuss power and efficiency, it is important to understand what work means in the context of physics. In physics, work is defined as the process of energy transfer that occurs when an object is moved a distance by an external force. The basic equation for work is:

W = F × d × cos(θ)

Here, W represents work, F is the magnitude of the applied force, d is the displacement of the object, and θ is the angle between the direction of force and the direction of displacement.

Example of work

Suppose you push a book across a table a distance of 2 meters with a force of 10 newtons. If the force you apply is in the direction of motion, the angle θ is 0, and:

W = 10 N × 2 m × cos(0) = 20 Joules

Since cos(0) = 1, the full force contributes to the work done, resulting in 20 joules of work.

Defining power

Power is the rate at which work is done or energy is transferred over time. In simple terms, it measures how quickly energy is being used or transferred. The formula for average power is:

P = W / t

Where P is power, W is the work done or energy transferred, and t is the time taken to do the work.

Instantaneous power

While average power gives the average rate of work over a time interval, instantaneous power gives the rate at any given instant. In calculus terms, instantaneous power is the derivative of work with respect to time:

P = dW/dt

This helps to understand how power may change at specific points during task performance.

Power unit

The standard unit of power in the International System of Units (SI) is the watt (W), where 1 watt is equal to 1 joule per second (1 W = 1 J/s).

Example of power

Imagine lifting a mass weighing 50 kg using a motor. If the motor lifts the mass to a height of 10 m in 5 seconds, the work done can be calculated using the force of gravity:

W = m × g × h = 50 kg × 9.8 m/s² × 10 m = 4900 Joules

The average power of the motor will be:

P = 4900 J / 5 s = 980 Watts

Thus, the motor generates 980 watts of power.

Visualization of power

Power = Work / Time P = W/T

Understanding efficiency

Efficiency is a measure of how well energy is converted from one form to another. It expresses the ratio of useful output energy to total input energy, often represented as a percentage. The efficiency equation is:

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

Since energy is often lost due to factors such as friction and heat, efficiency is always less than 100% in the real world.

Examples of efficiency

Consider a light bulb that consumes 60 joules of electrical energy to emit 15 joules of visible light. The remaining energy becomes heat:

Efficiency = (15 J / 60 J) × 100% = 25%

This means that the efficiency of the light bulb in converting electrical energy into light is 25%.

Visualization of efficiency

25%

Real-world applications of power and efficiency

Automobile

Cars are a practical example of power and efficiency. Engine power determines acceleration and speed, while a vehicle's fuel efficiency affects how far it can travel on a given amount of fuel.

Power plants

In power plants, efficiency affects how much of the fuel energy is converted into electrical energy. For example, coal-fired power plants often have an efficiency of 30% to 40%, meaning that a significant portion of the coal combustion energy becomes useful electricity.

Renewable energy

Technologies such as solar panels and wind turbines convert natural energy into electrical energy. Their power output and efficiency determine the power generation capabilities. For example, the efficiency of typical solar panels ranges between 15% and 20%.

Conclusion

Understanding power and efficiency provides invaluable information about how energy systems operate, which affects everything from household appliances to large-scale industrial systems. By understanding these concepts, anyone can appreciate the importance of energy conservation and innovation in creating more effective energy solutions.


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Power and efficiency

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