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Energy, Work, Power

Energy​

In physics, energy, as a quantitative property of a physical system, represents the capacity of a system to do work and cause movement. It is an abstract notation conserved in an isolated system, related to physical configuration of a system, and indispensable for understanding and creating modern tools, such as light bulb, fridge, car, and computer.

The SI unit of energy is joule: J=N⋅m=kg⋅m2/s2J=N\cdot m=kg\cdot m^2/s^2. Raising an apple one meter in the air is about 1 J of work. We often denote the amount of calories in food and beverage. 1 calorie (sometimes, Cal or kcal) equals to 4184 J = 4.184 kJ. Here are some typical ways to classify forces.

By motion​

  • Kinetic energy: energy related to the motion of an object
  • Potential energy: energy stored in the "position" of an object

By source​

  • Gravitational energy: potential energy related to the gravitational field
  • Elastic energy: potential energy related to restorative force under deformation
  • Radiant energy: potential energy related to electromagnetic radiation
  • Thermal energy: potential energy related to temperature change
  • Chemical energy: potential energy related to chemical bonds
  • Electrical energy: potential energy related to electric fields
  • Magnetic energy: potential energy related to magnetic fields
  • Nuclear energy: potential energy related to binding of nucleons in atoms
  • Chromodynamic energy: potential energy related to binding of quarks in hadrons
  • Rest energy: potential energy related to the rest mass of an object

Work​

In physics, work is the energy transferred from or to an object via the application of force along a displacement. It is a scalar quantity with the SI unit of joule (J). Its core definition is

W=∫F⃗⋅ds⃗W=\int \vec{F}\cdot d\vec{s}

where F⃗\vec{F} is the force along a path and ds⃗d\vec{s} is the infinitesimal displacement along a path, and ⋅\cdot is the dot product between two vectors.

If the force is constant in magnitude and in direction, and the displacement does not change direction, then we can simplify

W=Fscos⁡θW=Fs\cos\theta

where θ\theta is the angle between the direction of the force and the direction of the displacement.

fit

Power​

In physics, power is the rate of change of work done, the amount of energy transferred via the application of force per unit time.

P=dWdt=F⃗⋅v⃗P=\frac{dW}{dt}=\vec{F}\cdot \vec{v}

where F⃗\vec{F} is the force at a given moment and v⃗\vec{v} is the velocity at a given moment. It has the SI unit of watt W=J/s=kg⋅m2/s3W=J/s=kg\cdot m^2/s^3.

In the previous illustration, if the box moves a distance of ss to the right during a time of tt by a force FF with an angle of θ\theta to the horizontal direction, then the average power of FF is

P‾=Wt=Fscos⁡θt\overline{P}=\frac{W}{t}=\frac{Fs\cos\theta}{t}