d4t_formulas/assets/formulas/energy_and_power.d4rt

[
  {"name":"Kinetic Energy","description":r"""
Energy possessed by a moving object.

$$KE = \frac{1}{2}mv^2$$

Where:
- $m$: Mass (kg)
- $v$: Velocity (m/s)

![Kinetic energy (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Kinetic_energy.svg/1200px-Kinetic_energy.svg.png)
""","input":[{"name":"m","unit":"kilogram"},{"name":"v","unit":"meters per second"}],"output":{"name":"KE","unit":"joule"},"d4rtCode":"KE = 0.5 * m * pow(v, 2);","tags":["physics","energy","mechanics"]},
  {"name":"Work","description":r"""
Energy transferred when a force moves an object.

$$W = F d \cos(\theta)$$

Where:
- $W$: Work (Joules)
- $F$: Force (Newtons)
- $d$: Displacement (meters)
- $\theta$: Angle between force and displacement

![Work (diagram) (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Work.svg/800px-Work.svg.png)
""","input":[{"name":"F","unit":"newton"},{"name":"d","unit":"meter"},{"name":"theta","unit":"degree"}],"output":{"name":"W","unit":"joule"},"d4rtCode":"var thetaRad = theta * (pi / 180); W = F * d * cos(thetaRad);","tags":["physics","energy","mechanics"]},
  {"name":"Power","description":r"""
Rate at which work is done or energy is transferred.

$$P = \frac{W}{t}$$

Where:
- $P$: Power (Watts)
- $W$: Work or energy (Joules)
- $t$: Time (seconds)

![Power (diagram) (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/9/90/Power_equation.svg/800px-Power_equation.svg.png)
""","input":[{"name":"W","unit":"joule"},{"name":"t","unit":"second"}],"output":{"name":"P","unit":"watt"},"d4rtCode":"P = W / t;","tags":["physics","energy","mechanics"]},
  {"name":"Mass-Energy Equivalence","description":r"""
Einstein's mass-energy equivalence relation.

$$E = mc^2$$

Where:
- $E$: Energy (Joules)
- $m$: Mass (kg)
- $c$: Speed of light $299{,}792{,}458\ \mathrm{m/s}$

This shows mass can be converted to energy and vice versa.

![Einstein formula (Wikipedia)](https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/Einstein_light_beam.svg/800px-Einstein_light_beam.svg.png)
""","input":[{"name":"m","unit":"kilogram"}],"output":{"name":"E","unit":"joule"},"d4rtCode":"E = m * pow(299792458, 2);","tags":["physics","relativity","energy"]}
]