d4t_formulas/assets/formulas/energy_and_power.d4rt

[
  // Kinetic Energy
  {
    "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"]
  },

  // Work
  {
    "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"]
  },

  // Power
  {
    "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"]
  },

  // Mass-Energy Equivalence
  {
    "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"]
  }
]