176 lines
6.2 KiB
Text
176 lines
6.2 KiB
Text
[
|
|
|
|
{
|
|
"name": "Temperature converter",
|
|
"description": "Example of simple formula, just unit conversion",
|
|
"input": [
|
|
{"name": "Input", "unit": "Kelvin" }
|
|
],
|
|
"output": {"name": "Output", "unit": "Kelvin" },
|
|
"d4rtCode": "Output = Input;",
|
|
"tags": ["converter", "temperature" ]
|
|
},
|
|
// Free fall distance (vertical)
|
|
{
|
|
"name": "Free Fall Distance",
|
|
"description": r"""
|
|
Calculates vertical displacement under constant gravity
|
|
|
|
$$h = \\frac{1}{2}gt^2$$
|
|
|
|
Where:
|
|
- $g$: Gravitational acceleration ($9.81\\ \\mathrm{m/s^2}$ on Earth)
|
|
- $t$: Time in free fall (seconds)
|
|
|
|
""",
|
|
"input": [
|
|
{"name": "t", "unit": "second"}, // Time in seconds
|
|
{"name": "g", "unit": "meters per second"} // Gravitational acceleration
|
|
],
|
|
"output": {"name": "h", "unit": "meter"}, // Height in meters
|
|
"d4rtCode": "h = 0.5 * g * pow(t, 2);",
|
|
"tags": ["physics", "kinematics"]
|
|
},
|
|
|
|
// Newton's Law of Universal Gravitation
|
|
{
|
|
"name": "Gravitational Force",
|
|
"description": r'''
|
|
Newton's law of universal gravitation
|
|
|
|
\(F = G\\frac{m_1m_2}{r^2}\)
|
|
|
|
Where:
|
|
- $G$: Gravitational constant ($6.674\\times 10^{-11}\\ \\mathrm{N\\cdot m^2/kg^2}$)
|
|
- $m_1, m_2$: Masses of two objects
|
|
- $r$: Distance between centers of masses
|
|
|
|
''',
|
|
"input": [
|
|
{"name": "m1", "unit": "kilogram"}, // Mass 1
|
|
{"name": "m2", "unit": "kilogram"}, // Mass 2
|
|
{"name": "r", "unit": "meter"} // Distance between masses
|
|
],
|
|
"output": {"name": "F", "unit": "newton"}, // Force in newtons
|
|
"d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);",
|
|
"tags": ["physics", "astronomy", "gravity"]
|
|
},
|
|
|
|
// Kinetic Energy
|
|
{
|
|
"name": "Kinetic Energy",
|
|
"description": r'''
|
|
Energy possessed by a moving object
|
|
|
|
$$KE = \\frac{1}{2}mv^2$$
|
|
|
|
Where:
|
|
- $m$: Mass of object
|
|
- $v$: Velocity of object
|
|
|
|
''',
|
|
"input": [
|
|
{"name": "m", "unit": "kilogram"}, // Mass
|
|
{"name": "v", "unit": "meters per second"} // Velocity
|
|
],
|
|
"output": {"name": "KE", "unit": "joule"}, // Energy in joules
|
|
"d4rtCode": "KE = 0.5 * m * pow(v, 2);",
|
|
"tags": ["physics", "energy", "mechanics"]
|
|
},
|
|
|
|
// Projectile Motion Range
|
|
{
|
|
"name": "Projectile Range",
|
|
"description": r"""Calculates horizontal distance of projectile motion
|
|
$$R = \\frac{v^2 \\sin(2\\theta)}{g}$$
|
|
Where:
|
|
- $v$: Initial velocity
|
|
- $\\theta$: Launch angle
|
|
- $g$: Gravitational acceleration
|
|
""",
|
|
"input": [
|
|
{"name": "v", "unit": "meters per second"}, // Initial velocity
|
|
{"name": "a", "unit": "degree"} // Launch angle
|
|
],
|
|
"output": {"name": "R", "unit": "meter"}, // Horizontal distance
|
|
"d4rtCode": """
|
|
var radians = a * (pi / 180);
|
|
R = (pow(v, 2) * sin(2 * radians)) / 9.80665;
|
|
""",
|
|
"tags": ["physics", "kinematics", "projectile"]
|
|
},
|
|
|
|
{
|
|
"name": "Newton's Second Law",
|
|
"description": r'''
|
|
Force equals mass times acceleration
|
|
|
|
$$F = m \\cdot a$$
|
|
|
|
Where:
|
|
- $m$: Mass of object ($\\mathrm{kg}$)
|
|
- $a$: Acceleration ($\\mathrm{m/s^2}$)
|
|
|
|
''',
|
|
"input": [
|
|
{"name": "m", "unit": "kilogram"}, // Mass
|
|
{"name": "a", "unit": "meters per square second"} // Acceleration
|
|
],
|
|
"output": {"name": "F", "unit": "newton"}, // Force in newtons
|
|
"d4rtCode": "F = m * a;",
|
|
"tags": ["physics", "mechanics", "newton"]
|
|
},
|
|
|
|
// Apgar Score
|
|
{
|
|
"name": "Apgar Score",
|
|
"description": "Newborn health assessment scoring system\n\nScores 0-2 for:\n1. Heart rate\n2. Breathing\n3. Muscle tone\n4. Reflexes\n5. Skin color\nTotal score 0-10",
|
|
"input": [
|
|
{"name": "HeartRate", "values": ["Absent", "< 100 bpm>", "> 100 bpm"] },
|
|
{"name": "Breathing", "values": ["Absent", "Weak, irregular", "Strong, robust cry"] },
|
|
{"name": "MuscleTone", "values": ["None", "Some", "Flexed arms/leg, resists extension"] },
|
|
{"name": "Reflexes", "values": ["No response", "Grimace on aggressive stimulation", "Cry on stimulation"] },
|
|
{"name": "SkinColor", "values": ["Blue or pale", "Blue extremities, pink body", "Pink"] }
|
|
],
|
|
"output": {"name": "Result", "unit": "string"},
|
|
"d4rtCode": """
|
|
var total = indexOf("HeartRate") + indexOf("Breathing") + indexOf("MuscleTone") + indexOf("Reflexes") + indexOf("SkinColor");
|
|
late var interpretation;
|
|
if( total < 4 ) {
|
|
interpretation = 'Critical condition';
|
|
}
|
|
else if( total < 7 ){
|
|
interpretation = 'Needs assistance';
|
|
}
|
|
else {
|
|
interpretation = 'Normal';
|
|
}
|
|
Result = 'Score: \$total - \$interpretation';
|
|
""",
|
|
"tags": ["medical", "pediatrics", "assessment"]
|
|
}
|
|
,
|
|
{
|
|
"name": "Compare price per mass",
|
|
"description": "Compares two products by their price per mass and returns which is cheaper, including price per kg for each product.",
|
|
"input": [
|
|
{"name": "price1", "unit": "currency"},
|
|
{"name": "mass1", "unit": "kilogram"},
|
|
{"name": "price2", "unit": "currency"},
|
|
{"name": "mass2", "unit": "kilogram"}
|
|
],
|
|
"output": {"name": "Result", "unit": "string"},
|
|
"d4rtCode": """
|
|
var p1 = price1 / mass1;
|
|
var p2 = price2 / mass2;
|
|
if (p1 < p2) {
|
|
Result = 'first product is cheaper at \${p1.toStringAsFixed(2)} currency/kg vs \${p2.toStringAsFixed(2)} currency/kg';
|
|
} else if (p2 < p1) {
|
|
Result = 'second product is cheaper at \${p2.toStringAsFixed(2)} currency/kg vs \${p1.toStringAsFixed(2)} currency/kg';
|
|
} else {
|
|
Result = 'both products have the same price per mass at \${p1.toStringAsFixed(2)} currency/kg';
|
|
}
|
|
""",
|
|
"tags": ["comparison", "shopping", "economics"]
|
|
}
|
|
]
|