391 lines
12 KiB
Text
391 lines
12 KiB
Text
[
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{
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"name": "Temperature converter",
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"description": "Example of simple formula, just unit conversion",
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"input": [
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{"name": "Input", "unit": "Kelvin" }
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],
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"output": {"name": "Output", "unit": "Kelvin" },
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"d4rtCode": "Output = Input;",
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"tags": ["converter", "temperature" ]
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},
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// Free fall distance (vertical)
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{
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"name": "Free Fall Distance",
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"description": r"""
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Calculates vertical displacement under constant gravity
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$$h = \frac{1}{2}gt^2$$
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Where:
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- $g$: Gravitational acceleration $9.81\ \mathrm{m/s^2}$ on Earth
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- $t$: Time in free fall (seconds)
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""",
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"input": [
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{"name": "t", "unit": "second"}, // Time in seconds
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{"name": "g", "unit": "meters per second"} // Gravitational acceleration
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],
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"output": {"name": "h", "unit": "meter"}, // Height in meters
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"d4rtCode": "h = 0.5 * g * pow(t, 2);",
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"tags": ["physics", "kinematics"]
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},
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// Newton's Law of Universal Gravitation
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{
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"name": "Gravitational Force",
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"description": r'''
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Newton's law of universal gravitation
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\(F = G\frac{m_1m_2}{r^2}\)
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Where:
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- $G$: Gravitational constant ($6.674\times 10^{-11}\ \mathrm{N\cdot m^2/kg^2}$)
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- $m_1, m_2$: Masses of two objects
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- $r$: Distance between centers of masses
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''',
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"input": [
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{"name": "m1", "unit": "kilogram"}, // Mass 1
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{"name": "m2", "unit": "kilogram"}, // Mass 2
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{"name": "r", "unit": "meter"} // Distance between masses
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],
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"output": {"name": "F", "unit": "newton"}, // Force in newtons
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"d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);",
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"tags": ["physics", "astronomy", "gravity"]
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},
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// Kinetic Energy
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{
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"name": "Kinetic Energy",
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"description": r'''
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Energy possessed by a moving object
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$$KE = \frac{1}{2}mv^2$$
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Where:
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- $m$: Mass of object
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- $v$: Velocity of object
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''',
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"input": [
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{"name": "m", "unit": "kilogram"}, // Mass
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{"name": "v", "unit": "meters per second"} // Velocity
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],
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"output": {"name": "KE", "unit": "joule"}, // Energy in joules
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"d4rtCode": "KE = 0.5 * m * pow(v, 2);",
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"tags": ["physics", "energy", "mechanics"]
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},
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// Projectile Motion Range
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{
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"name": "Projectile Range",
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"description": r"""Calculates horizontal distance of projectile motion
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$$R = \frac{v^2 \sin(2\theta)}{g}$$
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Where:
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- $v$: Initial velocity
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- $\theta$: Launch angle
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- $g$: Gravitational acceleration
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""",
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"input": [
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{"name": "v", "unit": "meters per second"}, // Initial velocity
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{"name": "a", "unit": "degree"} // Launch angle
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],
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"output": {"name": "R", "unit": "meter"}, // Horizontal distance
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"d4rtCode": """
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var radians = a * (pi / 180);
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R = (pow(v, 2) * sin(2 * radians)) / 9.80665;
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""",
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"tags": ["physics", "kinematics", "projectile"]
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},
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{
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"name": "Newton's Second Law",
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"description": r'''
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Force equals mass times acceleration
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$$F = m \cdot a$$
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Where:
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- $m$: Mass of object ($\mathrm{kg}$)
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- $a$: Acceleration ($\mathrm{m/s^2}$)
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''',
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"input": [
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{"name": "m", "unit": "kilogram"}, // Mass
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{"name": "a", "unit": "meters per square second"} // Acceleration
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],
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"output": {"name": "F", "unit": "newton"}, // Force in newtons
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"d4rtCode": "F = m * a;",
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"tags": ["physics", "mechanics", "newton"]
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},
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// Apgar Score
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{
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"name": "Apgar Score",
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"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",
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"input": [
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{"name": "HeartRate", "values": ["Absent", "< 100 bpm>", "> 100 bpm"] },
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{"name": "Breathing", "values": ["Absent", "Weak, irregular", "Strong, robust cry"] },
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{"name": "MuscleTone", "values": ["None", "Some", "Flexed arms/leg, resists extension"] },
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{"name": "Reflexes", "values": ["No response", "Grimace on aggressive stimulation", "Cry on stimulation"] },
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{"name": "SkinColor", "values": ["Blue or pale", "Blue extremities, pink body", "Pink"] }
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],
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"output": {"name": "Result", "unit": "string"},
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"d4rtCode": """
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var total = indexOf("HeartRate") + indexOf("Breathing") + indexOf("MuscleTone") + indexOf("Reflexes") + indexOf("SkinColor");
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late var interpretation;
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if( total < 4 ) {
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interpretation = 'Critical condition';
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}
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else if( total < 7 ){
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interpretation = 'Needs assistance';
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}
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else {
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interpretation = 'Normal';
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}
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Result = 'Score: \$total - \$interpretation';
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""",
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"tags": ["medical", "pediatrics", "assessment"]
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}
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,
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{
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"name": "Compare price per mass",
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"description": "Compares two products by their price per mass and returns which is cheaper, including price per kg for each product.",
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"input": [
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{"name": "price1", "unit": "currency"},
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{"name": "mass1", "unit": "kilogram"},
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{"name": "price2", "unit": "currency"},
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{"name": "mass2", "unit": "kilogram"}
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],
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"output": {"name": "Result", "unit": "string"},
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"d4rtCode": """
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var p1 = price1 / mass1;
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var p2 = price2 / mass2;
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if (p1 < p2) {
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Result = 'first product is cheaper at \${p1.toStringAsFixed(2)} currency/kg vs \${p2.toStringAsFixed(2)} currency/kg';
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} else if (p2 < p1) {
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Result = 'second product is cheaper at \${p2.toStringAsFixed(2)} currency/kg vs \${p1.toStringAsFixed(2)} currency/kg';
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} else {
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Result = 'both products have the same price per mass at \${p1.toStringAsFixed(2)} currency/kg';
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}
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""",
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"tags": ["comparison", "shopping", "economics"]
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}
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,
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// Einstein's Mass-Energy Equivalence
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{
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"name": "Mass-Energy Equivalence",
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"description": r'''
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Einstein's famous equation showing the relationship between mass and energy
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$$E = mc^2$$
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Where:
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- $E$: Energy (Joules)
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- $m$: Mass (kilograms)
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- $c$: Speed of light $299,792,458$ $\mathrm{m/s}$
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This equation shows that mass can be converted to energy and vice versa.''',
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"input": [
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{"name": "m", "unit": "kilogram"} // Mass
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],
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"output": {"name": "E", "unit": "joule"}, // Energy
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"d4rtCode": "E = m * pow(299792458, 2);",
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"tags": ["physics", "relativity", "energy"]
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},
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// Ohm's Law
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{
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"name": "Ohm's Law",
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"description": r'''
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Relationship between voltage, current, and resistance in electrical circuits
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$$V = IR$$
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Where:
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- $V$: Voltage (Volts)
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- $I$: Current (Amperes)
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- $R$: Resistance (Ohms)
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This fundamental law describes how current flows through resistive materials.''',
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"input": [
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{"name": "I", "unit": "ampere"}, // Current
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{"name": "R", "unit": "ohm"} // Resistance
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],
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"output": {"name": "V", "unit": "volt"}, // Voltage
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"d4rtCode": "V = I * R;",
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"tags": ["physics", "electricity", "electronics"]
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},
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// Hooke's Law
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{
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"name": "Hooke's Law",
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"description": r'''
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Force exerted by a spring is proportional to its displacement
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$$F = -kx$$
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Where:
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- $F$: Restoring force (Newtons)
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- $k$: Spring constant (N/m)
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- $x$: Displacement from equilibrium (meters)
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The negative sign indicates the force opposes the displacement.''',
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"input": [
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{"name": "k", "unit": "newton per meter"}, // Spring constant
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{"name": "x", "unit": "meter"} // Displacement
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],
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"output": {"name": "F", "unit": "newton"}, // Force
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"d4rtCode": "F = -k * x;",
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"tags": ["physics", "elasticity", "oscillations"]
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},
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// Centripetal Force
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{
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"name": "Centripetal Force",
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"description": r'''
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Force required to keep an object moving in circular motion
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$$F = \frac{mv^2}{r}$$
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Where:
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- $F$: Centripetal force (Newtons)
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- $m$: Mass of object (kilograms)
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- $v$: Velocity (m/s)
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- $r$: Radius of circular path (meters)
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This force acts toward the center of the circle.''',
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"input": [
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{"name": "m", "unit": "kilogram"}, // Mass
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{"name": "v", "unit": "meters per second"}, // Velocity
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{"name": "r", "unit": "meter"} // Radius
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],
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"output": {"name": "F", "unit": "newton"}, // Force
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"d4rtCode": "F = (m * pow(v, 2)) / r;",
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"tags": ["physics", "circular motion", "centripetal"]
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},
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// Wave Equation
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{
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"name": "Wave Equation",
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"description": r'''
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Relationship between wave speed, frequency, and wavelength
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$$v = f\lambda$$
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Where:
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- $v$: Wave speed (m/s)
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- $f$: Frequency (Hertz)
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- $\lambda$: Wavelength (meters)
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This applies to all types of waves including sound and light.''',
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"input": [
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{"name": "f", "unit": "hertz"}, // Frequency
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{"name": "lambda", "unit": "meter"} // Wavelength
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],
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"output": {"name": "v", "unit": "meters per second"}, // Wave speed
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"d4rtCode": "v = f * lambda;",
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"tags": ["physics", "waves", "frequency"]
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},
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// Pythagorean Theorem
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{
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"name": "Pythagorean Theorem",
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"description": r'''
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Fundamental relation in Euclidean geometry among the three sides of a right triangle
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$$a^2 + b^2 = c^2$$
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Where:
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- $a$, $b$: Legs of the right triangle
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- $c$: Hypotenuse of the right triangle
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The square of the hypotenuse is equal to the sum of squares of the other two sides.''',
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"input": [
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{"name": "a", "unit": "meter"}, // First leg
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{"name": "b", "unit": "meter"} // Second leg
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],
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"output": {"name": "c", "unit": "meter"}, // Hypotenuse
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"d4rtCode": "c = sqrt(pow(a, 2) + pow(b, 2));",
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"tags": ["trigonometry", "geometry", "pythagorean"]
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},
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// Sine Rule
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{
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"name": "Sine Rule",
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"description": r'''
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Relationship between the sides and angles of any triangle
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$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
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Where:
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- $a$, $b$, $c$: Sides of the triangle
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- $A$, $B$, $C$: Angles opposite to sides $a$, $b$, $c$ respectively
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This rule is useful for solving triangles when certain combinations of angles and sides are known.''',
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"input": [
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{"name": "a", "unit": "meter"}, // Side a
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{"name": "A", "unit": "degree"}, // Angle A in degrees
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{"name": "B", "unit": "degree"} // Angle B in degrees
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],
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"output": {"name": "b", "unit": "meter"}, // Side b
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"d4rtCode": """
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var angleARad = A * (pi / 180);
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var angleBRad = B * (pi / 180);
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b = (a * sin(angleBRad)) / sin(angleARad);
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""",
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"tags": ["trigonometry", "triangle", "sine"]
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},
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// Cosine Rule
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{
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"name": "Cosine Rule",
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"description": r'''
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Generalization of the Pythagorean theorem for any triangle
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$$c^2 = a^2 + b^2 - 2ab\cos(C)$$
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Where:
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- $a$, $b$, $c$: Sides of the triangle
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- $C$: Angle opposite to side $c$
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This rule relates all three sides of a triangle to one of its angles.''',
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"input": [
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{"name": "a", "unit": "meter"}, // Side a
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{"name": "b", "unit": "meter"}, // Side b
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{"name": "C", "unit": "degree"} // Angle C in degrees
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],
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"output": {"name": "c", "unit": "meter"}, // Side c
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"d4rtCode": """
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var angleCRad = C * (pi / 180);
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c = sqrt(pow(a, 2) + pow(b, 2) - 2*a*b*cos(angleCRad));
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""",
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"tags": ["trigonometry", "triangle", "cosine"]
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},
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// Trigonometric Identity
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{
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"name": "Trigonometric Identity",
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"description": r'''
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Fundamental Pythagorean identity in trigonometry
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$$\sin^2(\theta) + \cos^2(\theta) = 1$$
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Where:
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- $\theta$: Any angle in radians or degrees
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This identity is derived from the Pythagorean theorem applied to the unit circle.''',
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"input": [
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{"name": "theta", "unit": "degree"} // Angle in degrees
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],
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"output": {"name": "result", "unit": "scalar"}, // Result (should be 1)
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"d4rtCode": """
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var thetaRad = theta * (pi / 180);
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result = pow(sin(thetaRad), 2) + pow(cos(thetaRad), 2);
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""",
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"tags": ["trigonometry", "identity", "sine", "cosine"]
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}
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]
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