109 lines
3.6 KiB
Text
109 lines
3.6 KiB
Text
[
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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": '''
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Calculates vertical displacement under constant gravity
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`h = ½gt²`
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Where:
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- `g` = Gravitational acceleration (9.81 m/s² 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": '''
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Newton's law of universal gravitation
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`F = G(m₁m₂)/r²`
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Where:
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- `G` = Gravitational constant (6.674×10⁻¹¹ N·m²/kg²)
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- `m₁`, `m₂` = 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": '''
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Energy possessed by a moving object
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`KE = ½mv²`
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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": "Calculates horizontal distance of projectile motion\n\n"
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"`R = (v² sin(2θ))/g`\n\n"
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"Where:\n"
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"- `v` = Initial velocity\n"
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"- `θ` = Launch angle\n"
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"- `g` = Gravitational acceleration\n\n"
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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": "θ", "unit": "degree"} // Launch angle
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],
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"output": {"name": "R", "unit": "meter"}, // Horizontal distance
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"d4rtCode": "R = (pow(v, 2) * sin(2 * radians(θ))) / 9.80665;",
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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": '''
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Force equals mass times acceleration
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`F = m * a`
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Where:
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- `m` = Mass of object (kg)
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- `a` = Acceleration (m/s²)
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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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]
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