112 lines
3.7 KiB
Text
112 lines
3.7 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": 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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]
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