Add collisions

physics/collisions.py

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+"""
+Collision types and final velocities are central to physics.
+This module computes final velocities for inelastic and elastic collisions.
+It also classifies the collision type from initial and final velocities.
+
+Description: Collisions happen when two masses interact head-on.
+There are two types: inelastic and elastic. In inelastic collisions, the
+masses stick together and share one final velocity. In elastic collisions,
+momentum and kinetic energy are conserved, and masses rebound.
+Momentum is mass times velocity; kinetic energy is 1/2 mv^2.
+The collision type comes from comparing initial and final momentum and
+kinetic energy of the system.
+
+Reference: https://en.wikipedia.org/wiki/Collision
+"""
+
+
+def inelastic_collisions(
+    mass1: float, mass2: float, velocity1: float, velocity2: float
+) -> float:
+    """Calculate final velocity after a perfectly inelastic collision.
+
+    The two objects stick together and share a common final velocity.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity1: Initial velocity of the first object.
+        velocity2: Initial velocity of the second object.
+
+    Returns:
+        The final combined velocity of the two objects.
+
+    Examples:
+        >>> inelastic_collisions(2.0, 3.0, 5.0, 6.0)
+        5.6
+        >>> inelastic_collisions(9.0, 8.1, -3.2, 3.1)
+        -0.22
+    """
+    initial_momentum = (mass1 * velocity1) + (mass2 * velocity2)
+    total_mass = mass2 + mass1
+    final_velocity = round((initial_momentum / total_mass), 2)
+
+    return final_velocity
+
+
+def elastic_collisions(
+    mass1: float, mass2: float, velocity1: float, velocity2: float
+) -> str:
+    """Calculate final velocities after a perfectly elastic collision.
+
+    The collision is head-on and conserves both momentum and kinetic energy.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity1: Initial velocity of the first object.
+        velocity2: Initial velocity of the second object.
+
+    Returns:
+        A formatted string containing the final velocities of both objects.
+
+    Examples:
+        >>> elastic_collisions(1.0, 2.0, -3.0, -1.0)
+        '-0.34 ; -2.34'
+        >>> elastic_collisions(9.0, 8.1, -3.2, 3.1)
+        '2.76 ; -3.54'
+    """
+    com_velocity = inelastic_collisions(mass1, mass2, velocity1, velocity2)
+    initial_velocities = [velocity1, velocity2]
+    final_velocities = []
+
+    for vel in initial_velocities:
+        new_vel = -1 * (vel - com_velocity)
+        final_vel = com_velocity + new_vel
+        final_velocities.append(round(final_vel, 2))
+
+    return f"{final_velocities[0]} ; {final_velocities[1]}"
+
+
+def type_collision(
+    mass1: float,
+    mass2: float,
+    velocity_initial1: float,
+    velocity_initial2: float,
+    velocity_final1: float,
+    velocity_final2: float,
+) -> str:
+    """Determine the collision type from initial and final velocities.
+
+    Compares initial and final momentum and kinetic energy to classify the collision.
+
+    Parameters:
+        mass1: Mass of the first object.
+        mass2: Mass of the second object.
+        velocity_initial1: Initial velocity of the first object.
+        velocity_initial2: Initial velocity of the second object.
+        velocity_final1: Final velocity of the first object.
+        velocity_final2: Final velocity of the second object.
+
+    Returns:
+        A string describing the collision type.
+
+    Examples:
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 2.0, 3.0)
+        'Perfectly Elastic Collision'
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 2.5, 2.5)
+        'Perfectly Inelastic Collision'
+        >>> type_collision(1.0, 1.0, 2.0, 3.0, 0.0, 0.0)
+        'Inelastic Collision'
+    """
+    momentum_initial = (mass1 * velocity_initial1) + (mass2 * velocity_initial2)
+    momentum_final = (mass1 * velocity_final1) + (mass2 * velocity_final2)
+    kinetic_initial = 0.5 * (
+        (mass1 * velocity_initial1**2) + (mass2 * velocity_initial2**2)
+    )
+    kinetic_final = 0.5 * ((mass1 * velocity_final1**2) + (mass2 * velocity_final2**2))
+
+    if kinetic_final == kinetic_initial and momentum_initial == momentum_final:
+        return "Perfectly Elastic Collision"
+    elif kinetic_final != kinetic_initial and momentum_initial == momentum_final:
+        return "Perfectly Inelastic Collision"
+    else:
+        return "Inelastic Collision"
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()