# Python code to apply the theorem of conservation of mechanical energy

# Constants
g = 9.81  # gravitational acceleration in m/s^2

# Function to calculate the total mechanical energy
def calculate_mechanical_energy(mass, height, velocity):
    # Potential energy
    potential_energy = mass * g * height

    # Kinetic energy
    kinetic_energy = 0.5 * mass * velocity ** 2

    # Total mechanical energy
    total_energy = potential_energy + kinetic_energy

    return potential_energy, kinetic_energy, total_energy

# Example usage
# Inputs
mass = 2.0  # mass in kg
initial_height = 10.0  # height in meters
initial_velocity = 0.0  # velocity in m/s

# Calculate energy at the initial position
potential_energy, kinetic_energy, total_energy = calculate_mechanical_energy(mass, initial_height, initial_velocity)

print("Initial state:")
print("Potential energy:", potential_energy, "J")
print("Kinetic energy:", kinetic_energy, "J")
print("Total mechanical energy:", total_energy, "J")

# Final state inputs
final_height = 0.0  # height in meters
final_velocity = (2 * g * initial_height) ** 0.5  # velocity at final state using energy conservation

# Calculate energy at the final position
potential_energy, kinetic_energy, total_energy = calculate_mechanical_energy(mass, final_height, final_velocity)

print("\nFinal state:")
print("Potential energy:", potential_energy, "J")
print("Kinetic energy:", kinetic_energy, "J")
print("Total mechanical energy:", total_energy, "J")