"""
Example 14: Statics & Equilibrium (Phase 2.6)
Demonstrates static equilibrium calculations including:
- Force balance
- Torque balance
- Center of mass
- Static friction
- Normal forces
- Complete equilibrium analysis
- Beam reactions
No external services required - uses analytic provider.
"""
import asyncio
from chuk_mcp_physics.tools.statics import (
check_force_balance,
check_torque_balance,
calculate_center_of_mass,
calculate_static_friction,
calculate_normal_force,
check_equilibrium,
calculate_beam_reactions,
)
async def main():
print("\n" + "=" * 70)
print("STATICS & EQUILIBRIUM EXAMPLES (Phase 2.6)")
print("=" * 70)
# Example 1: Force Balance - Bridge supports
print("\n1. Force Balance - Bridge Support Analysis")
print("-" * 70)
forces = [[0, 1000, 0], [0, 500, 0], [0, -1500, 0]] # Two upward, one downward
result = await check_force_balance(forces=forces, tolerance=0.01)
print("Forces on bridge:")
print(" Support 1: [0, 1000, 0] N (upward)")
print(" Support 2: [0, 500, 0] N (upward)")
print(" Load: [0, -1500, 0] N (downward)")
print("\nRESULTS:")
print(f" Net force: {result['net_force']}")
print(f" Net force magnitude: {result['net_force_magnitude']:.2f} N")
print(
f" Is balanced: {result['is_balanced']} ✓"
if result["is_balanced"]
else f" Is balanced: {result['is_balanced']} ✗"
)
# Example 2: Seesaw Balance
print("\n\n2. Torque Balance - Seesaw")
print("-" * 70)
torques = [[0, 0, 100], [0, 0, -100]] # Equal and opposite torques
result = await check_torque_balance(torques=torques, tolerance=0.01)
print("Torques on seesaw:")
print(" Child 1: 100 N⋅m (clockwise)")
print(" Child 2: -100 N⋅m (counter-clockwise)")
print("\nRESULTS:")
print(f" Net torque magnitude: {result['net_torque_magnitude']:.2f} N⋅m")
print(
f" Is balanced: {result['is_balanced']} ✓"
if result["is_balanced"]
else f" Is balanced: {result['is_balanced']} ✗"
)
# Example 3: Center of Mass
print("\n\n3. Center of Mass - Three-Body System")
print("-" * 70)
masses = [1.0, 2.0, 3.0]
positions = [[0, 0, 0], [1, 0, 0], [2, 0, 0]]
result = await calculate_center_of_mass(masses=masses, positions=positions)
print("System:")
for i, (m, p) in enumerate(zip(masses, positions)):
print(f" Mass {i + 1}: {m:.1f} kg at {p}")
print("\nRESULTS:")
print(f" Center of mass: {result['center_of_mass']}")
print(f" Total mass: {result['total_mass']:.1f} kg")
print(f" Balance point is at x = {result['center_of_mass'][0]:.2f} m")
# Example 4: Static Friction - Box on floor
print("\n\n4. Static Friction - Will the Box Slide?")
print("-" * 70)
normal = 100 # N (10 kg box)
mu_s = 0.5 # Coefficient of static friction
test_forces = [30, 45, 55]
print("Box on floor:")
print(f" Normal force: {normal} N")
print(f" Coefficient of friction: {mu_s}")
print(f"\n{'Applied Force (N)':<20} {'Will Slip?':<15} {'Friction Force (N)':<20}")
print("-" * 70)
for force in test_forces:
result = await calculate_static_friction(
normal_force=normal, coefficient_static_friction=mu_s, applied_force=force
)
will_slip = "Yes ✗" if result["will_slip"] else "No ✓"
print(f"{force:<20} {will_slip:<15} {result['friction_force']:<20.1f}")
# Example 5: Normal Force on Incline
print("\n\n5. Normal Force - Box on Inclined Plane")
print("-" * 70)
mass = 10.0 # kg
angles = [0, 15, 30, 45]
print("10 kg box on ramp at various angles:")
print(f"\n{'Angle (°)':<15} {'Normal Force (N)':<20} {'Parallel Component (N)':<25}")
print("-" * 70)
for angle in angles:
result = await calculate_normal_force(mass=mass, angle_degrees=angle)
print(
f"{angle:<15} {result['normal_force']:<20.1f} {result['weight_component_parallel']:<25.1f}"
)
# Example 6: Complete Equilibrium Check
print("\n\n6. Complete Equilibrium - Beam with Multiple Forces")
print("-" * 70)
forces = [[0, 100, 0], [0, -100, 0]]
positions = [[1, 0, 0], [1, 0, 0]] # Both at same point
result = await check_equilibrium(forces=forces, force_positions=positions, tolerance=0.01)
print("System with forces at positions:")
for i, (f, p) in enumerate(zip(forces, positions)):
print(f" Force {i + 1}: {f} N at {p} m")
print("\nRESULTS:")
print(
f" Force balanced: {result['force_balanced']} ✓"
if result["force_balanced"]
else f" Force balanced: {result['force_balanced']} ✗"
)
print(
f" Torque balanced: {result['torque_balanced']} ✓"
if result["torque_balanced"]
else f" Torque balanced: {result['torque_balanced']} ✗"
)
print(
f" In equilibrium: {result['in_equilibrium']} ✓"
if result["in_equilibrium"]
else f" In equilibrium: {result['in_equilibrium']} ✗"
)
# Example 7: Beam Reactions
print("\n\n7. Simply Supported Beam - Reaction Forces")
print("-" * 70)
result = await calculate_beam_reactions(
beam_length=10.0, # 10 m beam
loads=[1000, 500], # Point loads in N
load_positions=[3.0, 7.0], # Positions along beam
)
print("10 m beam with two point loads:")
print(" Load 1: 1000 N at 3 m from left")
print(" Load 2: 500 N at 7 m from left")
print("\nSupport Reactions:")
print(f" Left support: {result['reaction_left']:.1f} N")
print(f" Right support: {result['reaction_right']:.1f} N")
print(f" Total load: {result['total_load']:.1f} N")
print(
f" Is balanced: {result['is_balanced']} ✓"
if result["is_balanced"]
else f" Is balanced: {result['is_balanced']} ✗"
)
print(
f" Check: {result['reaction_left'] + result['reaction_right']:.1f} N = {result['total_load']:.1f} N"
)
print("\n" + "=" * 70)
print("Phase 2.6 Complete! ✓")
print("=" * 70 + "\n")
if __name__ == "__main__":
asyncio.run(main())
