Calculating resultant forces and moments is a fundamental skill for mechanical engineers. This challenge will help you automate these calculations using Python. You will use your knowledge of **vector addition** and **moments** to process a list of forces, each defined by its magnitude, direction, and point of application, and compute both the overall (`resultant`) force and the net moment about a given origin point.


import unittest
import user_code
import ast
import re   
import importlib
import csv
import unittest
import importlib
import math

class TestTask(unittest.TestCase):
    def test_arbitrary_forces_resultant(self):
        import user_code
        importlib.reload(user_code)
        forces = [
            (10, 0, 2, 3),   # 10N right at (2,3)
            (5, 90, 4, 1),   # 5N up at (4,1)
            (7, 180, 0, 0)   # 7N left at origin
        ]
        origin = (0, 0)
        result = user_code.resultant_force_and_moment(forces, origin)
        expected_magnitude = math.hypot(10 - 7, 5)
        expected_angle = math.degrees(math.atan2(5, 3))
        _dynamic_test(
            self,
            isinstance(result, tuple) and isinstance(result[0], tuple) and abs(result[0][0] - expected_magnitude) < 1e-6 and abs(result[0][1] - expected_angle) < 1e-6,
            "Correct resultant force magnitude and angle for arbitrary forces.",
            f"Expected resultant: ({expected_magnitude}, {expected_angle}), got {result[0]}"
        )

    def test_arbitrary_forces_moment(self):
        import user_code
        importlib.reload(user_code)
        forces = [
            (10, 0, 2, 3),   # 10N right at (2,3)
            (5, 90, 4, 1),   # 5N up at (4,1)
            (7, 180, 0, 0)   # 7N left at origin
        ]
        origin = (0, 0)
        result = user_code.resultant_force_and_moment(forces, origin)
        # Moment = x*Fy - y*Fx for each force
        m1 = 2 * 0 - 3 * 10  # (2,3), Fx=10, Fy=0
        m2 = 4 * 5 - 1 * 0   # (4,1), Fx=0, Fy=5
        m3 = 0 * 0 - 0 * (-7) # (0,0), Fx=-7, Fy=0
        expected_moment = m1 + m2 + m3
        _dynamic_test(
            self,
            abs(result[1] - expected_moment) < 1e-6,
            "Correct net moment about origin for provided forces.",
            f"Expected moment: {expected_moment}, got {result[1]}"
        )

    def test_zero_resultant_force(self):
        import user_code
        importlib.reload(user_code)
        forces = [
            (5, 0, 0, 0),
            (5, 180, 0, 0)
        ]
        origin = (0, 0)
        result = user_code.resultant_force_and_moment(forces, origin)
        _dynamic_test(
            self,
            abs(result[0][0]) < 1e-6 and abs(result[0][1]) < 1e-6,
            "Handles zero resultant force: returns (0,0) for magnitude and angle.",
            f"Expected (0,0), got {result[0]}"
        )

    def test_all_forces_at_origin(self):
        import user_code
        importlib.reload(user_code)
        forces = [
            (3, 45, 0, 0),
            (4, -45, 0, 0)
        ]
        origin = (0, 0)
        result = user_code.resultant_force_and_moment(forces, origin)
        _dynamic_test(
            self,
            abs(result[1]) < 1e-6,
            "Net moment is zero when all forces applied at origin.",
            f"Expected moment 0, got {result[1]}"
        )

    def test_negative_angles_and_positions(self):
        import user_code
        importlib.reload(user_code)
        forces = [
            (8, -90, -2, -2), # 8N down at (-2,-2)
            (6, 135, -3, 1)   # 6N up-left at (-3,1)
        ]
        origin = (0, 0)
        result = user_code.resultant_force_and_moment(forces, origin)
        # Just check the calculation is performed and values are floats
        _dynamic_test(
            self,
            isinstance(result, tuple) and isinstance(result[0], tuple) and isinstance(result[0][0], float) and isinstance(result[0][1], float) and isinstance(result[1], float),
            "Handles negative force angles and positions correctly.",
            f"Expected float values for resultant and moment, got {result}"
        )

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

def normalize_text(text):
    text = text.lower()
    text = re.sub(r"\\s{2,}", " ", text)
    text = re.sub(r"\\s*([,:?])\\s*", r"\\1 ", text)
    return text.strip()

def change_var(code: str, var_name: str, value: str) -> str:
    tree = ast.parse(code)
    lines = code.splitlines()
    changed = False
    # Collect all assignment nodes to modify
    assign_nodes = [
        (i, node)
        for i, node in enumerate(tree.body)
        if isinstance(node, ast.Assign)
        and any(isinstance(target, ast.Name) and target.id == var_name for target in node.targets)
    ]

    # If nothing to change, return unmodified code
    if not assign_nodes:
        return code

    # Perform replacements for all matching assignments (from last to first to not break line offsets)
    for i, node in reversed(assign_nodes):
        start_line = node.lineno - 1
        line = lines[start_line]
        indent = ' ' * (len(line) - len(line.lstrip()))
        lines[start_line] = f"{indent}{var_name} = {value}"
        next_line = len(lines)
        for next_node in tree.body[i+1:]:
            if hasattr(next_node, 'lineno'):
                next_line = next_node.lineno - 1
                break
        if next_line > start_line + 1:
            lines[start_line+1:next_line] = []
        changed = True

    return '\\n'.join(lines) if changed else code

if __name__ == "__main__":
    unittest.main()


test_main.py

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Challenge: Resultant Force and Moment

Ratkaisu