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Monday, October 13, 2025

Analysis of Moments of Forces — 3/3 Combined (HTML5) by jinsheng


Analysis of Moments of Forces — Combined (HTML5)

A lightweight lever simulator for teaching turning effects of forces

Overview

Analysis of Moments of Forces — Combined is a plain HTML5 + Canvas interactive that unifies horizontal and vertical lever scenarios in one tool. Learners can add up to eight forces, set each force’s magnitude, direction, side (left/right or above/below), and perpendicular distance (d) from the pivot, then immediately see:

03Analysis_of_Moments_of_Forces_-_Combined_20251013.zip

  • The sum of anti-clockwise (ACW) moments and sum of clockwise (CW) moments,

  • A clear verdict: balanced, rotates ACW, or rotates CW, and

  • A visual tilt preview of the lever about the pivot in the Result panel.

The UI is deliberately simple, runs offline, and drops straight into the Student Learning Space (SLS) as a Plain Web/HTML5 object—no plugins or frameworks needed.

What’s new in the Combined build

  • Dual orientation switcher: Toggle between Horizontal Lever (⬌) and Vertical Lever (⬍) from the top Lever Orientation control.

  • Unified control logic:

    • Horizontal mode: choose up/down direction and left/right position for each force.

    • Vertical mode: choose left/right direction and above/below position.

  • Single draggable pivot: Click/touch near the pivot to drag along the lever (horizontal: along the beam; vertical: up/down the beam).

  • Manual (d) entry per force: Teachers can set (d_i) directly for targeted tasks and quick number-sense checks (units are arbitrary by design).

  • Clean panels: DIAGRAM, CALCULATIONS, and RESULT are collapsible for projector-friendly lessons.

How the model reasons about moments

For each visible force with magnitude (F_i) and entered distance (d_i) from the pivot, the app computes a scalar moment (M_i = F_i \times d_i).
The rotation sense (ACW vs CW) is decided by the pair (direction, side) using the standard right-hand rules for each orientation:

  • Horizontal lever:

    • ACW if (up, right) or (down, left)

    • CW otherwise

  • Vertical lever:

    • ACW if (right, below) or (left, above)

    • CW otherwise

Then:
[
\sum M_{\text{ACW}} \quad \text{vs} \quad \sum M_{\text{CW}}
]

  • If (\bigl|\sum M_{\text{ACW}} - \sum M_{\text{CW}}\bigr| < 0.1): Equilibrium (balanced)

  • Else: “Rotates anti-clockwise” or “Rotates clockwise” with a small tilt visualization about the pivot.

Note: Distances are perpendicular lever-arm distances in arbitrary units—perfect for focusing on the relationship (M = F \times d) without unit conversions.

Learning objectives

By the end of this activity, learners can:

  1. Define moment of a force about a pivot and distinguish ACW vs CW.

  2. Identify and set the correct perpendicular distance (d) for a given force.

  3. Compute and compare (\sum M_{\text{ACW}}) and (\sum M_{\text{CW}}) to determine equilibrium.

  4. Predict how changing magnitude, direction, side/position, and pivot location affects balance.

  5. Explain common misconceptions, especially confusing slanted distances with perpendicular distance.

Suggested lesson flow

1) Elicit & predict

  • “If the pivot moves toward the heavier force, does the lever get more or less balanced?”

  • “Can a smaller force ever balance a larger force?”

2) Investigate

  • Horizontal mode: Place one downward force on the left and one upward on the right; vary (d) and (F) to hit balance.

  • Vertical mode: Place a right-pointing force below the pivot and a left-pointing force above it; achieve equilibrium by adjusting (d).

3) Explain

  • Use CALCULATIONS to connect symbolic terms (F_1 d_1 + F_3 d_3) to the numeric line.

  • In RESULT, link the comparison to the tilt preview.

4) Apply

  • Design a balance: “With (F_1=30\text{ N}) at (d_1=1.2), choose a second force to balance.”

  • Minimal change challenge: “You may change only one parameter—reach equilibrium.”

Misconceptions to address

  • Using slanted distances instead of perpendicular distance to the pivot.

  • Assuming bigger (F) always wins—highlight how small (F) with large (d) can balance large (F) with small (d).

  • Mixing up rotation sense when swapping sides or directions—anchor reasoning in the (direction, side) rules above.

Assessment ideas

  • Exit ticket: “Explain how a 10 N force can balance a 40 N force.” (Look for (d) reasoning.)

  • Error analysis: Provide a worked example that uses a slanted distance; ask students to fix it.

  • Mastery check: Hide the RESULT panel; have students compute both sums from CALCULATIONS and state the verdict before revealing.

SLS / site embedding

  • SLS: Upload the folder and select index.html using Add Media → Web/HTML5.

  • Blog/WordPress (iframe):

<iframe src="index.html" width="900" height="640" style="border:1px solid #ccc;border-radius:8px"></iframe>

Tip: Keep DIAGRAM open and collapse other panels when projecting to focus discussion.

Credits & links

Why this model works in class

  • Transparent maths: Students see (M=F\times d) built term-by-term.

  • Immediate feedback: ACW/CW sums and a tilt preview reinforce conceptual checks.

  • Flexible geometry: One control set covers both horizontal and vertical levers with a single draggable pivot.

  • Deployment-friendly: Pure HTML5—fast to load, robust in school networks, and SLS-ready.


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