Final library experiment

JSXGraph interaction lab

Slide the application point along the mast. Rotate the square handle. Watch the force, its moment arm, and the ground reaction follow.

Move the load

Application height

Force direction

0° inward · 90° up · 180° outward

Force P₁

Automatic label placement Add forces at the mass center Show moment-arm construction

Force and moment arm

Left support edge · u inward, z upward · meters

Round handle A: application height. Square handle: force direction. Shift + drag: pan. Arrow lengths are schematic. G: mass center; R: required ground reaction; W: weight; I: equivalent inertia; P₁ / P₂: applied forces; N / T: normal / tangential reactions.

Perpendicular arm d…From edge to P₁’s line

P₁ moment about edge…Restoring sign convention

R distance from edge…Negative is outside this edge

Preparing the calculation…

Force values and calculation notes

100 kg assembly, 1.2 m wheelbase, 0.8 m track, and G at 0.6 m height on level ground. A moves above the footprint center. The outline is illustrative. Positive moments restore about the selected left edge. Reactions are the resultants required for equilibrium; an outside reaction cannot be supplied by these contacts.

Force	Fᵤ (N)	Fz (N)	u (m)	z (m)	Moment (N·m)

Fᵤ: force inward from the edge; Fz: upward force; u, z: application coordinates. The crowded case adds 0.8 m/s² acceleration toward +u and a 160 N force directed 175° from +u at G. This experiment does not check sliding or individual contact loads.

What this tests in JSXGraph

The round handle is a point constrained to a segment; the square handle is constrained to a circle. Dependent points keep the arrow attached. An orthogonal projection constructs the moment arm, and a measurement label follows its length. Toggle automatic label placement and try the crowded case to inspect overlaps and label movement.

Geometry responds during dragging. Python recalculates forces and reactions after a short pause; pending reactions and moments are hidden until the current calculation finishes. The existing stability solver remains the calculation source. This page reuses the gallery’s JSXGraph runtime and loads the same Pyodide version as the calculator.

References: constrained points, orthogonal projection, measurement labels, and automatic label placement.