STEM REASONING AND EVIDENCE WORKBENCH
Group two-dimensional point masses, calculate weighted center coordinates, and audit one repeated learner claim per system.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
For positive point masses mi at coordinates xi and yi, total mass M is the sum of mi. Center coordinate x bar equals the sum of mi times xi divided by M, and y bar equals the sum of mi times yi divided by M. The weighted center must lie within the coordinate bounds of positive component masses, although it need not lie on material. Supported means both learner coordinates match the mass-weighted calculation. A simple midpoint works only for equal masses arranged symmetrically. Review contribution products, coordinate signs, origin, component inclusion, and units when a claim differs. A calculated location is a model result and still requires physical geometry, uncertainty, and system-boundary review.
Confirm the question, approved source, units, notation, signs, response coding, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner evidence.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, representation, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use for discrete point-mass systems, simplified beams, plates represented by sampled masses, or introductory balance models. It shows every contribution and total mass. It does not integrate a continuous density, infer component masses, locate a center of gravity in a nonuniform field, handle negative effective masses, validate a physical suspension test, or decide which components belong inside the system.
A two-kilogram point at x zero and one-kilogram point at x three balance at x one. Equal masses at zero-zero and two-two give center one-one. In the review system, mass one at x zero and mass three at x four give weighted x three; the repeated learner claim x two treats the points as equally weighted and is flagged.
For positive point masses mi at coordinates xi and yi, total mass M is the sum of mi. Center coordinate x bar equals the sum of mi times xi divided by M, and y bar equals the sum of mi times yi divided by M. The weighted center must lie within the coordinate bounds of positive component masses, although it need not lie on material.
Supported means both learner coordinates match the mass-weighted calculation. A simple midpoint works only for equal masses arranged symmetrically. Review contribution products, coordinate signs, origin, component inclusion, and units when a claim differs. A calculated location is a model result and still requires physical geometry, uncertainty, and system-boundary review.
Do not average coordinates without weights, divide each contribution by its own mass, use weight for some rows and mass for others without consistent gravity, mix origins, reverse axes, omit a component, assume the center must touch material, or use an arithmetic midpoint for unequal masses. Make a contribution table, sum columns, divide once, and check symmetry.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish a chemical structure, or replace teacher, laboratory, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
