EDUCATION DECISION WORKBENCH
Resolve force vectors into components, calculate net force and acceleration, and audit whether the entered system is balanced.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous, policy-approved information. Results remain in this browser tab until you copy or download them.
Transparent method
For a force magnitude F at angle θ, horizontal component Fₓ = F cos θ and vertical component Fᵧ = F sin θ. Net components are the sums of all entered components. Net magnitude equals √(ΣFₓ² + ΣFᵧ²), direction equals atan2(ΣFᵧ, ΣFₓ), and acceleration magnitude equals net force divided by mass. The balance screen uses a 0.1% relative tolerance. A near-equilibrium label means the numerical sum is small relative to all entered force magnitudes; it does not prove that no force was omitted. A nonzero vertical result may reveal an incorrect normal force or a missing angled component. Acceleration follows the net vector for a constant-mass model, while the actual motion also depends on initial velocity and how forces change with time.
Confirm the question, variables, units, source data, measurement precision, and the model expected by the current course or laboratory. Keep an untouched copy of observations before excluding or transforming any value.
Run the worked example first, inspect every intermediate row, compare units and signs, and look for a result that conflicts with the graph, physical system, chemical equation, or learning objective.
Record the method, assumptions, units, rounding, data limitations, and any excluded observations. Compare the exported report with an independent calculation or approved reference before assessment or laboratory use.
How to interpret the result
Use this planner after drawing a free body diagram for a single defined system. It supports checking horizontal and vertical balances, identifying a missing force, and applying Newton’s second law to the resultant. The numerical table complements a diagram but cannot determine which forces exist; the learner must identify contact, field, tension, drag, normal, friction, or applied forces first.
A 12 kg crate has a 45 N pull to the right, 18 N friction to the left, 117.72 N weight downward, and an equal normal force upward. Vertical components cancel while the horizontal net is 27 N. The workbench reports the net direction and divides its magnitude by mass to obtain the modeled acceleration.
For a force magnitude F at angle θ, horizontal component Fₓ = F cos θ and vertical component Fᵧ = F sin θ. Net components are the sums of all entered components. Net magnitude equals √(ΣFₓ² + ΣFᵧ²), direction equals atan2(ΣFᵧ, ΣFₓ), and acceleration magnitude equals net force divided by mass. The balance screen uses a 0.1% relative tolerance.
A near-equilibrium label means the numerical sum is small relative to all entered force magnitudes; it does not prove that no force was omitted. A nonzero vertical result may reveal an incorrect normal force or a missing angled component. Acceleration follows the net vector for a constant-mass model, while the actual motion also depends on initial velocity and how forces change with time.
Do not include action-reaction pairs acting on another object, treat mass as weight, add force magnitudes without directions, reverse sine and cosine for the stated angle convention, or assume normal force always equals weight. Draw the system boundary, label axes, verify units, and decide whether friction, drag, buoyancy, tension, or an incline component belongs in the model.
Learning boundary
This browser-local workbench calculates only from the entered model and observations. It cannot validate an experiment, balance an equation, establish causation, certify laboratory safety, diagnose learning, or replace the method required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. The calculation runs in the current browser tab. Avoid personal information and retain laboratory data in the system authorized by the school.
Treat it as an editable analysis aid. Show your own reasoning, cite the required sources, follow academic-integrity rules, and use the method requested by your course.
No. Check dimensions, graph shape, assumptions, measurement uncertainty, significant figures, and whether another model explains the observations better.
YOUR NIRMION
