Description
Return forceX × displacementX + forceY × displacementY as work.
Mechanics formulas relate forces, motion, energy, and geometry within a specified model. Signed coordinates and consistent units determine each component; a formula evaluation does not verify measured loads or the suitability of the physical model.
Return forceX × displacementX + forceY × displacementY as work.
When to use this tool
Use Small Displacement Work Projection when you need one elementary mechanics component under an explicit coordinate and unit convention.
How to use the tool and how it works
- Enter forceX, forceY, displacementX, displacementY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read work. Use the output convention below.
Return forceX × displacementX + forceY × displacementY as work.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| forceX | Force X | Required. Finite number. |
| forceY | Force Y | Required. Finite number. |
| displacementX | Displacement X | Required. Finite number. |
| displacementY | Displacement Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| work | Work | Required. Finite number. |
{
"input": {
"forceX": 3,
"forceY": 4,
"displacementX": 2,
"displacementY": -1
},
"output": {
"work": 2
}
}Limitations and assumptions
- Coherent newtons and meters produce joules; this is a constant-force two-dimensional dot product, not an integral for varying force or a full trajectory.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Check the complete physical model and consult a qualified professional when the result informs equipment or structural safety.
References
Similar or alternative tools
- Work Energy Signed Ledger Step
Add signed netWorkJoules to nonnegative initialKineticEnergyJoules, requiring the sum nonnegative, and return finalKineticEnergyJoules.
- Center Of Mass Two Point Coordinate
Return the mass-fraction-weighted sum of firstCoordinate and secondCoordinate.