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Momentum & 1D collision calculator

Free physics calculator for 1D collisions using conservation of momentum and coefficient of restitution. Compute final velocities and energy loss with step-by-step explanations.

Compute final velocities, momentum balance, and kinetic energy loss for 1D collisions (elastic, perfectly inelastic, or coefficient e).

All calculations run locally in your browser; no data leaves this calculator.

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How to use (3 steps)

  1. Pick a collision type: elastic (e = 1), perfectly inelastic (stick together), or inelastic with your own e.
  2. Enter masses and initial velocities u₁ and u₂. Use negative values to show the opposite direction on the 1D line.
  3. Press Compute to get v₁, v₂, momentum and energy before/after, then copy the URL to share the setup.

Default example: m₁ = 1 kg, u₁ = 3 m/s, m₂ = 2 kg, u₂ = 0 m/s, elastic. It auto-computes on load so you can see the result instantly.

Inputs

Use kg and m/s. This calculator keeps the sign of each velocity; rightward is positive by convention.

Elastic: e = 1.0 (fixed).
kg
m/s
kg
m/s

Use positive/negative values to show direction along the line (rightward is positive).

Results

How it's calculated

    How to use this calculator effectively

    This guide helps you use Momentum & 1D collision calculator in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

    How it works

    The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

    When to use

    Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

    Common mistakes to avoid

    Interpretation and worked example

    Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

    See also

    FAQ

    What is the difference between elastic and inelastic collisions?

    Elastic collisions conserve both momentum and kinetic energy (e = 1). Inelastic collisions conserve momentum but lose some kinetic energy. In a perfectly inelastic collision the objects stick together and move with one final speed.

    Can I enter negative speeds?

    Yes. Set rightward as positive on the 1D line. A negative value means the object travels to the left, and the calculator keeps that sign when summing momentum.

    What does the coefficient of restitution e mean?

    It is the ratio of relative speed after impact to relative speed before impact. e = 1 is perfectly elastic, e = 0 is perfectly inelastic, and values between 0 and 1 describe partially elastic collisions.

    What should I do first on this page?

    Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.

    Why does this page differ from another tool?

    Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.

    How to use Momentum & 1D collision calculator effectively

    What this calculator does

    This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.

    Input meaning and unit policy

    Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.

    Use-case sequence

    A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.

    Common mistakes to avoid

    Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.

    Interpretation guidance

    Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.

    Operational checkpoint 1

    Record the exact values and intent before you finalize any comparison. Confirm the unit system, date context, and business constraints. Compare outputs side by side and check whether differences are explained by one changed variable or by hidden assumptions. This checkpoint often reveals the single factor that changed everything.

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