Conservation of Momentum Calculator
Quickly compute total and individual momenta before and after interactions. Supports 1D/2D collisions, elastic/inelastic cases, and vector inputs for accurate momentum analysis.
conservation of momentum calculator:
A Conservation of Momentum Calculator is based on the idea that the total momentum of a closed system does not change in the course of interaction. Masses and velocities of input (vectors or scalars), elastic/inelastic, and the calculator generates pre/final momenta, final velocities based on p=mv, conservation equations - needed in the analysis of collisions, problems in dynamics.
momentum conservation tool Formula:
Conservation of Momentum Calculator calculates the momentum of the total system and solves collisions of 1D and 2D. Input masses and velocity vectors of each object (or velocity scalar vectors of 1D), and the type of collision (elastic or perfectly inelastic) and the tool enforces the momentum conservation.
\[ \sum mivi,pre = \sum mivi,post \]
In the case of elastic collisions, it optionally uses momentum conservation plus kinetic-energy conservation to find final velocities; and in the case of inelastic collisions common velocity of post-stick-together impacts is computed. This momentum collision calculator is a tool used by students, physics teachers, and engineers to analyze and study the transfer of momentum, responses of collisions, and the change of trajectory. It can be used to solve lab problems, check homework, or prototype very fast during dynamic simulations.
⚡ Work & Installation (Input → Output):
Inputs:
- Number of objects (n)
- For each object: mass mi and velocity (scalar for 1D or vector components vx, vy for 2D)
- Collision type: elastic, perfectly inelastic (stick), or partially inelastic (coefficient of restitution e)
- (Optional) Choose coordinate system and unit (SI recommended)
Process / Work:
- Convert inputs to consistent units.
- Compute each object’s momentum \( P_{i} = m_{i} v_{i} \)
- Sum pre-collision momenta \( P_{pre} = \sum P_{i} \)
- For perfectly inelastic: compute common post-collision velocity \( V_{f} = \frac{P_{pre}}{\sum m_{i}} \)
- For elastic (1D) or elastic 2-body: solve simultaneous equations for momentum and kinetic energy (or use standard closed-form solutions when applicable). For coefficient of restitution e: use \( v_{rel}, post = -ev_{rel}, pre \) along impact line.
- Output post-collision velocities, individual and total momenta, and (if requested) kinetic energy before/after.
Outputs:
- Vector and scalar momenta (pre & post)
- Final velocities for each object (components and magnitude)
- Total system momentum confirmation (pre = post within numerical tolerance)
- Optional: kinetic energy change and note on energy loss (inelastic cases)
- Step-by-step working summary for verification
Installation notes: Provide unit dropdowns, vector input toggles, default examples (elastic 1D, head-on inelastic), and validation (nonzero masses, numeric velocities). Show workings and numeric tolerance for conservation checks.
Testing and Final Adjustments:
Check calculator on canonical cases: (1) 2-body 1D elastic collision in which you have known results (test against known formulae), (2) perfectly inelastic collision and (3) 2D glancing elastic collision. Numerical stability Unit consistency Numerical stability: manufactured edge cases (zero velocity, equal masses, one very large mass). The restitution of a check where e = different decreases with decrease in e towards the value of 1 (elastic) to 0 (perfectly inelastic). Add tolerance tests (e.g. relative error 1e-6), and show differences when momentum is not conserved due to round off. Display clear messages of errors in the input (mass 0, missing components). Finally, the results provided by round were reasonable (3 or 5 significant digits) and steps of the show could be applied in educational environment.
Frequently Asked Questions - Conservation of Momentum Calculator:
What is conservation of momentum?
The total momentum of an isolated system remains constant during interactions (no external impulse).
What inputs does the calculator need?
Masses and velocities (scalars for 1D or vector components for 2D), and collision type (elastic/inelastic).
How is momentum computed?
Momentum p = m × v (vector form p = m·v⃗).
Can it handle 2D collisions?
Yes — enter velocity components (vx, vy) and the tool solves momentum per axis.
Does it conserve kinetic energy?
Only in elastic collisions; inelastic collisions dissipate kinetic energy but conserve momentum.
What is coefficient of restitution (e)?
A number (0≤e≤1) that quantifies relative speed after/before along the impact line; e=1 elastic, e=0 perfectly inelastic.
Can it solve for final velocities?
Yes — for two-body problems it returns final velocities using conservation laws and e if provided.
Is the calculator suitable for students?
Yes — it shows intermediate steps, checks conservation, and explains energy loss for inelastic cases.
What units should I use?
Use consistent units (SI: kg for mass, m/s for velocity) to get momentum in kg·m/s.
What if external forces act?
The basic conservation applies only if external impulses are negligible; otherwise include external impulse terms.
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