Model elastic or inelastic impacts with clear, unit‑aware energy breakdowns today online. See post‑collision speeds, lost energy, and center‑frame energy in seconds right here.
This calculator assumes a one-dimensional collision along a line. The coefficient of restitution e models elasticity: e = (v2' − v1') / (v1 − v2), with 0 ≤ e ≤ 1.
Notes: In perfectly elastic collisions, E_diss ≈ 0. For inelastic collisions, E_diss ≥ 0, while total momentum remains conserved.
| # | m1 | m2 | v1 | v2 | e | Scenario |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 5 | -1 | 1 | Elastic, opposite directions |
| 2 | 1.5 | 1.5 | 4 | 0 | 0.6 | Inelastic, one at rest |
| 3 | 0.25 | 1 | 12 | 8 | 0 | Perfectly inelastic limit |
Units shown in the table are kg for mass and m/s for velocity.
The tool evaluates kinetic energy before and after a one‑dimensional impact and reports both the laboratory energies and the center‑of‑mass relative‑motion energy. It is useful for carts, air‑track gliders, bumper tests, and any setup where motion is mainly along one line.
Momentum is conserved for an isolated system, but kinetic energy can decrease when deformation, vibration, heat, and sound are produced. The calculator reports this as Ediss = Ki − Kf. For nearly elastic steel‑on‑steel taps, Ediss can be close to zero; for soft bumpers it can be large.
The coefficient of restitution e summarizes how “bouncy” the collision is. Values near e≈0.9 are typical for hard, well‑aligned impacts; rubber‑like contacts may fall around e≈0.5; and the perfectly inelastic limit is e=0. Because e is sensitive to alignment, surface condition, and speed, measuring it across several trials improves reliability.
In the lab, one object might be at rest while the other moves. In the center‑of‑mass frame the system’s bulk motion is removed, revealing the energy available for deformation. The calculator provides vcm and Ecm so you can compare collisions performed at different overall speeds.
The center‑frame collision energy is computed as Ecm = ½ μ (v1 − v2)², where μ = m1 m2 / (m1 + m2). This highlights two controls: the reduced mass and the closing speed. Doubling the relative speed quadruples Ecm.
Record masses, then measure pre‑impact velocities with photogates, video tracking, or motion sensors. Run the calculator, then verify that the reported momentum p is consistent across trials. For classroom carts, a closing speed of 2–6 m/s commonly yields energies from a few joules to tens of joules, depending on mass.
The largest errors usually come from velocity measurement and sign conventions. Use negative velocities for opposite directions, and keep units consistent. If results appear unphysical, check that both masses are positive and that 0 ≤ e ≤ 1. Repeat trials to estimate uncertainty bands.
Compare Ki and Kf to quantify losses, and use Ecm to compare different setups fairly. Export CSV for lab reports, and use the PDF summary when documenting test conditions and results.
It refers to kinetic energy before and after impact, plus the center‑of‑mass relative‑motion energy that represents energy available for deformation during contact.
Yes. Set e = 1. The calculator will typically show Ediss near zero, with any tiny difference due to rounding.
Enter v2 = 0 for the stationary object. The formulas remain valid and the results will show final velocities and the energy change.
Energy can convert into heat, sound, and deformation. Softer materials, misalignment, and higher closing speed usually increase dissipation.
If you measured pre‑ and post‑impact speeds, compute e from relative speeds along the collision line. Otherwise, use literature values as a starting point and adjust to match tests.
No. It models one‑dimensional motion along a line. For angled impacts, project velocities onto the collision normal or use a full 2D/3D collision model.
It removes the system’s bulk motion and isolates relative‑motion energy. This helps compare collisions performed with different overall speeds or different lab frames.
Accurate collision insights, exports, and clear steps for everyone.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.