Advanced Inelastic Collision Calculator

Analyze inelastic impacts with momentum, velocity, and energy outputs. Compare bodies, inspect losses, and visualize every collision step clearly.

Calculator Inputs

Use a negative velocity for opposite motion. Perfectly inelastic mode makes both bodies move together after impact.

Collision Graph

The graph compares initial and final velocities and shows how the collision changes kinetic energy.

Example Data Table

Scenario Mass 1 (kg) Mass 2 (kg) Initial v1 (m/s) Initial v2 (m/s) e Final v1 (m/s) Final v2 (m/s) Energy Lost (J)
Cart impact 2 3 8 -1 0.4 0.8 5.8 43.2
Perfect stick 1.5 2.5 6 1 0 2.875 2.875 9.375
Slow rebound 4 1 3 0 0.2 2.4 2.4 1.44

Formula Used

Linear momentum conservation
m1u1 + m2u2 = m1v1 + m2v2
Restitution relation
e = (v2 - v1) / (u1 - u2)
Final velocities for general inelastic collision
v1 = [m1u1 + m2u2 - m2e(u1 - u2)] / (m1 + m2)
v2 = [m1u1 + m2u2 + m1e(u1 - u2)] / (m1 + m2)
Perfectly inelastic collision
v = (m1u1 + m2u2) / (m1 + m2)
Kinetic energy
KE = ½mv², and Energy Lost = KEinitial - KEfinal

How to Use This Calculator

  1. Select General Inelastic or Perfectly Inelastic.
  2. Enter both masses in kilograms.
  3. Enter initial velocities in meters per second.
  4. Use negative values for objects moving in the opposite direction.
  5. For general inelastic cases, enter restitution between 0 and 1.
  6. Press Calculate Collision to display the result above the form.
  7. Review velocities, momentum check, kinetic energy change, and impulse.
  8. Use the CSV or PDF buttons to export the result set.

Frequently Asked Questions

1. What is an inelastic collision?

An inelastic collision conserves total momentum but not total kinetic energy. Some energy changes into sound, heat, deformation, or internal vibration during impact.

2. What makes a collision perfectly inelastic?

A perfectly inelastic collision is the strongest inelastic case. The bodies stick together after impact and move with one shared final velocity.

3. Why does the calculator ask for restitution?

The coefficient of restitution measures how strongly bodies separate after impact. A value near 0 means stronger energy loss. A value near 1 behaves more elastically.

4. Can I use negative velocities?

Yes. Negative velocity represents motion opposite to the chosen positive direction. This is useful for head-on collisions or objects approaching each other.

5. Why can momentum stay constant when energy drops?

Momentum conservation follows from external force balance. Kinetic energy can still decrease because part of it converts into other energy forms during deformation or heating.

6. What units should I use?

Use kilograms for mass and meters per second for velocity. The outputs then appear in standard SI units such as joules and kilogram meter per second.

7. What does the momentum check difference show?

It shows final momentum minus initial momentum. A value very close to zero confirms the calculation is numerically consistent with momentum conservation.

8. When should I choose general versus perfect mode?

Choose general mode when the objects separate after impact. Choose perfect mode when they lock together and continue with a shared velocity.

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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.