Find the shared velocity and kinetic energy lost when two objects collide and stick together. Enter both masses in kilograms and their velocities immediately before impact in metres per second. Choose one positive direction and use negative velocities for motion in the opposite direction.
- Enter the two masses in kilograms. This calculator accepts masses of at least 0.000000001 kg.
- Enter both velocities in m/s using the same reference frame and positive direction. Enter 0 for a stationary object.
- Read the combined final velocity: its sign gives the direction, and its magnitude gives the speed.
- Compare the initial and final kinetic energies. The energy lost is the decrease in translational kinetic energy, measured in joules.
For a head-on collision, the initial velocities have opposite signs. For a rear-end collision, they can have the same sign. The calculator assumes an impact occurs; it does not determine whether the objects meet from their positions.
A 2 kg object moving at +3 m/s strikes a stationary 1 kg object and sticks to it. The combined velocity is (2 × 3 + 1 × 0) / (2 + 1) = +2 m/s. Initial kinetic energy is 9 J, and final kinetic energy is 6 J, so 3 J of translational kinetic energy is lost.
| Mass 1 (kg) | Velocity 1 (m/s) | Mass 2 (kg) | Velocity 2 (m/s) | Final velocity (m/s) | Energy lost (J) |
|---|---|---|---|---|---|
| 2 | 3 | 1 | 0 | 2 | 3 |
| 1 | 2 | 1 | -2 | 0 | 4 |
| 1 | 0 | 3 | -4 | -3 | 6 |
| 2 | 3 | 1 | 3 | 3 | 0 |
This is a classical, one-dimensional model for two objects that remain joined after impact, with negligible net external impulse during the collision. It models translational motion and does not include rotation, rebound or relativistic effects. Use velocities immediately before and after impact in the same inertial reference frame.
Kinetic energy lost is transferred into other forms, such as deformation, internal energy and sound; total energy is conserved. A perfectly inelastic collision does not necessarily remove all kinetic energy. The joined objects retain translational kinetic energy whenever their final velocity is nonzero.
Equal initial velocities give zero energy loss and represent a no-relative-motion limiting case. They do not establish that an impact occurs. Results are displayed to six decimal places, so very small nonzero values may appear as zero. Unavailable results from invalid or excessively large inputs do not mean zero.
Why can the final velocity be negative?
A negative result means the joined objects move opposite to your chosen positive direction. Keep the sign of each initial velocity when entering the values.
When do the joined objects stop?
They stop when the total initial momentum is zero: m1 × u1 + m2 × u2 = 0. In that reference frame, all initial translational kinetic energy is lost.
Can I use this for objects that bounce apart?
No. This calculator assumes both objects share one final velocity and remain together. A collision with rebound needs a different model, such as one using a coefficient of restitution.