How this calculation works
Use a fixed signed axis and body ordering. Solve momentum conservation and restitution together. Report kinetic energy before and after and the equal/opposite impulse interpretation without estimating contact force.
Conserve m1u1 + m2u2, with v2 − v1 = e(u1 − u2)A worked example
Body 1 has 2 kg at +3 m/s; body 2 has 1 kg at −1 m/s. With e = 0.5, final velocities are +1 and +3 m/s. Momentum stays 5 kg·m/s, while kinetic energy falls from 9.5 to 5.5 J.
Good to know
An isolated two-body collision on one line with e from 0 through 1. No rotation, external impulse, collision duration or force-time peak. Already-separating states are rejected under the entered ordering.
Reference: Reference: model, definitions and assumptions (opens in a new tab) ↗
Keep the body ordering and the velocity signs together
This page places body 1 on the left and body 2 on the right at contact, with positive velocity pointing right. A first velocity of +3 m/s and second velocity of −1 m/s give a 4 m/s closing speed. Negative velocity means direction along the chosen axis, not negative speed magnitude.
If u1 is less than u2, the pair is already separating under that ordering and the input is rejected. Equal velocities give no closing speed and no modeled impulse. The tool solves a contact event, not the travel time until two initially separated bodies meet.
The kinetic energy calculator can check each object’s energy before and after impact. A momentum calculation additionally needs the signed velocities.
Momentum conservation does not require kinetic-energy conservation
For 2 kg at +3 m/s and 1 kg at −1 m/s, initial momentum is 5 kg·m/s and kinetic energy is 9.5 J. At restitution 0.5, the final velocities are +1 and +3 m/s. Momentum stays 5 kg·m/s, while final kinetic energy is 5.5 J.
The 4 J difference represents kinetic energy transformed into other forms under the model. At e = 1, kinetic energy is conserved. At e = 0, the two bodies share a final velocity of 5/3 m/s for these inputs. The table compares those outcomes without changing the initial masses or velocities.
Impulse is not the same as peak contact force
In the default collision, body 1 changes momentum from 6 to 2 kg·m/s, giving a signed impulse of −4 N·s. Body 2 receives the opposite +4 N·s. That exchange can be found without knowing how long the contact lasts.
A force-time shape and contact duration would be needed to infer average or peak force. The force calculator alone cannot supply those missing collision details. The kinetic energy calculator can check each body’s energy using its speed magnitude, whereas momentum requires the signed velocity used on this page.
A few questions, answered
What does restitution 0 mean here?
The two bodies leave with a common velocity. Under the isolated one-dimensional model, this is a perfectly inelastic outcome.
Does restitution 1 conserve kinetic energy?
Yes, for this supported ideal collision model. Momentum is conserved for every supported restitution value.
Can final velocity be negative?
Yes. It indicates motion toward the negative side of the chosen axis.
Does the calculator predict impact force?
No. It reports momentum change and impulse, without collision duration or a force-time curve.