Conservation of Momentum (Two Bodies)
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
Learning zone
With no external force acting, the total momentum of two colliding bodies before the impact equals the total after — always, whether they bounce, stick, or shatter. Kinetic energy is not so obliging; it survives only in a perfectly elastic collision. The principle was nailed down in 1668 when the Royal Society set the collision problem as a challenge and John Wallis, Christopher Wren and Christiaan Huygens independently sent in the answer.
Signs are everything in one dimension: pick a positive direction and stick with it, so a body moving the other way carries a negative velocity. A 2 kg cart at 5 m/s striking a stationary 3 kg cart and slowing to 1 m/s leaves the second cart at (10 + 0 − 2) ⁄ 3 ≈ 2.67 m/s. Because momentum is conserved in every collision, crash investigators use exactly this equation with skid-mark evidence to back out pre-impact speeds, and it works equally well for recoil: the rifle and the bullet start with zero total momentum and must end with zero.
- = Mass 1
- = Initial velocity 1
- = Mass 2
- = Initial velocity 2
- = Final velocity 1
- = Final velocity 2
- Mass 1 — Newton's Second Law, Kinetic Energy
- Initial velocity 1 — Final Velocity (Uniform Acceleration), Displacement (Uniform Acceleration)
- Mass 2 — Newton's Second Law, Kinetic Energy
- Initial velocity 2 — Final Velocity (Uniform Acceleration), Displacement (Uniform Acceleration)
- Final velocity 1 — Final Velocity (Uniform Acceleration), Velocity-Displacement Relation (v² = v₀² + 2ad)
- Final velocity 2 — Final Velocity (Uniform Acceleration), Velocity-Displacement Relation (v² = v₀² + 2ad)