Elastic Collision Calculator
In a perfectly elastic collision, both kinetic energy and momentum are conserved. Given two objects' masses and initial velocities, this calculator determines their final velocities after a one-dimensional elastic collision and verifies the conservation laws.
An elastic collision is one in which the total kinetic energy of the system is conserved (no energy is lost to heat, sound, or deformation). The conservation of both momentum and kinetic energy yields two equations that can be solved simultaneously for the two final velocities:
v1f = ((m1 - m2)v1 + 2m2v2) / (m1 + m2)
v2f = ((m2 - m1)v2 + 2m1v1) / (m1 + m2)
Special cases are instructive: when two equal masses collide, they exchange velocities. When a small object bounces off a much larger stationary one, the small object reverses direction at nearly the same speed. When a large object hits a small stationary one, the small one flies off at nearly twice the large object's speed. True elastic collisions occur in atomic and subatomic physics; macroscopic collisions always lose some energy to deformation and heat.