Question 1

What is the difference between elastic and perfectly inelastic collisions?

Accepted Answer

An elastic collision (e=1) conserves both momentum and kinetic energy. For equal masses, the velocities are completely exchanged. A perfectly inelastic collision (e=0) means the objects stick together and move with a common final velocity. Kinetic energy loss is maximum: ΔKE = μ(v1−v2)²/2 where μ = m1m2/(m1+m2) is the reduced mass. Real collisions fall between these extremes, with metal-on-metal typically around e=0.5–0.9 and rubber around e=0.7–0.9.

Question 2

How do you calculate post-collision velocities using the coefficient of restitution?

Accepted Answer

Using the generalized restitution equations: v1' = [(m1−e·m2)v1 + (1+e)m2·v2] / (m1+m2) and v2' = [(m2−e·m1)v2 + (1+e)m1·v1] / (m1+m2). For example, two equal 5 kg masses with v1=+5 m/s and v2=−3 m/s at e=1 (elastic): v1'=−3 m/s and v2'=+5 m/s (velocities exchange). At e=0 (perfectly inelastic): v1'=v2'=+1 m/s (they stick together).

Question 3

Is momentum always conserved in a collision?

Accepted Answer

Yes. In an isolated system with no external forces, total linear momentum m1v1 + m2v2 = m1v1' + m2v2' is always conserved regardless of whether the collision is elastic or inelastic. This follows directly from Newton's third law (equal and opposite impulses). Kinetic energy, however, is only conserved in elastic collisions; in inelastic collisions it is converted to heat, deformation, sound, and vibration. In LS-DYNA crash simulations, momentum balance is routinely verified as a quality check.

Question 4

How is the coefficient of restitution used in LS-DYNA contact definitions?

Accepted Answer

In LS-DYNA, the restitution coefficient is set via the RESTITUTION parameter in *CONTACT keyword cards. A value of e=0 models fully plastic impact (maximum energy absorption), while e=1 models elastic bounce. Typical values: metal-to-metal e=0.5–0.9, rubber bumpers e=0.7–0.9, drop tests on concrete e=0.3–0.6. This simulator lets you quickly verify expected post-impact velocities and energy loss before running the full FE analysis.

Quantity	Before	After
v₁ [m/s]	—	—
v₂ [m/s]	—	—
Total momentum p [kg·m/s]	—	—
Total kinetic energy KE [J]	—	—
Energy loss ΔKE [J]	—	—

1D Collision Simulator (Elastic & Inelastic)

Theory — Generalized Coefficient of Restitution