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MotionLab
Both momentum and kinetic energy are conserved — solve for both final velocities in one step.
In a perfectly elastic collision, total kinetic energy is conserved — no energy is lost to heat, sound, or deformation. Billiard balls are approximately elastic; car crashes are highly inelastic. The distinction determines whether you need one conservation law (momentum only) or two (momentum + energy).
Newton's cradle (the desk toy with swinging steel balls) demonstrates elastic collisions beautifully — when one ball strikes, it stops and the ball on the opposite end flies out at the same speed, simultaneously conserving both momentum and kinetic energy.
v₁′ (m/s)
-3.4
Conservation of momentum + KE
What you entered
v₁′ = [(m₁−m₂)/(m₁+m₂)]v₁ + [2m₂/(m₁+m₂)]v₂
[(2−3)/(2+3)]×5 + [2×3/(2+3)]×-2= -3.4 m/sv₂′ = [2m₁/(m₁+m₂)]v₁ + [(m₂−m₁)/(m₁+m₂)]v₂
[2×2/(2+3)]×5 + [(3−2)/(2+3)]×-2= 3.6 m/sKE initial = ½m₁v₁² + ½m₂v₂²
0.5×2×5² + 0.5×3×-2²= 31 JKE final (conserved in elastic collision)
0.5×2×-3.4² + 0.5×3×3.6²= 31 JResult
v₁′ (m/s): -3.4
After the elastic collision: object 1 (2 kg) moves at -3.4 m/s, object 2 (3 kg) at 3.6 m/s. Total KE conserved at 31 J.