Embedding collision: 0.5 kg into 1.5 kg

A 0.5 kg ball moving at 4 m/s hits a 1.5 kg ball moving in the same direction at 2 m/s. The two balls embed and move together (a perfectly inelastic collision). Find their common speed after the collision.

Step-by-step

1. m₁v₁ + m₂v₂ = (m₁ + m₂)v
   Momentum is conserved in the collision (no external horizontal force)
2. v = (0.5×4 + 1.5×2) ÷ (0.5+1.5) = 2.5
   Perfectly inelastic collision: the bodies share one speed afterwards

Why it works

Total momentum is conserved because no external force acts along the direction of motion: m₁v₁ + m₂v₂ = (m₁ + m₂)v. The embedded bodies end up with a single shared velocity.

Common mistakes

• Forgetting that the total mass after the collision is 0.5 + 1.5 = 2 kg.
• Forgetting to multiply the 1.5 kg ball's momentum by its own speed.

Related

inelastic-collision elastic-collision-two-balls-speed inelastic-collision-0-1kg-0-2kg-embed