Embedding collision: 0.1 kg into 0.2 kg

A 0.1 kg ball moving at 6 m/s hits a 0.2 kg ball moving in the same direction at 3 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 = (0.1×6 + 0.2×3) ÷ (0.1+0.2) = 4
   Perfectly inelastic collision: the bodies share one speed afterwards

Why it works

With no external force along the line of motion, total momentum is conserved: m₁v₁ + m₂v₂ = (m₁ + m₂)v. In a perfectly inelastic collision the bodies stick together, so they share one final velocity.

Common mistakes

• Using the sum of the momenta but forgetting to divide by the combined mass.
• Averaging the two speeds as (6 + 3) ÷ 2 instead of using the masses.

Related

inelastic-collision bullet-embed-block-common-speed elastic-collision-two-balls-speed