Bullet embeds in a block: common speed

A 10 g bullet at 500 m/s embeds in a 0.99 kg block at rest. Find their common speed.

Step-by-step

1. m₁v₁ + m₂v₂ = (m₁ + m₂)v
   Momentum is conserved in the collision (no external horizontal force)
2. v = (0.01×500 + 0.99×0) ÷ (0.01+0.99) = 5
   Perfectly inelastic collision: the bodies share one speed afterwards

Why it works

In a perfectly inelastic collision momentum is conserved but kinetic energy is not. The total momentum before equals the momentum of the combined mass afterwards.

Common mistakes

• Conserving kinetic energy (that only holds for elastic collisions).
• Forgetting to add the masses after the collision.

Related

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