Collisions
- Distinguish elastic from inelastic collisions
- Solve a perfectly inelastic collision where objects stick together
- Recognize that kinetic energy is conserved only in elastic collisions
Momentum is always conserved; energy is not
In every collision within an isolated system, momentum is conserved. Kinetic energy is a different story. An elastic collision conserves kinetic energy too (think of hard billiard balls). An inelastic collision loses some kinetic energy to heat, sound, and deformation, even though momentum is untouched. The key habit: reach for momentum conservation first, and only invoke energy if the collision is stated to be elastic.
Perfectly inelastic: they stick together
A perfectly inelastic collision is the extreme case where the objects stick together and move as one afterward, sharing a single final velocity. Because the two masses combine, m₁v₁ + m₂v₂ = (m₁ + m₂)v′. This type loses the most kinetic energy of any collision, yet momentum is still perfectly conserved — a great reminder that the two conservation laws are separate.
A 3 kg cart moving at 4 m/s collides with and sticks to a 1 kg cart at rest. Find their common speed afterward.
- 1.Total momentum before: 3 × 4 + 1 × 0 = 12 kg·m/s.
- 2.They stick, so afterward the combined mass is 3 + 1 = 4 kg moving at v′.
- 3.Conserve momentum: 12 = 4 × v′.
- 4.Solve: v′ = 12 ÷ 4 = 3 m/s.
For a "stick together" problem, add the masses on the after-side and use one shared velocity. Total momentum stays the same; you divide it by the combined mass to get the final speed.
A 3 kg cart moving at 4 m/s collides with and sticks to a stationary 1 kg cart. What is the speed of the combined carts?
In which type of collision is kinetic energy conserved?
Two equations, two situations: momentum conservation works for every collision, but the kinetic-energy conservation equation is only valid for collisions the problem calls elastic. Never assume energy is conserved unless told so.
Answer the 2 checkpoints as you read.
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