풀이 방법 탄성 and 비탄성 충돌s (1D 공식s)
풀기 1D elastic and inelastic collisions with 운동량 conservation, restitution e, and 일ed examples. Verify final 속력s with a free collision calculator.
What a 1D 충돌 Problem Asks
A one-dimensional collision is two 질량es interacting along a line. During the short impact, external 힘s are usually neglected, so linear 운동량 is conserved: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. 운동 에너지 may or may not be conserved — that is what separates elastic from inelastic cases.
Pick a positive direction (usually right) and keep it for every 속도 before and after the collision. Opposing motion uses opposite signs.
If you already have the 질량es and 속력s and only need 확인ed final velocities, open the free collision calculator first, then return here for the 공식s and traps.
Three Standard Cases
Perfectly inelastic (stick together)
The 질량es share one final 속력. Conserve 운동량 only: v = (m₁u₁ + m₂u₂) / (m₁ + m₂). This loses the maximum kinetic 에너지 allowed by 운동량 conservation. The coefficient of restitution is e = 0.
탄성 (e = 1)
Conserve both 운동량 and kinetic 에너지. The closed-form 1D results are:
Special case: equal 질량es exchange velocities. If m₁ = m₂ and one 질량 starts at rest, the moving 질량 stops and the other takes its 속력.
Partial restitution (0 < e < 1)
Real collisions often bounce with some 에너지 loss. The restitution coefficient e 비교s relative 속력 of separation to relative 속력 of approach. Use the general 1D 공식s with e inserted (the calculator’s partial mode).
단위 and Signs
Trap: treating a sticky collision as elastic conserves too much 에너지 and gives the wrong final 속력s.
풀이 예제
예제 1: equal 질량es, elastic
m₁ = m₂ = 2.0 kg, u₁ = 3.0 m/s, u₂ = 0. 탄성 공식s give v₁ = 0 and v₂ = 3.0 m/s. 운동량 before and after is 6.0 kg·m/s; KE stays 9.0 J.
예제 2: perfectly inelastic stick
m₁ = 3.0 kg at 4.0 m/s hits m₂ = 1.0 kg at rest and they stick. v = (12 + 0)/4 = 3.0 m/s. KE falls from 24 J to 18 J.
예제 3: 확인 with 운동량
Always verify m₁u₁ + m₂u₂ equals m₁v₁ + m₂v₂ within rounding. If it does not, a sign or 공식 mix-up is likely.
To build p = mv before you tackle two-body collisions, use the 운동량 calculator.
To 비교 에너지 before and after, use the kinetic 에너지 calculator.
흔한 실수
Sanity 확인: after a sticky collision the common 속력 lies between the two initial 속력s (or at an extreme if one 질량 is much larger).
확인 With the 무료 계산기
The collision calculator solves elastic, perfectly inelastic, and partial-restitution cases with visible steps, 운동량 확인s, and KE before/after.
충돌 calculator — 1D elastic and inelastic.
운동량 calculator — p = mv and impulse.
운동 에너지 calculator — KE = ½mv².
속도 calculator — find 속력s before colliding.
학습 the three cases, keep signs consistent, then confirm every answer on the calculator.