계산 방법 운동량 (p = mv): 충격량 & Conservation

계산 운동량 with p = mv and impulse J = FΔt = Δp. Conservation in collisions, unit traps, 일ed examples, and a free 운동량 calculator.

What 운동량 Asks

운동량 measures how much motion a 질량 has. A heavy object moving slowly can have the same 운동량 as a light object moving fast — 질량 and 속도 both matter.

Linear 운동량 is p = m × v. 질량 m in kilograms times 속도 v in metres per second gives 운동량 in kg·m/s. 운동량 is a vector: direction matches 속도.

If you have m and v (or p and one unknown), open the free 운동량 calculator first, then return here for impulse, conservation, and collision links.

The 공식s

  • p = mv — 운동량 from 질량 and 속도.
  • m = p / v — find 질량.
  • v = p / m — find 속도.
  • J = F Δt = Δp — impulse equals change in 운동량.
  • F = Δp / Δt — average 힘 from a 운동량 change over time.

    • 충격량 J has the same 단위 as 운동량 (kg·m/s, also written N·s). A constant 힘 acting for time Δt transfers impulse J = FΔt to the object.

    Conservation of 운동량

    When external 힘s are negligible during a short interaction (like a collision), total 운동량 before equals total 운동량 after.

  • Two objects: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
  • Pick one direction as positive and keep signs consistent.
  • 운동 에너지 is not always conserved — 운동량 usually is.

    • For final 속력s after elastic, sticky, or partial-bounce collisions, use the collision calculator and the full

    collisions guide.

    운동량 vs 운동 에너지

    운동 에너지 is KE = ½mv² — it depends on v squared. 운동량 is mv — linear in v. See kinetic 에너지 when the question asks about 에너지 loss in a crash, not just 운동량 balance.

    단위

  • m → kg (convert g to kg).
  • v → m/s (divide km/h by 3.6).
  • p → kg·m/s (same as N·s).
  • F → N, Δt → s for J = FΔt.

    • 풀이 예제

    예제 1: 2.0 kg at 3.0 m/s

    p = mv = (2.0)(3.0) = 6.0 kg·m/s in the direction of motion.

    예제 2: find 속도

    p = 12 kg·m/s, m = 4.0 kg. v = p/m = 12/4.0 = 3.0 m/s.

    예제 3: impulse from a 힘

    F = 50 N for Δt = 0.20 s. J = FΔt = (50)(0.20) = 10 N·s = 10 kg·m/s change in 운동량.

    예제 4: conservation 확인

    m₁ = 2 kg at 4 m/s hits m₂ = 2 kg at rest and they stick. v = (2×4 + 2×0)/(2+2) = 2 m/s. Total p before = 8, after = (4)(2) = 8 kg·m/s.

    흔한 실수

  • Using grams with m/s without converting 질량 to kg.
  • Leaving km/h in p = mv without converting to m/s.
  • Treating 운동량 as always positive — direction and sign matter.
  • Assuming KE is conserved whenever 운동량 is (only elastic collisions conserve both).

    • 확인 It on the 계산기

    운동량 calculator — p = mv and J = FΔt.

    충돌 calculator.

    운동 에너지 calculator.

    힘 calculator.

    학습 p = mv and confirm every home일 number on the calculator.

    문서

    • 탄성 위치 에너지 공식 (U = ½kx²): 계산기 & 예제
    • 계산 방법 전기 전력 (P = VI, I²R, V²/R)
    • 계산 방법 파동 속도 (v = fλ): 주파수 × 파장
    • 계산 방법 무게 (W = mg): 질량 vs 힘
    • 계산 방법 밀도 (ρ = m/V): 질량 ÷ Volume
    • 계산 방법 가속도 (a = (v − u)/t)

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