Atwood Machine 공식 (a & T): 무료 계산기 & 풀이 예제
풀기 Atwood a = g|m₂−m₁|/(m₁+m₂) and T = 2m₁m₂g/(m₁+m₂). 무료-body signs, unit traps, examples, and a free Atwood calculator.
풀이 방법 an Atwood Machine (Quick 답)
An ideal Atwood machine is two 질량es on a string over a 질량less, frictionless pulley. Both 질량es share the same 가속도 magnitude a, and the string tension T is the same throughout.
Need 확인ed a and T now? Open the free Atwood machine calculator — then come back for free-body signs and traps.
Atwood Machine 공식s (a and T)
학생 often search “atwood machine 공식” or “atwood 가속도” for these two results. Once both 질량es and g are known, a and T are fixed — that is why a rearranging calculator covers most home일 확인s.
풀기 both on the free Atwood machine calculator.
무료-Body Diagrams
Descending (heavier) 질량: m_h g − T = m_h a.
Rising (lighter) 질량: T − m_l g = m_l a.
Add the equations and the tensions cancel: a = g(m_h − m_l)/(m_h + m_l). Substitute back for T.
Each hanging 질량 is an F = ma problem — refresh with the 힘 calculator.
단위
Trap: leaving 질량es in grams while g is 9.8 m/s² makes T look thousands of times too small.
풀이 예제
예제 1: 1.0 kg and 3.0 kg
g = 9.8 m/s². a = 9.8 × |3 − 1| / 4 = 4.9 m/s². T = 2(1)(3)(9.8)/4 = 14.7 N. The 3.0 kg 질량 descends. 확인: T = 1(9.8 + 4.9) = 14.7 N.
예제 2: equal 질량es
m₁ = m₂ = 2.0 kg → a = 0 and T = mg = 19.6 N. No 가속도; tension equals each 무게.
예제 3: find the heavier 질량
m₁ = 2.0 kg, a = 2.45 m/s², g = 9.8, m₂ heavier. m₂ = m₁(g + a)/(g − a) = 2.0(12.25)/7.35 ≈ 3.333 kg.
확인 예제 1–3 on the Atwood machine calculator.
흔한 실수
Sanity 확인: 0 ≤ a < g, and T sits between the two 무게s.
무료 Atwood Machine 계산기
Use the free Atwood machine calculator for 가속도, tension, and which 질량 descends, with substituted steps.
힘 calculator — F = ma on each 질량.
가속도 calculator — a = Δv/t.
Inclined plane calculator — another connected-질량 setup.
Master a = g|Δm|/Σm and T = 2m₁m₂g/Σm — then verify every home일 answer.