
Re: [問題] 動量不守恆(有摩擦力)

: 如題
: 答案是C
: 可是有摩擦力,怎麼算還是不會
將題目拆成兩個過程:一、A碰撞B後合體
二、合體後減速到停止
過程一,兩個觀念:1、碰撞前後動量守恆
2、碰撞前後動能不守恆(非彈性碰撞)
列式:碰撞前動量 = 4x10 = 40(m.kg) = 碰撞後動量
過程二,運用牛頓運動定律及運動學公式(F=摩擦力、Δmv=動量變化、Δt=減速時間、
s=移動距離=10、v=末速=0、v0=初速)
F = Δmv/Δt => 8 = 40 /Δt ,Δt = 5
又 s = v0t + 1/2 at^2 => 10 = -at^2 + 1/2 at^2,t=5帶入 => a = -0.8(m/s^2)
v = v0 + at => v0 = -at v0 = 4(m/s)
帶回碰撞後動量 = v0‧(ma+mb) = 40 => 4‧(4+mB) = 40 => mB = 6(kg)
或 F = ma => -8 = (4+mB)‧-0.8 => mB = 6(kg) #
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