(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two packages at UPS start sliding down the 20° ramp shown in Figure P8.25. Package A has a mass of 5.0 kg and a *coefficient of friction of 0.20. Package B has a mass of 10 kg and a coefficient of friction of 0.15. How long does it take package A to reach the bottom?

I call the larger mass m_{2}and the smaller mass m_{1}.

http://img166.imageshack.us/img166/1899/p825.gif [Broken]

2. Relevant equations

F=ma

f_{k}=μ_{k}n

3. The attempt at a solution

I have drawn two free body diagrams.

m_{1}

up: n_{1}

down:m_{1}gCos(θ)

left:F_{2 on 1}, m_{1}gSin(θ)

right: f_{k}_{1}

m_{2}

up: n_{2}

down: m_{2}gCos(θ)

left: m_{2}gSin(θ)

right:F_{1 on 2}, f_{k}_{2}

From this I wrote.

Σ μ θ

ΣF_{x}_{1}=f_{k}_{1}-F_{2 on 1}-m_{1}gSin(θ) = m_{1}a_{x}_{1}

ΣF_{y}_{1}=n_{1}-m_{1}gCos(θ)

therefore

n_{1}=m_{1}gCos(θ)

ΣF_{x}_{2}=F_{1 on 2}+f_{k}_{2}-m_{2}gSin(θ)=m_{2}a_{x}_{2}

ΣF_{y}_{2}=n_{2}-m_{2}gCos(θ)

therefore

n_{2}=m_{2}gCos(θ)

Now where to go from here? I am not sure but I believe I need to find the acceleration of the system since both are bound together by this law. By finding that I would then know a_{x}_{1}and a_{x}_{2}.

I'm just not sure how... two different μ_{k}confuse me, how can I find the total acceleration of the system if both are dragged by different coefficients?

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# Two Mass In Contact On Slope

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