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

[PLAIN]http://rawrspace.com/Capture.JPG [Broken]

So when you draw out a force diagram, we find these two equations

mg-T=ma

rewriting in terms of T

T=mg-ma

and

T-MgSin[tex]\vartheta[/tex]-f=Ma

rewriting in terms of T

T=Ma+MgSin[tex]\vartheta[/tex]+f

I set the two equations equal to each other so I could solve for the acceleration since it is as rest when it starts (I figured that means that initial velocity is 0 )

setting them equal I get:

mg-ma=Ma+MgSin[tex]\vartheta[/tex]+f

Then I moved them so that I could start factoring out terms:

g(m-MSin[tex]\vartheta[/tex])-f=a(M+m)

finally, solving for a:

[g(m-MSin[tex]\vartheta[/tex])-f]/(M+m)=a

I also know that y-y_0=V_0t-(1/2)at^2

Since y final is 0 and y_0 is h, I get this equation:

-h=-(1/2)at^2

So this means that

(2h/a)^(1/2)=t

Pluging in a that I solved for above, I get

{(2h)/[g(m-MSin[tex]\vartheta[/tex])-f]/(M+m)}^(1/2)=t

That was my answer of the time it takes for the mass m to fall a distance h. Does that seem correct to you, or am I overlooking something ?

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# Homework Help: How long does it take mass m to fall distance h?

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