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Originally written by Kelandon:

Perpendicular to the plane, the normal force balances the component of gravity:
F_net = 0
n - Mg cos&#x03B8 = 0
n = Mg cos&#x03B8

Parallel to the plane, tension opposes friction and another component of gravity:
F_net = Ma
T - f - Mg sin&#x03B8 = Ma
T = f + Mg sin&#x03B8 + Ma
Since f = &#x03BCn, and n was found above:
T = &#x03BCMg cos&#x03B8 + Mg sin&#x03B8 + Ma

Now the hanging mass. I'll define up as positive, which means, since it's falling, its acceleration is in the negative direction. Use that the tension is equal to the tension found above.
F_net = 2Ma
T - 2mg = -2Ma
&#x03BCMg cos&#x03B8 + Mg sin&#x03B8 + Ma - 2Mg = -2Ma
Cancel M's and move the a's to one side:
&#x03BCg cos&#x03B8 + g sin&#x03B8 - 2g = -2a - a
Factor out the g:
a = (g)(-1/3)(&#x03BC cos&#x03B8 + sin&#x03B8 - 2)

Plugging in values, this yields a = 3.43 m/s^2.

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Originally written by Jumpin' Salmon:

...I think we all need to take a breath of semi-stale air and think about how we react to the world around us,...

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Originally written by root:

[QUOTE]Taliesin: I think the real would-be tyrants are incognito and hiding in the third quadrant - way down in the corner so no one will suspect m--- them.

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Originally written by Jewel:

Of course they can, God created science and the people who like to study it.

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Originally written by Nioca:
The
Lord of the Rings trilogy was... well, to be honest, I didn't actually care much for it. I found that it had way too many story lines going at once, moved too slowly, and at times was repetitive or tedious. It focused way too much on details that had to be remembered for later and not enough on telling the story. Maybe that's why I preferred [i]The Hobbit[i].[/QB]

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