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In the y direction
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I write N - m · g · cos(θ) = m · ay.
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That's simply writing down Newton's Laws as two laws,
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one along x and one along y,
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and putting in whatever we know.
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What happens next is up to what else we know.
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Well, we know that this block is sliding down the hill,
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it's not going into the block,
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nor is it flying out of the block; it's moving along the block.
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That's the reason we chose a coordinate to be perpendicular to the block,
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because that coordinate,
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the y coordinate, it's not changing.