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_{y}= N - mg cos ø = ma = 0".

And "[tex]\Sigma[/tex]F

_{x}= mg sin ø = ma" (frictionless).

So, in the y direction, "

**N = mg cos ø**".

But on a banked curve, "[tex]\Sigma[/tex]F

_{y}= N cos ø - mg = ma= 0".

And "[tex]\Sigma[/tex]F

_{x}= N sin ø = ma = mv²/r" (frictionless).

So, in the y direction, "

**N cos ø = mg**".

I know how to get "tan ø = v²/rg".

The two free body diagrams look identical to me so why doesn't "

**N = mg cos ø**" (from inclined plane) work to get "tan ø = v²/rg"?