for a block traveling around a frictional loop-de-loop
N=m(v2/r + g cos θ )
E lost to friction = r∫0θ N μk
½
½ (v0)2 = ½ v2 + gr(1 - cos θ ) + μk r∫0θ (v2/r + g cos θ ) dθ
½ v2 = ½ (v0)2 - gr(1 - cos θ ) - μk r∫0θ (v2/r + g cos θ ) dθ
[v(θ )]2 = (v0)2 - 2gr(1 - cos θ ) - 2μk r∫0θ ([v(θ )]2/r + g cos θ ) dθ
...
v(θ ) = ?










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Today's life lesson: There are some truely lovable people out there, the rest are complete assholes.
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=Apophysis
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Fractal and 3D Landscape Artist!
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