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About Me Member Fractal Artist wanderingnobody25/Male/United States Recent Activity Deviant for 4 Years
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Physics

Mon Apr 24, 2006, 3:54 PM
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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 m (v0)2 = ½ m v2 + mgr(1 - cos θ ) + r∫0θ [(v2/r + g cos θ ) m μk] dθ

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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