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Re: Calculation

Posted by VictorM on Fri Jan 7 15:05:10 2005, in response to Re: Calculation, posted by Jeff H. on Thu Jan 6 20:53:25 2005.

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Sorry to disagree with your analysis, but sin(x) should be replaced with tan(x) in your formulas. On a perfectly banked curve there is only a force normal to the track acting on the train, so the train (and its passengers) feel no sideways force. This normal force (call it N) can resolved into two components: N*cos(x) balancing the force of gravity (m*g) and N*sin(x) providing the centripetal force (m*v**2/r). Therefore:
N*sin(x)=m*v**2/r, and
N*cos(x)=m*g
Dividing these two equations gives us tan(x)=v**2/(r*g)
Your formula for E is correct: E=56.5*sin(x)
Since, for small x, the sine and the tangent are almost equal, your final formula, E=(56*5/g)*(v**2/r), is a good approximation.

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