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Conceptual question

by ballahboy
Tags: conceptual
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ballahboy
#1
Nov20-04, 05:04 PM
P: 34
An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the necessary force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. Show that for a given speed v and a radius of r , the curve must be banked at the angle (theta) such that tan(theta)=v^2/r*g
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vsage
#2
Nov20-04, 05:08 PM
P: n/a
What have you tried? think about what tan(theta) is in terms of sine and cosine and what sine and cosine would represent in this case.
ballahboy
#3
Nov20-04, 05:24 PM
P: 34
this is what i was thinking...

Fn sin(theta) = mv^2/r
(mg/cos(theta))sin(theta) = mg tan(theta) = mv^2/r
tan theta = v^2/(rg)

does that look right?


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