|Nov20-04, 05:04 PM||#1|
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
|Nov20-04, 05:08 PM||#2|
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.
|Nov20-04, 05:24 PM||#3|
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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