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1. The problem statement, all variables and given/known data

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 force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the path

a.Show that for a given speed v and radius r the curve must be banked at an angle [tex]\Theta[/tex] such that tan[tex]\Theta[/tex] = v^2/r * g

2. Relevant equations

a_c (centripetal acceleration) = V^2 / r

[tex]\Sigma[/tex]F_y = m * a = 0

3. The attempt at a solution

i hope this diag. makes sense to you.....

According to the question a_c = n * Sin[tex]\Theta[/tex] ---- (1)

Then

[tex]\Sigma[/tex]F_y = m * a = 0

(n * Cos [tex]\Theta[/tex]) - (m * g) = 0

n = (m * g) / (Cos [tex]\Theta[/tex]) -------- (2)

substitute 2 in 1 for n

a_c = (m * g) / (Cos [tex]\Theta[/tex]) * Sin[tex]\Theta[/tex]

= (m * g) Tan [tex]\Theta[/tex]

now a_c (centripetal acceleration) = V^2 / r

therefore (V^2 / r) = (m * g) Tan [tex]\Theta[/tex]

and Tan [tex]\Theta[/tex] = (V^2) /(m * g * r)

what am i doing wrong ?.?

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# Homework Help: Centripetal Acceleration of curved exit ramp

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