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A car rounds a banked curve. The radius of curvature of the road is R, the banking angle is theta, and the coefficient of friction is u.

a) Determine the range of speeds the car can have without slipping up or down the banked surface.

This is what I've done for when the car is on the verge of sliding up the embankment. According to the way I've done it, the equation for sliding down the embankment is the same.

The sum of the forces in the radially inward direction is:

(the sum of the normals on the right and left tires) (N1 + N2)sintheta + (force of friction)costheta = ma(radially inward) = mvtan/R.

The sum of the forces in the vertical directions are:

(N1 + N2)costheta - (force of friction)sintheta - mg = 0

If I divide the first equation by the second I get:

vtangent = (R(tantheta - cottheta))^1/2 so tantheta - cottheta >= 0, but when tantheta = cottheta, vtan = 0 and when cottheta = 0, tantheta goes to infinity, so my ranges for vtangent are zero to infinity.

That can't be right. Can anyone tell me where I went wrong?

Thanks.[?]