A circular curve of radius R in a new highway is designed so that a car travelin

Question

A circular curve of radius R in a new highway is designed so that a car traveling at speed v0, can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from vmin to tmax. Derive formulas for vmin and vmax as functions of mu s, v0, and R. Express your answers in terms of the variables mu s, v0, and R, and appropriate constants. Enter your answers separated by a comma. v min, v max=

Explanation / Answer

In Vmin, frictional force acts towards outside.
So, forces parallel to the road are

mgsin = mv^2/r cos + mgcos

v^2/r cos = g(sin - cos)

v^2 = rg(tan - )

Vmin = [rg(tan-)]

For Vmax, friction acts towards center

mgsin + mgcos = mv^2/r cos

v^2/r cos = g(sin + cos)

v^2 = rg(tan + )

Vmin = [rg(tan+)]

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