One safety concern when designing highways is making sure that vehicles can stay

Question

One safety concern when designing highways is making sure that vehicles can stay on the road even in inclement weather. This consideration is perhaps most obvious with curves - if coecients of friction change with rain or ice, cars may slide o the road entirely if not carefully designed. As a result, curves on highways are often banked, or angled slightly upward, in order to allow cars to turn even with low friction forces. A certain segment of a highway is banked, with = 15, and the car shown is traveling out of the page. The turn makes part of a circle with a radius 350m. At what speed will cars be able to make the turn even without any friction (that is, assume that there is no friction)?

Explanation / Answer

Given

   banking angle is theta = 15 degrees

   radius of the curve is r = 350 m
  

   the speed of the car with which can able to make turn is v = ?

we know that the formula for bankin angle is

       Tan theta = v^2/r*g

       V = sqrt(r*g*tan theta)

       v =sqrt(350*9.8*tan15) m/s

       V = 30.3161 m/s

       V = 109.138 kmph

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