A curve with a 200-m radius on a level road in banked at the correct angle for a

Question

A curve with a 200-m radius on a level road in banked at the correct angle for a speed of 60 km/h, i.e. a car traveling at this speed would remain on the road, even if the surface were frictionless. If a car travels around this curve at a speed of 90 km/h, what is the minimum coefficient of static friction between the tires and the road that will prevent skidding? If the surface were wet, would the speeding car in part (a) remain on the road? If it was raining, and the car had to slow down to a crawl (for example, to safely pass a stranded vehicle), would it slide down the inclined roadway?

Explanation / Answer

60 km/hr = 16.67 m/s
90 km/hr = 25 m/s

Intially, mv^2/r = mg sin

16.67^2 / 200 = 9.8 sin

= 8.15 degrees

(a) mv^2 /r = mgsin8.15 + mg cos 8.15

= (25^2 / 200 - 1.39)/9.7

= 1.79

(b)No.

The car slides up.

(c)Yes. If the speed goes less than 60 km/hr, it slides down...

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