At what speed will a car round a 52-m-radius curve, banked at a 45° angle, if no friction is required between the road and tires to prevent the car from slipping? (g = 9.8 m/s2 )

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At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s2)

Θ= 16º

Explanation:

With no friction, the up-slope centripetal acceleration must equal the down-slope gravitational acceleration, or

(v²/r)cosΘ = gsinΘ

v² /gr = sinΘ/cosΘ

v² /gr= tanΘ

Θ = arctan((12m/s)² / (9.8m/s² * 52m))

Θ= 16º