An unbanked circular highway curve on level ground makes a turn of 90°. The highway carries traffic at 108 km-hr–1, and the centripetal force on a vehicle is not to exceed 1/10 of its weight. What is the minimum length of the curve?
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Question

An unbanked circular highway curve on level ground makes a turn of 90°. The highway carries traffic at 108 km-hr–1, and the centripetal force on a vehicle is not to exceed 1/10 of its weight. What is the minimum length of the curve?

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G1 Physics · Accepted Answer

The allowed centripetal acceleration is 0.1g. With v=108 km/h=30 m/s, r(min)=v²/(0.1g)=900 m. A 90° arc has length (π/2)r≈1.41 km. Hence A.