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Kinetic and Static Friction

AP Physics 1· difficulty 4/5

θ v

A car rounds a circular banked curve of radius rr banked at angle θ\theta. For what speed vv can the car traverse the curve with no friction required between the tires and the road?

  • A

    v=grtan⁡θv = gr\tan\theta

  • B

    v=gr/tan⁡θv = \sqrt{gr/\tan\theta}

  • C

    v=grsin⁡θv = \sqrt{gr\sin\theta}

  • D

    v=grtan⁡θv = \sqrt{gr\tan\theta}

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Explanation

With no friction, Nsin⁡θ=mv2/rN\sin\theta = mv^2/r (centripetal) and Ncos⁡θ=mgN\cos\theta = mg (vertical). Dividing: tan⁡θ=v2/(gr)\tan\theta = v^2/(gr), so v=grtan⁡θv = \sqrt{gr\tan\theta}.

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