Conservation of Energy

AP Physics 1· difficulty 3/5

At the <strong>top</strong> of a vertical loop of radius RR, what is the minimum speed needed for a ball on a frictionless track to maintain contact?

  • A

    gRgR

  • B

    2gR\sqrt{2gR}

  • C

    gR\sqrt{gR}

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  • D

    2gR2\sqrt{gR}

Explanation

At the top, gravity alone supplies centripetal force when normal force is zero: mg=mv2/Rvmin=gRmg = m v^2 / R \Rightarrow v_{\min} = \sqrt{gR}.

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