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Newton's Second Law (Translational Dynamics)

AP Physics 1· difficulty 3/5

m F 30°

A horizontal force FF is applied to a 2 kg2~\text{kg} block resting on a frictionless 30∘30^\circ incline. What must FF be so that the block stays at rest? (g≈10 m/s2g \approx 10~\text{m/s}^2.)

  • A

    10 N10~\text{N}

  • B

    17 N17~\text{N}

  • C

    20 N20~\text{N}

  • D

    12 N12~\text{N}

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Explanation

Along the incline: Fcos⁡30∘=mgsin⁡30∘⇒F=mgtan⁡30∘=(2)(10)(1/3)≈11.5 NF\cos 30^\circ = mg\sin 30^\circ \Rightarrow F = mg\tan 30^\circ = (2)(10)(1/\sqrt{3}) \approx 11.5~\text{N}, rounded to 12 N12~\text{N}.

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