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Newton's First Law (Translational Equilibrium)

AP Physics 1· difficulty 3/5

W T₁ T₂ 45° 45°

A 100 N100~\text{N} weight hangs from two ropes attached to a horizontal ceiling, each at 45∘45^\circ below the ceiling (i.e., 45∘45^\circ from horizontal). What is the tension in each rope?

  • A

    71 N71~\text{N}

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  • B

    50 N50~\text{N}

  • C

    141 N141~\text{N}

  • D

    100 N100~\text{N}

Explanation

Vertical equilibrium: 2Tsin⁡45∘=W⇒T=W/(2sin⁡45∘)=100/(2)≈71 N2T\sin 45^\circ = W \Rightarrow T = W/(2\sin 45^\circ) = 100/(\sqrt{2}) \approx 71~\text{N}.

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