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Newton's First Law (Translational Equilibrium)

AP Physics 1· difficulty 3/5

A weight WW hangs from two ropes attached to a ceiling. Rope 1 makes 30∘30^\circ with vertical and rope 2 makes 60∘60^\circ with vertical. The tension T1T_1 in rope 1 (the more vertical one) is

  • A

    Larger than T2T_2.

    check_circle
  • B

    Equal to T2T_2.

  • C

    Not enough info.

  • D

    Smaller than T2T_2.

Explanation

Vertical components must sum to WW: T1cos⁡30+T2cos⁡60=WT_1\cos 30 + T_2\cos 60 = W. Horizontal components cancel: T1sin⁡30=T2sin⁡60T_1\sin 30 = T_2\sin 60, giving T2=T1sin⁡30/sin⁡60=T1/3<T1T_2 = T_1\sin 30/\sin 60 = T_1/\sqrt 3 < T_1.

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