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WAEC 2022 · Paper 2 · Q7

A body of mass 18 kg18\text{ kg} is suspended by an inextensible string from a rigid support and is pulled by a horizontal force FF until the angle of inclination of the string to the vertical is 35∘35^\circ. If the system is in equilibrium, calculate the:

  1. (a)

    value of FF;

  2. (b)

    tension in the string.

Worked solution (try it first)
  1. The weight is 18×10=180 N18 \times 10 = 180\text{ N}.
  2. The string is at 35∘35^\circ to the vertical.
  3. Up: Tcos⁡35∘=180T\cos35^\circ = 180.
  4. Across: Tsin⁡35∘=FT\sin35^\circ = F.

(a)

  1. Divide: F=180tan⁡35∘F = 180\tan35^\circ
    ≈126.04 N\approx 126.04\text{ N}.

(b)

  1. T=180cos⁡35∘T = \dfrac{180}{\cos35^\circ}
    ≈219.74 N\approx 219.74\text{ N}.

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