WAEC 2012 · Paper 2 · Q8

Not to scale.

(a)
The diagram shows a uniform rod of mass $2.4\text{ kg}$ , held in equilibrium by means of two strings inclined at $25^\circ$ and $54^\circ$ to the horizontal. Calculate the tensions in the strings. $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The weight is $2.4 \times 10 = 24\text{ N}$ .
Across: $T_1\cos25^\circ = T_2\cos54^\circ$ , so $T_2 = 1.5419\,T_1$ .
Up: $T_1\sin25^\circ + T_2\sin54^\circ = 24$ , so $T_1(0.4226 + 1.2474) = 24$ .
$T_1 = \dfrac{24}{1.6700}$
$\approx 14.37\text{ N}$ (the string at $25^\circ$ ).
$T_2 = 1.5419 \times 14.37$
$\approx 22.16\text{ N}$ (the string at $54^\circ$ ).