WAEC 2011 · Paper 2 · Q18

(a)
A uniform bar $PQ$ of length $60\text{ cm}$ and weight $20\text{ N}$ is supported at two points $C$ and $D$ such that $|PC| = 10\text{ cm}$ and $|QD| = 15\text{ cm}$ . Two forces $10\text{ N}$ and $15\text{ N}$ are placed at $P$ and $Q$ respectively. If the system remains in equilibrium under the action of these forces, calculate the reactions at $C$ and $D$ .
Separate values with commas, e.g. 3, −2
(b)
Two forces $3\mathbf i\text{ N}$ and $4\mathbf j\text{ N}$ act on an object of mass $5\text{ kg}$ . Find the acceleration of the object.

Worked solution (try it first)

Measured from $D$ : $P$ is 45 cm, $C$ is 35 cm and the centre is 15 cm on one side.
$Q$ is 15 cm on the other.
Moments about $D$ : $35R_C + 15 \times 15 = 20 \times 15 + 10 \times 45$ .
$35R_C = 300 + 450 - 225 = 525$ , so $R_C = 15\text{ N}$ .
Up = down: $R_C + R_D = 10 + 20 + 15 = 45$ , so $R_D = 30\text{ N}$ .

The forces are at right angles: $|\mathbf F| = \sqrt{3^2 + 4^2}$
$= 5\text{ N}$ .
$a = \dfrac{F}{m}$
$= \dfrac55$
$= 1\text{ m s}^{-2}$ .