WAEC 2013 · Paper 2 · Q8

Kinematics & dynamics

The diagram shows a light inextensible string that passes over a smooth pulley and carries masses of $6\text{ kg}$ and $5\text{ kg}$ at its ends. When the system is released from rest: $[\text{Take } g = 10\text{ m s}^{-2}]$

Not to scale.

(a)
find the acceleration of each mass;
(b)
calculate, correct to two decimal places, the distance moved in 2 seconds.

Worked solution (try it first)

The weights are $6 \times 10 = 60\text{ N}$ and $5 \times 10 = 50\text{ N}$ , so the 6 kg mass moves down and the 5 kg mass moves up.

(a)

Let $T$ be the tension.
For the 6 kg mass (moving down): $60 - T = 6a$ .
For the 5 kg mass (moving up): $T - 50 = 5a$ .
Add the two equations to remove $T$ : $10 = 11a$ .
So $a = \frac{10}{11}$
$\approx 0.91\text{ m s}^{-2}$ for each mass.

(b)

Use $s = ut + \frac12at^2$ with $u = 0$ and $t = 2$ .
So $s = \frac12 \times \frac{10}{11} \times 4$
$= \frac{20}{11}$ .
Each mass moves about $1.82\text{ m}$ in 2 seconds.

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