A force of 5 N gives a mass $m_{1}$ . an acceleration of 10 m $s^{- 2}$ and a mass $m_{2}$ . an acceleration of 20 m $s^{- 2}$ . What acceleration would it give if both the masses were tied together?

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Solution

For mass $m_{1}$
newton 2nd law
$F = m_{1} a_{1}$
$5 = m_{1} \times 10$
$m_{1} = \frac{1}{2} k g$
For mass $m_{2}$
$F = m_{2} a_{2}$
$5 = m_{2} \times 20$
$m_{2} = \frac{1}{4} k g$
if tied together
Total mass = $m_{1} + m_{2} = \frac{1}{2} + \frac{1}{4} = \frac{3}{4} k g$
Now
$F = M_{T} Q_{T}$
$a_{T} = \frac{5}{m_{T}} = \frac{5 \times 4}{3} = \frac{20}{3} m / s^{2}$

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