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Tension in a String

The masses ...

Question

The masses $m_{1}, m_{2}$ and $m_{3}$ of the three bodies shown are $5 k g$ , $2 k g$ and $3 k g$ respectively. Calculate the values of tensions $T_{1}, T_{2}$ and $T_{3}$ when:
(i) the whole system is going upwards with an acceleration of $2 m / s^{2}$ and (ii) the whole system is stationary.
( $g = 9.8 m / s^{2}$ )

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Solution

Given,
$\begin{matrix} a = 2 m s^{- 2} g = 9.8 m s^{- 2} \end{matrix}$
For $T_{1}$
$\begin{matrix} T_{1} - 5 g - T_{2} = 5 \times 2 = 10 T_{1} - 5 g - T_{2} = 10 \end{matrix}$
For $T_{2}$
$\begin{matrix} T_{2} - T_{3} - 2 g = 2 \times 2 = 4 T_{2} - T_{3} - 2 g = 4 \end{matrix}$
For $T_{3}$
$\begin{matrix} T_{3} - 3 g = 3 \times 2 = 6 T_{3} - 2 = 6 g T_{3} = 36 N \end{matrix}$
Solving the equtions,
$\begin{matrix} T_{2} - 36 - 20 = 4 T_{2} = 60 N T_{1} = 10 + 50 + 60 = 120 N \end{matrix}$

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