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Work-Energy Theorem

In terms of m...

Question

In terms of masses $m_{1}$ , $m_{2}$ and $g$ find the acceleration of both the blocks shown in Fig. .Neglects all friction and masses of the pulley

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Solution

Given,

Acceleration of lock $m_{1}$ is $a_{1}$ .

Acceleration of lock $m_{2}$ is $a_{2}$ .

String is non-stretchable

$a_{2} = 2 a_{1} . . . . . . . (1)$

$m_{2} g - 2 T_{1} = m_{2} a_{2} . . . . (2)$

$T_{1} = m_{1} a_{1} . . . . . . (3)$

From (1), (2) and (3)

$a_{2} = \frac{m_{2} g}{m_{1} + m_{2}}$ and $a_{1} = \frac{m_{2} g}{2 (m_{1} + m_{2})}$

Hence, acceleration of lock $m_{1} i s \frac{m_{2} g}{2 (m_{1} + m_{2})}$ and acceleration of lock $m_{2} i s \frac{m_{2} g}{(m_{1} + m_{2})}$

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