In a simple Atwood machine, two unequal masses $m_{1}$ and $m_{2}$ are connected by a string going over a clamped light smooth pulley. In a typical arrangement shown in figure , $m_{1} = 300 g$ and $m_{2} = 600 g$ . The system is released from rest. Find the force exerted by the clamp on the pulley.

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Solution

$m_{1} = 0.3 k g, m_{2} = 0.6 k g$
$T - (m_{1} g + m_{2} a) = 0$ ... (i)
$\Rightarrow T = m_{1} g + m_{1} a$
$T + m_{2} a - m_{2} g = 0$ .... (ii)
$\Rightarrow T = m_{2} g - m_{2} a$
From equation (i) and equation (ii)
$m_{2} g + m_{1} a + m_{2} a - m_{2} g = 0$ ,
from $(i)$
$\Rightarrow a (m_{1} + m_{2}) = g (m_{2} - m_{1})$
$\Rightarrow a = f (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) = 9.8 (\frac{0.6 - 0.3}{0.6 + 0.3}) = 3.266 m s^{- 2}$
The force exerted by the clamp on the pulley is given by
$F - 2 T = 0$ $F = 2 T = 2 \times 3.9 = 7.8 N$

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In a simple Atwood machine, two unequal masses m1 and m2 are connected by a string going over a clamped light smooth pulley. In a typical arrangement shown in figure , m1=300g and m2=600g. The system is released from rest. Find the force exerted by the clamp on the pulley.