In figure $m_{1} = 5 k g, m_{2} = 2 k g$ and $F = 1 N$ . Find the acceleration of either block. Describe the motion of $m_{1}$ if the string breaks but $F$ continues to act.

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Solution

Let the acceleration of the blocks be a.
The free- body diagrams for the both the blocks are shown below.
From the free- body diagram
$m_{1} a = m_{1} g + F - T . . . . . . . (i)$
Again from the free- body diagram,
$m_{2} a = T - m_{2} g - F . . . . . . (i i)$
Adding equation $(i)$ and $(i i)$ we have
$a = g \frac{m_{1} - m_{2}}{m_{1} + m_{2}}$

$\Rightarrow a = \frac{3 g}{7} = \frac{29.4}{7}$

$= 4.2 m / s^{2}$
Hence, acceleration of the block is $4.2 m / s^{2}$
After the string breaks, $m_{1}$ moves downwords with force $F$ acting downward. Then,
$m_{1} a = F + m_{1} g$
$5 a = 1 + 5 g$
$\Rightarrow a = \frac{5 g + 1}{5}$
$= g + 0.2 m / s^{2}$

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In figure m1=5 kg,m2=2 kg and F=1 N. Find the acceleration of either block. Describe the motion of m1 if the string breaks but F continues to act.

In figure $m_{1} = 5 k g, m_{2} = 2 k g$ and $F = 1 N$ . Find the acceleration of either block. Describe the motion of $m_{1}$ if the string breaks but $F$ continues to act.