Question

In the following 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.

Answer 1

Let the acceleration of the blocks be a.
The free-body diagrams for both the blocks are shown below:

From the free-body diagram,
m₁a = m₁g + F − T    ...(i)

Again, from the free-body diagram,
m₂a = T − m₂g − F    ...(ii)

Adding equations (i) and (ii), we have:
\[a = g\frac{m_1 - m_2}{m_1 + m_2}\]
\[\Rightarrow a = \frac{3g}{7} = \frac{29 . 4}{7}\]
\[ = 4 . 2 m/ s^2\]

Hence, acceleration of the block is 4.2 m/s².
After the string breaks, m₁ moves downward with force F acting downward. Then,

m₁a = F + m₁g
5a = 1 + 5g
\[\Rightarrow a = \frac{5g + 1}{5}\]
\[ = g + 0 . 2 m/ s^2\]