$2.1.11.$ Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.
Let's write Newton's second law for the vertical axis $$ \left\{\begin{matrix} m_1a = T - m_1g\\ m_2a = m_2g - T \end{matrix}\right. $$ From here we express the acceleration, which will be the same for both loads due to the inelasticity of the thread. $$ \fbox{$a = g\frac{m_2-m_1}{m_2+m_1}$} $$ We substitute into the system of equations and find the tension force of the thread $T$ $$ \fbox{$T = \frac{2m_1m_2g}{m_1+m_2}$} $$
$$a = g\frac{m_2-m_1}{m_2+m_1}$$ $$T = \frac{2m_1m_2g}{m_1+m_2}$$
Straton