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.

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    <h3> Statement </h3>
    <p>
        $2.1.11.$ 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.

    <h3>Solution</h3>
    <p>
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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 $T$ $$\fbox{$T = \frac{2m_1m_2g}{m_1+m_2}$}$$

    <h4>Answer</h4>
    <p>
                <p>
    $$a = g\frac{m_2-m_1}{m_2+m_1}$$
    $$T = \frac{2m_1m_2g}{m_1+m_2}$$</p>
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