Two bodies of the same mass connected by a thread slide along an inclined plane. Thread tension force T. There is no friction between one body and the board. Determine the friction force between the board and another body.

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    <h3> Statement </h3>
    <p>
        $2.1.46.$ Two bodies of the same mass connected by a thread slide along an inclined plane. Thread tension force $T$. There is no friction between one body and the board. Determine the friction force between the board and another body.
    </p>

    <h3>Solution</h3>
    <p>
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1. Since bodies of the same mass move down the plane with a stretched thread, the upper body will have a rough surface. The bodies will have the same accelerations with a stretched thread.

2. Let's write the equations of Newton's second law in projection on the direction of motion for each body separately: $$\left\{\begin{matrix} m_1g\\,\sin\alpha -T=m_1a_1 & \\ m_1g\\,\sin\alpha +T-F_т=m_2a_2 & \end{matrix}\right.$$

$$a_1=a_2$$

$$m_1=m_2$$

$$mg\,\sin\alpha +T-F_т=mg\,\sin\alpha -T$$

$$F_т=2T$$

    <h4>Answer</h4>
    <p>
        $$F = 2T$$
    </p>



    <p style="text-align: right; font-style: italic; font-size: 14;">   
      Aliaksandr Melnichenka<br>
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