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.

Savchenko Solutions

Solutions of Savchenko Problems in Physics
knowledge must be free

    <h3 id="back-link"><a href="/#2.1">$\leftarrow$Back</a></h3>

    <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>
        <center>

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>


<footer class="row container">
  <br>
    <p>
        <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
    </p>
    <p>
        <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
    </p>
</footer>