A coin is placed on a wedge with an angle \alpha. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?

Savchenko Solutions

Solutions of Savchenko Problems in Physics
knowledge must be free

    <h3 id="back-link"><a href="/#1.5">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.5.4.$ A coin is placed on a wedge with an angle $\alpha$. With what minimum acceleration should the wedge move along the horizontal plane so that the coin falls freely down?
    </p>

    <h3>Solution</h3>
    <p>
        <p>During the time interval $t$, the coin changed its horizontal and vertical coordinates to $x$ and $y$, respectively</p>

Considering the horizontal acceleration $a$ and the acceleration of gravity $g$, we find $x$ and $y$

$$x = \frac{at^2}{2}$$

$$y = \frac{gt^2}{2}$$

Considering that the body did not come off the wedge

$$y = x \tan \alpha$$

From where

$$\fbox{$a = g \text{ ctg} \alpha $}$$

    <h4>Answer</h4>
    <p>
        $$a = g \text{ ctg} \alpha $$
    </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>