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?

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Solutions of Savchenko Problems in Physics
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    <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>


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