The edge of a smooth horizontal table is rounded along a circle of radius r. What is the lowest speed you need to put a small body on the table so that it reaches the rounding and immediately flies along the parabola?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.3">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.3.26.$ The edge of a smooth horizontal table is rounded along a circle of radius $r$. What is the lowest speed you need to put a small body on the table so that it reaches the rounding and immediately flies along the parabola?

    <h3>Solution</h3>
    <p>

For a body to fly along a parabola, it is necessary that at the moment of separation it be in a state of weightlessness

The force of gravity will be compensated by centrifugal force

$$mg = \frac{mv^2}{r}$$

Where do we express $v$

$$\boxed{v = \sqrt{gr}}$$

    <h4>Answer</h4>
    <p>
        $$v = \sqrt{gr}$$
    </p>


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