To save space, the entrance to one of the highest bridges in Japan is arranged in the form of a spiral line that wraps around a cylinder of radius R. The roadbed forms an angle \alpha with the horizontal plane. What is the acceleration of a car moving along it at a constant modulo velocity v?

Savchenko Solutions

Solutions of Savchenko Problems in Physics
knowledge must be free

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

    <h3> Statement </h3>
    <p>
        $1.3.29.$ To save space, the entrance to one of the highest bridges in Japan is arranged in the form of a spiral line that wraps around a cylinder of radius $R$. The roadbed forms an angle $\alpha$ with the horizontal plane. What is the acceleration of a car moving along it at a constant modulo velocity $v$?
    </p>

    <h3>Solution</h3>
    <p>
        <center>

Find the value of acceleration $a$:

$$a = \sqrt{a_{\tau}^2 + a_{n}^2}$$

Let $a_{\tau} = 0$, then $a_{n} = \frac{v^2}{R}$, where $v$ is the horizontal component of the velocity directed perpendicular to the axis of rotation.

Then the required acceleration will be equal to:

$$a = a_n$$

$$\fbox{$ a = \frac{v^2}{R} \cdot \cos^2 \alpha $}$$

    <h4>Answer</h4>
    <p>
        $$a = \frac{v^2}{R} \cdot \cos^2  \alpha $$
    </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>