Savchenko Solutions

Solutions of Savchenko Physics Textbook

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#2.3">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $2.3.41.$ A part of the mass $m$ is detached from the load hanging on the spring of stiffness $k$. To what height will the remaining part of the cargo then rise?

    <h3>Solution</h3>
    <p>
        Since there is no interaction with external factors other than breakaway, all the work goes into changing the length of the spring. $E_k=0$!

Small change in the pontential energy of gravity $$dA = mg \\, dx$$ Small change in the pontential energy of the spring $$dE = kx \\, dx$$ Law of conservation of energy $$dA = dE$$ $$mg \\, dx = kx \\, dx$$ $$mg \int dx = k \int x \\, dx$$ From where $$mg \\, x = \frac{kx^2}{2} \Rightarrow \boxed{x = \frac{2mg}{k}}$$

    <h4>Answer</h4>
    <p>
        $$x = \frac{2mg}{k}$$
    </p>
    
    <p style="text-align: right; font-style: italic; font-size: 14;">   
      Almaskhan Arsen<br>
    </p>


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