The load is secured to the cart by four strung threads. The tension force of horizontal threads is T_1 and T_2, respectively, and that of vertical threads is T_3 and T_4. How fast does the cart move along the horizontal plane?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

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    <h3> Statement </h3>
    <p>
        $2.1.4.$ The load is secured to the cart by four strung threads. The tension force of horizontal threads is $T_1$ and $T_2$, respectively, and that of vertical threads is $T_3$ and $T_4$. How fast does the cart move along the horizontal plane?

    <h3>Solution</h3>
    <p>
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Newton's second law: $$\vec{T_1} + \vec{T_2} + \vec{T_3} + \vec{T_4} + m\vec{g}=m\vec{a}$$ Let us write the system of equations in projections onto the $Ox$ and $Oy$ axes: $$\left\{\begin{matrix} T_4-T_3=Mg & \\ T_2-T_1=ma & \end{matrix}\right.$$ From here $$a = g \frac{T_2 − T_1}{T_4 − T_3}$$

    <h4>Answer</h4>
    <p>
        $$a = g(T_2 − T_1)/(T_4 − T_3)$$
    </p>


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