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| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> |
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| <p class="author"> | | <p class="author"> |
| Solutions of Savchenko Problems in Physics <br> | | Solutions of Savchenko Problems in Physics <br> |
| <i><b>knowledge must be free</b></i> | | <i><b>knowledge must be free</b></i> |
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| <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3> |
| | | |
| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <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? | | $2.1.4.$ 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? |
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| <figcaption> | | <figcaption> |
| For problem $2.1.4$ | | For problem $2.1.4$ |
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| <p> | | <p> |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.4/sol.png" | | <img src="https://savchenkosolutions.com/2/2.1.4/sol.png" |
| loading="lazy" width="250" /> | | loading="lazy" width="250" /> |
| <figcaption> | | <figcaption> |
| Forces acting on the load | | Forces acting on the load |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| Newton's second law: | | Newton's second law: |
| $$ \vec{T_1} + \vec{T_2} + \vec{T_3} + \vec{T_4} + m\vec{g}=m\vec{a} $$ | | $$ \vec{T_1} + \vec{T_2} + \vec{T_3} + \vec{T_4} + m\vec{g}=m\vec{a} $$ |
| Let us write the system of equations in projections onto the $Ox$ and $Oy$ axes: | | Let us write the system of equations in projections onto the $Ox$ and $Oy$ axes: |
| $$ | | $$ |
| \left\{\begin{matrix} | | \left\{\begin{matrix} |
| T_4-T_3=Mg & \\ | | T_4-T_3=Mg & \\ |
| T_2-T_1=ma & | | T_2-T_1=ma & |
| \end{matrix}\right. $$ | | \end{matrix}\right. $$ |
| From here | | From here |
| $$ a = g \frac{T_2 − T_1}{T_4 − T_3} $$ | | $$ a = g \frac{T_2 − T_1}{T_4 − T_3} $$ |
| </p> | | </p> |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $$a = g(T_2 − T_1)/(T_4 − T_3)$$ | | $$a = g(T_2 − T_1)/(T_4 − T_3)$$ |
