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| <meta name="author" content="Aliaksandr Melnichenka"> | | <meta name="author" content="Aliaksandr Melnichenka"> |
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| <title>Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.</title> | | <title>Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.</title> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $2.1.11.$ Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction. | | $2.1.11.$ Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction. |
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| For problem $2.1.11$ | | For problem $2.1.11$ |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| loading="lazy" width="100" /> | | loading="lazy" width="100" /> |
| <figcaption> | | <figcaption> |
| Forces acting on loads | | Forces acting on loads |
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| <p> | | <p> |
| Let's write Newton's second law for the vertical axis | | Let's write Newton's second law for the vertical axis |
| $$ \left\{\begin{matrix} | | $$ \left\{\begin{matrix} |
| m_1a = T - m_1g\\ | | m_1a = T - m_1g\\ |
| m_2a = m_2g - T | | m_2a = m_2g - T |
| \end{matrix}\right. $$ | | \end{matrix}\right. $$ |
| From here we express the acceleration, which will be the same for both loads due to the inelasticity of the thread. | | From here we express the acceleration, which will be the same for both loads due to the inelasticity of the thread. |
| $$ \fbox{$a = g\frac{m_2-m_1}{m_2+m_1}$} $$ | | $$ \fbox{$a = g\frac{m_2-m_1}{m_2+m_1}$} $$ |
| We substitute into the system of equations and find the tension force of the thread $T$ | | We substitute into the system of equations and find the tension force of the thread $T$ |
| $$ \fbox{$T = \frac{2m_1m_2g}{m_1+m_2}$} $$ | | $$ \fbox{$T = \frac{2m_1m_2g}{m_1+m_2}$} $$ |
| </p> | | </p> |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| <p> | | <p> |
| $$a = g\frac{m_2-m_1}{m_2+m_1}$$ | | $$a = g\frac{m_2-m_1}{m_2+m_1}$$ |
| $$T = \frac{2m_1m_2g}{m_1+m_2}$$</p> | | $$T = \frac{2m_1m_2g}{m_1+m_2}$$</p> |
| <p style="text-align: right; font-style: italic; font-size: 16;">Straton</p> | | <p style="text-align: right; font-style: italic; font-size: 16;">Straton</p> |
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