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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> |
| </p> | | </p> |
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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> |
| $2.1.12.$ The painter works in a suspended cradle. He needed to get up quickly. He begins to pull the rope with such force that the force of his pressure on the floor of the cradle is reduced to $400$ H. Cradle weight $12$ kg, painter weight $72$ kg. What is the acceleration of the cradle? | | $2.1.12.$ The painter works in a suspended cradle. He needed to get up quickly. He begins to pull the rope with such force that the force of his pressure on the floor of the cradle is reduced to $400$ H. Cradle weight $12$ kg, painter weight $72$ kg. What is the acceleration of the cradle? |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.12/sol.jpg" | | <img src="https://savchenkosolutions.com/2/2.1.12/sol.jpg" |
| loading="lazy" width="350" /> | | loading="lazy" width="350" /> |
| <figcaption> | | <figcaption> |
| Painter on a hanging cradle | | Painter on a hanging cradle |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| Let's denote the mass of the painter as $M_1$, and the mass of the chair as $M_2$. Let's write the equations of motion of the painter and the chair: | | Let's denote the mass of the painter as $M_1$, and the mass of the chair as $M_2$. Let's write the equations of motion of the painter and the chair: |
| $$ | | $$ |
| \left\{\begin{matrix} | | \left\{\begin{matrix} |
| M_{1}a = T - M_{1}g + P & \\ | | M_{1}a = T - M_{1}g + P & \\ |
| M_{2}a = T - M_{2}g - P & | | M_{2}a = T - M_{2}g - P & |
| \end{matrix}\right. $$ | | \end{matrix}\right. $$ |
| where $P$ is the painter's pressure force on the chair. </p> | | where $P$ is the painter's pressure force on the chair. </p> |
| <p> | | <p> |
| Subtracting the lower equation from the upper one, we find | | Subtracting the lower equation from the upper one, we find |
| $$ a = \frac{2P - (M_{1} - M_{2})g}{M_{1} - M_{2} } = \frac{1}{3}g $$ | | $$ a = \frac{2P - (M_{1} - M_{2})g}{M_{1} - M_{2} } = \frac{1}{3}g $$ |
| Then adding up the equations of motion, we find | | Then adding up the equations of motion, we find |
| $$ 2T = (M_{2} + M_{2}) (a+g) = \frac{4}{3}(M_{1} + M_{2})g = 1.1 \cdot 10^3 \,N $$ | | $$ 2T = (M_{2} + M_{2}) (a+g) = \frac{4}{3}(M_{1} + M_{2})g = 1.1 \cdot 10^3 \,N $$ |
| This is the full load on the block: | | This is the full load on the block: |
| $$ N = 2T = 1.1 \cdot 10^3 \,N $$ | | $$ N = 2T = 1.1 \cdot 10^3 \,N $$ |
| </p> | | </p> |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $$a = 3.5 \,m/s^2$$ | | $$a = 3.5 \,m/s^2$$ |
| $$T \approx 1.1 \cdot 10^3 \,N$$ | | $$T \approx 1.1 \cdot 10^3 \,N$$ |
