Правка разделов «Statement», «Solution», «Answer»
en/3.3.14.md
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| ### Statement | |||
| − | $3.3.14.$ A thin homogeneous bar of length $l$ slides along a smooth horizontal plane | ||
| − | with speed $\upsilon$. The bar hits an extensive rough section of the plane. How long | ||
| − | will it take for the bar to stop if the coefficient of friction is $\mu$? | ||
| + | $3.3.14.$ A thin homogeneous bar of length $l$ slides along a smooth horizontal plane with speed $\upsilon$. The bar hits an extensive rough section of the plane. How long will it take for the bar to stop if the coefficient of friction is $\mu$? | ||
| ### Solution | |||
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| #### Answer | |||
| − | [See $\textbf{1-javob}$ and $\textbf{2-javob}$] | ||
| + | \[t = \frac{\pi}{2} \sqrt{\frac{l}{\mu g}} \quad \text{for} \quad v \leq \sqrt{\mu g l}, \quad | ||
| + | t = \frac{v'}{\mu g} + \sqrt{\frac{l}{\mu g}} \arccos \frac{v'}{v} \quad \text{for} \quad v > \sqrt{\mu g l}, \quad \text{where} | ||
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| + | \[ | ||
| + | v' = \sqrt{v^2 - \mu g l}. | ||
| + | \] | ||
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| ### Statement | ### Statement | ||
| $3.3.14.$ A thin homogeneous bar of length $l$ slides along a smooth horizontal plane | $3.3.14.$ A thin homogeneous bar of length $l$ slides along a smooth horizontal plane with speed $\upsilon$. The bar hits an extensive rough section of the plane. How long will it take for the bar to stop if the coefficient of friction is $\mu$? | ||
| with speed $\upsilon$. The bar hits an extensive rough section of the plane. How long | |||
| will it take for the bar to stop if the coefficient of friction is $\mu$? | |||
| ### Solution | ### Solution | ||
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| #### Answer | #### Answer | ||
| [See $\textbf{1-javob}$ and $\textbf{2-javob}$] | \[t = \frac{\pi}{2} \sqrt{\frac{l}{\mu g}} \quad \text{for} \quad v \leq \sqrt{\mu g l}, \quad | ||
| t = \frac{v'}{\mu g} + \sqrt{\frac{l}{\mu g}} \arccos \frac{v'}{v} \quad \text{for} \quad v > \sqrt{\mu g l}, \quad \text{where} | |||
| \] | |||
| \[ | |||
| v' = \sqrt{v^2 - \mu g l}. | |||
| \] | |||