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<html> | ||
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<title>Решебник Савченко</title> | ||
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<h1>Решение задач из Савченко О.Я.</h1> | ||
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<a href="../../#1">1.Кинематика</a> | ||
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<a href="../../#3">3.Колебания</a> | ||
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<h3> | ||
Условие: | ||
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<p> | ||
\(3.2.9.\) На сколько отстанут за сутки маятниковые часы, поднятые на высоту | ||
Эвереста (8,9 км)? Останкинской башни (0,5 км)?. | ||
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<h3> | ||
Решение: | ||
</h3> | ||
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$T_0=2\pi\sqrt{\frac{l}{g}}$, $T_1=2\pi\sqrt{\frac{l}{g^*}}$<br><br> | ||
$g=\frac{GM}{R^2}$, | ||
$g^*=\frac{GM}{(R+H)^2}$<br><br> | ||
$\frac{g}{g^*}=\frac{(R+H)^2}{R^2}\Rightarrow g^*=\frac{gR^2}{(R+H)^2}$<br><br> | ||
$T_1=2\pi\frac{R+H}{R}\sqrt{\frac{l}{g}}$<br><br> | ||
$\Delta T_1=T_1-T_0=T_0(\frac{R+H}{R}-1)=2min$<br><br> | ||
$\Delta T_2=T_2-T_0=T_0(\frac{R+h}{R}-1)=6,75c$<br><br> | ||
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<h3> | ||
Ответ: $\Delta T_1=2min$, $\Delta T_2=6.75c$. | ||
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