<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:title" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<title>Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.</title>
$2.6.52^*.$ Two touching each other globular blocks of mass $m$ and radius $r$ each move in a circular orbit around a planet of mass $M$. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet $R$. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is $R_0 \gg r$. Take the density of the boulders to be equal to the average density of the planet.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="200" />
<figcaption>
For problem $2.6.52^*$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="draw.png"
loading="lazy" width="250" />
<figcaption>
Forces acting on the system
</figcaption>
</figure>
</center>
<p>
Newton's second law for two bodies:
$$\left\{\begin{matrix}
F_1+N-F_0=m\omega^2(R-r) \\
F_1-N+F_0=m\omega^2(R+r)
\end{matrix}\right.$$
Dividing one equation by the other, we get
$$\frac{F_1+N-F_0}{F_1-N+F_0}=\frac{R-r}{R+r}$$
Transforming the obtained expression, we obtain
$$N=F_0-\frac{F_1(R+r)-F_2(R-r)}{2R}$$
The forces of gravitational attraction of the clumps between themselves and the planet
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta name="description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:title" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:title" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<meta property="og:description" content="Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.">
<title>Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.</title>
<title>Two touching each other globular blocks of mass m and radius r each move in a circular orbit around a planet of mass M. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet R. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is R_0 \gg r. Take the density of the boulders to be equal to the average density of the planet.</title>
$2.6.52^*.$ Two touching each other globular blocks of mass $m$ and radius $r$ each move in a circular orbit around a planet of mass $M$. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet $R$. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is $R_0 \gg r$. Take the density of the boulders to be equal to the average density of the planet.
$2.6.52^*.$ Two touching each other globular blocks of mass $m$ and radius $r$ each move in a circular orbit around a planet of mass $M$. The centers of the boulders are located at the same radius, the distance from their point of contact to the center of planet $R$. With what force does one block press on another? At what radius of the orbit will the mutual attraction of the lumps cease to hold them together? The radius of the planet is $R_0 \gg r$. Take the density of the boulders to be equal to the average density of the planet.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="200" />
loading="lazy" width="200" />
<figcaption>
<figcaption>
For problem $2.6.52^*$
For problem $2.6.52^*$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="draw.png"
<img src="draw.png"
loading="lazy" width="250" />
loading="lazy" width="250" />
<figcaption>
<figcaption>
Forces acting on the system
Forces acting on the system
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Newton's second law for two bodies:
Newton's second law for two bodies:
$$\left\{\begin{matrix}
$$\left\{\begin{matrix}
F_1+N-F_0=m\omega^2(R-r) \\
F_1+N-F_0=m\omega^2(R-r) \\
F_1-N+F_0=m\omega^2(R+r)
F_1-N+F_0=m\omega^2(R+r)
\end{matrix}\right.$$
\end{matrix}\right.$$
Dividing one equation by the other, we get
Dividing one equation by the other, we get
$$\frac{F_1+N-F_0}{F_1-N+F_0}=\frac{R-r}{R+r}$$
$$\frac{F_1+N-F_0}{F_1-N+F_0}=\frac{R-r}{R+r}$$
Transforming the obtained expression, we obtain
Transforming the obtained expression, we obtain
$$N=F_0-\frac{F_1(R+r)-F_2(R-r)}{2R}$$
$$N=F_0-\frac{F_1(R+r)-F_2(R-r)}{2R}$$
The forces of gravitational attraction of the clumps between themselves and the planet
The forces of gravitational attraction of the clumps between themselves and the planet
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
