<meta name="description" content="The tube of radius r is filled with a porous substance of density
+
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
+
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
+
ho, and to the left-
+
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
+
<meta property="og:title" content="The tube of radius r is filled with a porous substance of density
+
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
+
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
+
ho, and to the left-
+
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
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<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
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<meta property="og:description" content="The tube of radius r is filled with a porous substance of density
+
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
+
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
+
ho, and to the left-
+
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
<title>The tube of radius r is filled with a porous substance of density
+
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
+
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
+
ho, and to the left-
+
ho_0? At the initial moment, this boundary coincides with the surface of the piston.</title>
$2.2.39.$ The tube of radius $r$ is filled with a porous substance of density $\rho_0$. The piston, which acts on a constant force $F$, moving in the pipe, compacts the substance to a density $\rho$. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is $\rho$, and to the left-$\rho_0$? At the initial moment, this boundary coincides with the surface of the piston.
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="draw.png"
loading="lazy" width="280" />
<figcaption>
Geometry of the problem
</figcaption>
</figure>
</center>
<p>
From the drawing
$$\Delta L=L_0-L$$
During the time $\Delta t$ the piston with velocity $v$ has moved by the amount $\Delta l$
$$\Delta L=v\Delta t$$
Given a constant cross-sectional area $S=\pi r^2$, the expression from above can be rewritten as
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
ho, and to the left-
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
<meta property="og:title" content="The tube of radius r is filled with a porous substance of density
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
ho, and to the left-
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
<meta property="og:description" content="The tube of radius r is filled with a porous substance of density
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
ho, and to the left-
ho_0? At the initial moment, this boundary coincides with the surface of the piston.">
<title>The tube of radius r is filled with a porous substance of density
ho_0. The piston, which acts on a constant force F, moving in the pipe, compacts the substance to a density
ho. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is
ho, and to the left-
ho_0? At the initial moment, this boundary coincides with the surface of the piston.</title>
$2.2.39.$ The tube of radius $r$ is filled with a porous substance of density $\rho_0$. The piston, which acts on a constant force $F$, moving in the pipe, compacts the substance to a density $\rho$. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is $\rho$, and to the left-$\rho_0$? At the initial moment, this boundary coincides with the surface of the piston.
$2.2.39.$ The tube of radius $r$ is filled with a porous substance of density $\rho_0$. The piston, which acts on a constant force $F$, moving in the pipe, compacts the substance to a density $\rho$. At what speed does the piston move if the compaction of the substance occurs in a jump, i.e. the interface moves at a certain speed in the pipe, to the right of which the density of the substance is $\rho$, and to the left-$\rho_0$? At the initial moment, this boundary coincides with the surface of the piston.
</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="280" />
loading="lazy" width="280" />
<figcaption>
<figcaption>
Geometry of the problem
Geometry of the problem
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
From the drawing
From the drawing
$$\Delta L=L_0-L$$
$$\Delta L=L_0-L$$
During the time $\Delta t$ the piston with velocity $v$ has moved by the amount $\Delta l$
During the time $\Delta t$ the piston with velocity $v$ has moved by the amount $\Delta l$
$$\Delta L=v\Delta t$$
$$\Delta L=v\Delta t$$
Given a constant cross-sectional area $S=\pi r^2$, the expression from above can be rewritten as
Given a constant cross-sectional area $S=\pi r^2$, the expression from above can be rewritten as
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
