<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<meta property="og:title" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<title>To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?</title>
$2.1.9.$ To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time $\Delta t$ with a force $F = nmg$, where $m$ is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if $\Delta t = 0.04$ s, and $n = 125$?
</p>
<h3>Solution</h3>
<p>
<p>
1. The container's movement can be divided into three sections: in the acceleration section $OA$. the piston exerts a force $F = nmg$, which accelerates the container to the speed $v_0$; in the second section $AB$ the container moves like a body thrown vertically upwards, in the third section, after stopping, the container with the equipment will freely fall to the bottom of the shaft.
</p>
<p>
2. Let us write the equation of the fundamental law of dynamics for the acceleration section, which, in combination with the kinematic conditions of uniformly accelerated motion, allows us to determine the values $y_1$, $t_1$ and $v_0$
$$ nmg-mg = ma $$
$$ a = g(n-1) = 1240 \,m/s^2 $$
$$ V_0 = a \Delta t = g(n-1) \Delta t = 50 \,m/s $$
<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="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<meta name="description" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<meta property="og:title" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<meta property="og:title" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<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="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<meta property="og:description" content="To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?">
<title>To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?</title>
<title>To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time \Delta t with a force F = nmg, where m is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if \Delta t = 0.04 s, and n = 125?</title>
$2.1.9.$ To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time $\Delta t$ with a force $F = nmg$, where $m$ is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if $\Delta t = 0.04$ s, and $n = 125$?
$2.1.9.$ To test the equipment in zero-gravity conditions, the container is thrown up by a pneumatic piston device located at the bottom of the evacuated shaft. The piston acts on the container for a time $\Delta t$ with a force $F = nmg$, where $m$ is the mass of the container with the equipment. How long will it take for the container to fall to the bottom of the mine? How long does the zero-gravity state last for the equipment, if $\Delta t = 0.04$ s, and $n = 125$?
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
1. The container's movement can be divided into three sections: in the acceleration section $OA$. the piston exerts a force $F = nmg$, which accelerates the container to the speed $v_0$; in the second section $AB$ the container moves like a body thrown vertically upwards, in the third section, after stopping, the container with the equipment will freely fall to the bottom of the shaft.
1. The container's movement can be divided into three sections: in the acceleration section $OA$. the piston exerts a force $F = nmg$, which accelerates the container to the speed $v_0$; in the second section $AB$ the container moves like a body thrown vertically upwards, in the third section, after stopping, the container with the equipment will freely fall to the bottom of the shaft.
</p>
</p>
<p>
<p>
2. Let us write the equation of the fundamental law of dynamics for the acceleration section, which, in combination with the kinematic conditions of uniformly accelerated motion, allows us to determine the values $y_1$, $t_1$ and $v_0$
2. Let us write the equation of the fundamental law of dynamics for the acceleration section, which, in combination with the kinematic conditions of uniformly accelerated motion, allows us to determine the values $y_1$, $t_1$ and $v_0$
$$ nmg-mg = ma $$
$$ nmg-mg = ma $$
$$ a = g(n-1) = 1240 \,m/s^2 $$
$$ a = g(n-1) = 1240 \,m/s^2 $$
$$ V_0 = a \Delta t = g(n-1) \Delta t = 50 \,m/s $$
$$ V_0 = a \Delta t = g(n-1) \Delta t = 50 \,m/s $$
<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>
