<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
<meta property="og:title" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
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<meta property="og:description" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
<title>The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8</title>
$1.1.8.$ The conveyor belt has speed $w$. Above the belt moves a machine, throwing $\nu$ balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is $v < w$, the speed of the counter is $u < w$?
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem 1.1.8
</figcaption>
</figure>
</center>
</p>
<h3>Solution</h3>
<p>
<p>
1. If the automaton and the counter are at rest, T.e. $v=u=0$, then the counter will register $N_0$, balls during the time $\Delta t$.
</p>
<p style="text-align: center;">
$$N_0 = \nu\Delta t$$
</p>
<p>
2. If the automaton is at rest ($v = 0$) and the counter is moving with speed $u$, the number of registered particles is
</p>
<p style="text-align: center;">
$$N_1 = \nu\frac{w-u}{w+v}\Delta t$$
</p>
<p>
3. When the automaton and the counter move, the number of particles during the time $\Delta t$ is defined 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>
<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="The conveyor belt has speed w. Above the belt moves a machine, throwing
<meta name="description" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
<meta property="og:title" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
<meta property="og:title" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
<meta property="og:description" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
<meta property="og:description" content="The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8">
<title>The conveyor belt has speed w. Above the belt moves a machine, throwing
<title>The conveyor belt has speed w. Above the belt moves a machine, throwing
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8</title>
u balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is v < w, the speed of the counter is u < w? For problem 1.1.8</title>
$1.1.8.$ The conveyor belt has speed $w$. Above the belt moves a machine, throwing $\nu$ balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is $v < w$, the speed of the counter is $u < w$?
$1.1.8.$ The conveyor belt has speed $w$. Above the belt moves a machine, throwing $\nu$ balls per unit time. The balls stick to the belt. A ball counter with a photocell counts only the balls that have passed directly under it. How many balls will the counter count in a unit of time if the speed of the machine is $v < w$, the speed of the counter is $u < w$?
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem 1.1.8
For problem 1.1.8
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
1. If the automaton and the counter are at rest, T.e. $v=u=0$, then the counter will register $N_0$, balls during the time $\Delta t$.
1. If the automaton and the counter are at rest, T.e. $v=u=0$, then the counter will register $N_0$, balls during the time $\Delta t$.
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$$N_0 = \nu\Delta t$$
$$N_0 = \nu\Delta t$$
</p>
</p>
<p>
<p>
2. If the automaton is at rest ($v = 0$) and the counter is moving with speed $u$, the number of registered particles is
2. If the automaton is at rest ($v = 0$) and the counter is moving with speed $u$, the number of registered particles is
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$$N_1 = \nu\frac{w-u}{w+v}\Delta t$$
$$N_1 = \nu\frac{w-u}{w+v}\Delta t$$
</p>
</p>
<p>
<p>
3. When the automaton and the counter move, the number of particles during the time $\Delta t$ is defined as
3. When the automaton and the counter move, the number of particles during the time $\Delta t$ is defined 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>
