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<meta name="description" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<meta property="og:title" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<title>In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.</title>
$2.4.35.$ In a spherical bowl of radius $R$, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length $l$, weight of each ball $m$.
</p>
<center>
<figure>
<img src="2.4.35.png"
loading="lazy" width="200" />
<figcaption>
For problem $2.4.35$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="2.4.35_1.png"
loading="lazy" width="260" />
<figcaption>
Figure 1
</figcaption>
</figure>
</center>
<p>
From the figure
$$R\cos\alpha = \frac{l}{2}$$
Whereas
$$\cos\alpha = \frac{l}{2R}$$
In the meantime, the vertical distance of the balls
<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">
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<meta name="description" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<meta name="description" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<meta property="og:title" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<meta property="og:title" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<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="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<meta property="og:description" content="In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.">
<title>In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.</title>
<title>In a spherical bowl of radius R, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length l, weight of each ball m.</title>
$2.4.35.$ In a spherical bowl of radius $R$, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length $l$, weight of each ball $m$.
$2.4.35.$ In a spherical bowl of radius $R$, hold the dumbbell in the position when one of the balls is at the bottom of the bowl, and then release it. How much heat will be released by the time the dumbbell stops moving due to the low friction between the bowl and the dumbbell? Dumbbell length $l$, weight of each ball $m$.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.4.35.png"
<img src="2.4.35.png"
loading="lazy" width="200" />
loading="lazy" width="200" />
<figcaption>
<figcaption>
For problem $2.4.35$
For problem $2.4.35$
</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="2.4.35_1.png"
<img src="2.4.35_1.png"
loading="lazy" width="260" />
loading="lazy" width="260" />
<figcaption>
<figcaption>
Figure 1
Figure 1
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
From the figure
From the figure
$$R\cos\alpha = \frac{l}{2}$$
$$R\cos\alpha = \frac{l}{2}$$
Whereas
Whereas
$$\cos\alpha = \frac{l}{2R}$$
$$\cos\alpha = \frac{l}{2R}$$
In the meantime, the vertical distance of the balls
In the meantime, the vertical distance of the balls
<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>
