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<meta name="description" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<meta property="og:title" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<title>There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.</title>
$1.4.15^*.$ There is a bundle of identical nuclei moving with velocity $v$. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is $3v$. Find the velocity of the fragments moving in the direction perpendicular to the beam.
</p>
<h3>Solution</h3>
<p>
<p>Let's move to the beam center of mass frame.</p>
<p>In this frame of reference, the relative velocity is related to the velocity in the NFR by the relation</p>
<p>Where $\vec{v'}$ and $\vec{v}$ are the velocity in the inertial reference frame and the velocity of the reference frame of the system, respectively.</p>
<p>By the condition, when $\vec{v}_{rel}$ and $\vec{v}$ are co-directed $v' = 3 v$</p>
<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="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<meta name="description" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<meta property="og:title" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<meta property="og:title" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<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="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<meta property="og:description" content="There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.">
<title>There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.</title>
<title>There is a bundle of identical nuclei moving with velocity v. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is 3v. Find the velocity of the fragments moving in the direction perpendicular to the beam.</title>
$1.4.15^*.$ There is a bundle of identical nuclei moving with velocity $v$. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is $3v$. Find the velocity of the fragments moving in the direction perpendicular to the beam.
$1.4.15^*.$ There is a bundle of identical nuclei moving with velocity $v$. The nuclei in the beam spontaneously divide into pairs of identical fragments. The velocity of the fragments moving in the direction of the beam is $3v$. Find the velocity of the fragments moving in the direction perpendicular to the beam.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>Let's move to the beam center of mass frame.</p>
<p>Let's move to the beam center of mass frame.</p>
<p>In this frame of reference, the relative velocity is related to the velocity in the NFR by the relation</p>
<p>In this frame of reference, the relative velocity is related to the velocity in the NFR by the relation</p>
<p>Where $\vec{v'}$ and $\vec{v}$ are the velocity in the inertial reference frame and the velocity of the reference frame of the system, respectively.</p>
<p>Where $\vec{v'}$ and $\vec{v}$ are the velocity in the inertial reference frame and the velocity of the reference frame of the system, respectively.</p>
<p>By the condition, when $\vec{v}_{rel}$ and $\vec{v}$ are co-directed $v' = 3 v$</p>
<p>By the condition, when $\vec{v}_{rel}$ and $\vec{v}$ are co-directed $v' = 3 v$</p>
<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>
