Question

Massive stars ending their lives in supernova explosions produce the nuclei of all the atoms in the bottom half of the periodic table by fusion of smaller nuclei. This problem roughly models that process. A particle of mass $m=1.99 \times 10^{-26} \mathrm{kg}$ moving with a velocity $\overrightarrow{\mathbf{u}}=0.500 c$ i collides head-on and sticks to a particle of mass $m^{\prime}=m / 3$ moving with the velocity $\overrightarrow{\mathbf{u}}=-0.500 c \mathbf{i} .$ What is the mass of the resulting particle?

Name: Problem 49, Chapter 9: Principles of Physics a Calculus Based Text
Uploaded: 2020-07-13T18:56:10-08:00
Duration: 3 min 36 s
Channel: Rehmat Kazmi

   Massive stars ending their lives in supernova explosions produce the nuclei of all the atoms in the bottom half of the periodic table by fusion of smaller nuclei. This problem roughly models that process. A particle of mass $m=1.99 \times 10^{-26} \mathrm{kg}$ moving with a velocity $\overrightarrow{\mathbf{u}}=0.500 c$ i collides head-on and sticks to a particle of mass $m^{\prime}=m / 3$ moving with the velocity $\overrightarrow{\mathbf{u}}=-0.500 c \mathbf{i} .$ What is the mass of the resulting particle?

Principles of Physics a Calculus Based Text

Raymond A. Serway,… 5th Edition

Chapter 9, Problem 49

Instant Answer

Solved by Expert Rehmat Kazmi

07/13/2020

Step 1

The total momentum before the collision is given by \[m \frac{u}{\sqrt{1-\frac{u^2}{c^2}}} - m' \frac{u}{\sqrt{1-\frac{u^2}{c^2}}}\] where $m$ and $m'$ are the masses of the particles, $u$ is the velocity, and $c$ is the speed of light. The total momentum after Show more…

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Massive stars ending their lives in supernova explosions produce the nuclei of all the atoms in the bottom half of the periodic table by fusion of smaller nuclei. This problem roughly models that process. A particle of mass $m=1.99 \times 10^{-26} \mathrm{kg}$ moving with a velocity $\overrightarrow{\mathbf{u}}=0.500 c$ i collides head-on and sticks to a particle of mass $m^{\prime}=m / 3$ moving with the velocity $\overrightarrow{\mathbf{u}}=-0.500 c \mathbf{i} .$ What is the mass of the resulting particle?