Question

A particle of mass $m$ moving along the $x$ -axis with a velocity component $+u$ collides head-on and sticks to a particle of mass $m / 3$ moving along the $x$ axis with the velocity component $-u .$ What is the mass $M$ of the resulting particle?

Name: Problem 31, Chapter 2: Modern Physics
Uploaded: 2023-09-30T07:31:51-08:00
Duration: 2 min 13 s
Channel: Vishal Gupta
Description: A particle of mass m moving along the x -axis with a velocity component +u collides head-on and sticks to a particle of mass m / 3 moving along the x axis with the velocity component -u . What is the mass M of the resulting particle?

   A particle of mass $m$ moving along the $x$ -axis with a velocity component $+u$ collides head-on and sticks to a particle of mass $m / 3$ moving along the $x$ axis with the velocity component $-u .$ What is the mass $M$ of the resulting particle?

Modern Physics

Raymond A. Serway,… 3rd Edition

Chapter 2, Problem 31

Instant Answer

Solved by Expert Vishal Gupta

09/30/2023

Step 1

This gives us the equation: \[mu \left( \frac{1}{1 - \frac{u^2}{c^2}} \right) + m \left( -\frac{u}{3} \right) \left( \frac{1}{1 - \frac{u^2}{c^2}} \right) = Mv_{\text{final}} \left( \frac{1}{1 - \frac{v_{\text{final}}^2}{c^2}} \right)\] Simplifying this equation Show more…

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A particle of mass $m$ moving along the $x$ -axis with a velocity component $+u$ collides head-on and sticks to a particle of mass $m / 3$ moving along the $x$ axis with the velocity component $-u .$ What is the mass $M$ of the resulting particle?

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Key Concepts

Conservation of Momentum

In any closed system where external forces are negligible, the total momentum before a collision is equal to the total momentum after the collision. This principle is used to determine the final state of the system when two bodies interact, even if the collision involves energy transformations, such as in inelastic collisions.

Perfectly Inelastic Collision

In a perfectly inelastic collision, the colliding bodies stick together after impact, moving as a single combined mass. Although kinetic energy is not conserved in such collisions, momentum is conserved, and the final velocity and mass of the merged particle can be determined using the conservation of momentum and the simple addition of masses.

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