John Taylor Classical Mechanics Chapter 3, Problem 1

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SUMMARY

The discussion focuses on solving Problem 1 from Chapter 3 of John Taylor's "Classical Mechanics," which involves a gun of mass M firing a shell of mass m with a muzzle speed v. The key conclusion is that using conservation of momentum, the shell's speed relative to the ground is derived as v/(1+m/M). The equations of momentum before and after firing are critical to the solution, specifically Pinitial = m1v1 + m2v2 and Pfinal = (m1 + m2)v.

PREREQUISITES
  • Understanding of conservation of momentum principles
  • Familiarity with classical mechanics concepts
  • Ability to manipulate algebraic equations
  • Knowledge of mass and velocity relationships in physics
NEXT STEPS
  • Study the derivation of conservation of momentum in one-dimensional collisions
  • Explore the implications of recoil in firearms and projectile motion
  • Learn about the differences between elastic and inelastic collisions
  • Review introductory physics resources for foundational concepts in mechanics
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the principles of momentum and recoil in classical mechanics.

karmonkey98k
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John Taylor "Classical Mechanics" Chapter 3, Problem 1

Homework Statement


Consider a gun of mass M (when unloaded) that fires a shell of mass m with muzzle speed v. (shell's speed relative to gun is v). Assuming gun is completely free to recoil (no ext. forces on gun or shell), use conservation of momentum to show that shell's speed relative to ground is v/(1+m/M)


Homework Equations


Pinitial=m1v1+m2v2 Pfinal=m1v + m2v=(m1+m2)v vfinal=(m1v1+m2v2/(m1+m2)


The Attempt at a Solution


I got v/(m/M), not the "+1
 
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karmonkey98k said:
Pfinal=m1v + m2v
The gun and shell are not moving together after firing.
Btw, this is the wrong forum. Should be in introductory physics.
 

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