I\'m trying to solve this using center of mass but I can\'t seem to come to an a

Question

I'm trying to solve this using center of mass but I can't seem to come to an answer. Any help would be greatly appreciated!

Study Problems: Module 6 Part 1 - Conservation of momentum (Chapter 9) 1. A cannon and a supply of cannon balls are inside a sealed railroad car as in the diagram below. The cannon fires to the right, the car recoiling to the left. The cannon balls remain in the car after hitting the far wall. Show that no matter how the cannon balls are fired the railroad car cannot travel more than its length L, assuming it starts from rest.

Explanation / Answer

This question is based on the concept of conservation of position of center of mass of canon ball +canon + car system

please note that all the forces acting between canon + canon ball + car is internal force .

and external forces are only along vertical direction (normal + weight )

so X component of center of mass of the mentioned system will be conserved

lets consider two extreme situation (which are also limiting condition)

condition1 .

lets assume mass of canon ball is negligible (=0 mathemetically )

in this case movement of the ball will not affect the motion of car (to maintain the position of center of mass) since mass of ball is zero .

so no movement of car

condition 2

lets assume that mass of canon ball is much much larger than mass of car plus canon ( or mathematically mass of car plus canon is zero ) so center of mass of the system will be location at the position of canon ball , so as soon as the ball move relative to the car center of mass will move so to conserve the position of center of mass of the system car will move in opposite direction with same distance so that net motion of canon ball becomes zero

thus

since maximum displacement of canon ball with respect to car = L so the maximum displacement of car with respect to ground will be L in opposite direction

thus you can understand that any other situation will lie between the described two condition so the displacement of car will be between 0 to L

i hope i made it clear for you to understand .

Physics was alwao analyze any phenomena with practical point of view

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