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Linear Momentum



(4) Recoil of a gun



  • Consider the gun and bullet in its barrel as an isolated system
  • In the begining when bullet is not fired both the gun and bullet are at rest.So the momentum of the before firing is zero
    pi=0
  • Now when the bullet is fired ,it moves in the forward direction and gun recoil back in the opposite direction
  • Let mb be the mass and vb of velocity of the bullet And mg and vg be the velcoity of the gun after the firing
  • Total momentum of the system after the firing would be

    pf=mbvb +mgvg

  • since no external force are acting on the system,we can apply the law of conservation of linear momentum to the system
    Therfore
    pf=pi
    or mbvb +mgvg=0
    or vg=-(mbvb/mg)

  • The negative sign in above equation shows that velocity of the recoil of gun is opposite to the velocity of the bullet
  • Since mass of the gun is very large as compared to the mass of the bullet,the velocity of the recoil is very small as compared to the velocity of the bullet



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