Question

Why does a gun recoil? Derive the recoil velocity of the gun.

Answer 1

Hint: The reason behind the recoil of guns is related to momentum. We will also use Newton’s third law of motion. It states that the force required to fire the gun will have an equal and opposite reaction force. It also follows conservational law.

Complete answer:
Recoil means a kickback or a backward movement that a shooter feels when the bullet is discharged. It can also be said as a backward velocity. The recoil of the gun is actually a result of conservation of linear momentum. Every system that projects experiences a recoil velocity if it is a gun, arrow, bow, crossbow or rocket launcher.
Now we will calculate the recoil velocity of a gun.
Let us consider the mass of a gun and the mass of a bullet. Be the velocity of the bullet and be the velocity of the gun.
Now the initial momentum of the gun and the bullet will be zero. After the gun is fired at that moment final momentum will be equal to the momentum of the gun and momentum of the bullet.
This can be written as
Initial momentum of system=0
Final momentum of system= \[mv+Mv'\]
Now we will apply conservation of linear momentum
\[\begin{align}
  & 0=mv+Mv' \\
 & v'=\dfrac{-mv}{M} \\
\end{align}\]
Therefore, the recoil velocity of the gun is \[\dfrac{-mv}{M}\]. The negative sign tells us that the direction of velocity of the bullet is opposite to that of the direction of velocity of the gun.

Note:
Law of conservation of momentum is a general law of physics. It states that if no external force is applied to the system then the total momentum of the system is conserved. That means the body retains its total momentum.