Question

Why does a gun recoil when a bullet is fired?

Answer 1

Hint: Recoil refers to the term kicking backward by a gun. Theoretically, it is the back force implied by the gun as the bullet is fired, to conserve the linear momentum. Another way we can say according to Newton’s Third Law is that when a force is applied on an accelerating bullet known as action force, then there will be an equal and opposite force known as reaction force which causes the recoil.

Complete step-by-step solution:
Recoil of a gun is a case of conservation of linear momentum. In order to conserve the linear momentum a gun always recoils when a bullet is fired. Also, recoil of a gun occurs as there is an equal and opposite reaction force that takes up into action when an action force occurs just like the bullet being fired.
Here, we will derive the recoil velocity of a gun,
Let ${v_1}$ be the velocity of the bullet after firing.
${v_2}$ be the velocity of the gun after firing.
${m_1}$ be the mass of the bullet and ${m_2}$ be the mass of the gun.
According to law of conservation of linear momentum,
Linear momentum before firing$ = $ Linear momentum after firing
$0 = {m_1}{v_1} + {m_2}{v_2}$
Thus we get,
${v_2} = - \dfrac{{{m_1}}}{{{m_2}}}{v_1}$
The negative sign implies that the gun moves backward.

Note: Recoil of a gun can be lowered by the installation of shock absorbing suspensions, silencer and others. The velocity of recoil is very small as the mass of the bullet fired is very less compared to the mass of the gun. It is actually the accelerating bullet that produces the recoil.