A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s¯¹, what is the recoil speed of the gun ?
Given: The mass of shell is 0 .020 kg , mass of gun is 100 kg and the muzzle speed of the shell is 80 ms – 1 .
Initially, both the gun and the shell are at rest therefore, the initial momentum of the system is zero.
The final momentum of the system is given as,
p f = m v + M V
Where, m is the mass of shell, M is the mass of gun, v is the velocity of shell and V is the recoil velocity of gun.
From the conservation of momentum,
p f = p i m v + M V = 0
By substituting the given values in the above equation, we get
0.020 × 80 + 100 × V = 0 V = − 0.020 × 80 100 = − 0.016 ms − 1 = − 1.6 cms − 1
Thus, the recoil velocity of gun is 1.6 cms − 1 .
Given: The mass of shell is
Initially, both the gun and the shell are at rest therefore, the initial momentum of the system is zero.
The final momentum of the system is given as,
Where,
From the conservation of momentum,
By substituting the given values in the above equation, we get
Thus, the recoil velocity of gun is
