Question

After bullet is fired, gun recoils freely. Compare the K.E of bullet and gun.

Answer 1

Suppose the mass of the gun us M and that of the bullet is m. After being fired the velocity of bullet is ‘u’ and recoil velocity of the gun is say ‘v’

Momentum of the bullet before firing = (m)(0) = 0

Momentum of the gun before firing = (M)(0) = 0

Total momentum before firing = 0

Momentum of bullet after firing = mu

Momentum of gun after firing = Mv

Total momentum after firing = mu + Mv

By law of conservation of momentum,

Total momentum after firing = total momentum before firing

=> mu + Mv = 0

=> v = -mu/M

Now,

KE of bullet after firing, KE_b = ½ mu²

KE of gun after firing, KE_g = ½ Mv² = ½ M(-mu/M)²

=> KE_g = ½ m²u²/M

Now,

KE_b/KE_g = (½ mu²)/ (½ m²u²/M) = M/m

Or, KE_b : KE_g = M : m

Since, M > m so, KE_b > KE_g.