Question

A bullet of mass 20g is horizontaly fire with a velocity of 150m/s from a piston of 2kg . What is the refile velocity of piston

Answer 1

Let the velocity be x
Since the momentum is conserved,
m₁v₁=m₂v₂
20*150=2000*x
therefore, x= 3000/2000= 1.5m/s.

Answer 2

The mass of bullet m = 20 g i.e 0.02 kg

The mass of piston m' = 2 kg.

The velocity of bullet v = 150 m/s

Let the velocity of piston i.e the recoil velocity is v'.

We are asked to calculate the recoil velocity of piston.

The momentum of a body is defined as the product of mass and its velocity.

Before firing, the momentum of the bullet -piston system is zero.

As per the law of conservation of linear momentum, the momentum of bullet and piston before firing must be equal to momentum after firing.

Hence   mv + m'v' = 0

     ⇒0.02×150 +2×v' = 0

     ⇒3 + 2×v' = 0

     ⇒2v' = -3

     ⇒v' = - 1.5 m/s              [ans]

Here, the negative sign is used due to the fact that recoil velocity is opposite to the bullet velocity.