A gun of mass fires a bullet of mass with maximum speed . Given that what is the kinetic energy of the gun?
Step 1. Given data
Mass of the gun
Mass of the bullet
Maximum speed
Step 2. Formula used
Kinetic energy
Momentum of a body
where, is the mass and is the velocity
Step 3. Calculate the velocity of the gun
A gun recoils when a bullet is discharged from it. Both the pistol and the bullet travel in the polar opposite directions. In this instance, the gun's linear momentum and the bullet's linear momentum are equal. Since mass and velocity have an inversely proportional relationship, the mass of the gun is very big compared to the mass of the bullet, and the rifle's recoil velocity is very slow compared to the forward velocity of the bullet.
Mass of bullet
Mass of gun
velocity of bullet
Velocity of the gun
Since the gun and bullet are both at rest before to firing, their combined linear momentum is zero. Following firing, the total linear momentum is given by
The negative sign in the above equation shows that the direction of is exactly opposite of .
Mass of the gun
Mass of the bullet
Velocity of bullet
Velocity of Gun
Now applying the law of conservation we have
Step 4. Calculate the kinetic energy of the gun
The kinetic energy of the gun is
Hence, the kinetic energy of the gun is .