A bullet of mass 50g is fired from a gun of mass 6kg with a velocity of 400m/s. calculate the recoil velocity of the gun?
To calculate the recoil velocity of the gun after firing a bullet, we can apply the principle of conservation of momentum. According to this principle, in the absence of external forces, the total momentum before an event should be equal to the total momentum after the event.
The momentum of an object is calculated by multiplying its mass by its velocity. Let's denote the bullet's mass as m1, bullet's velocity as v1, gun's mass as m2, and recoil velocity of the gun as v2.
The initial momentum of the system (bullet + gun) can be calculated as:
Initial momentum = (mass of bullet × velocity of bullet) + (mass of gun × velocity of gun)
Plugging in the given values:
Initial momentum = (0.05 kg × 400 m/s) + (6 kg × 0)
Since the gun is initially at rest, the velocity of the gun is zero.
Simplifying the equation:
Initial momentum = 20 kg·m/s
According to the principle of conservation of momentum, the initial momentum of the system should be equal to the final momentum after firing the bullet. The final momentum can be calculated as:
Final momentum = (mass of bullet × velocity of bullet) + (mass of gun × recoil velocity of gun)
Plugging in the given values:
Final momentum = (0.05 kg × 0) + (6 kg × v2)
Since the bullet comes to rest after it is fired, its velocity becomes zero.
Simplifying the equation:
Final momentum = 6 kg × v2
Now, equating the initial momentum and final momentum:
20 kg·m/s = 6 kg × v2
Dividing both sides by 6 kg:
v2 = 20 kg·m/s / 6 kg
Calculating the recoil velocity of the gun:
v2 = 3.33 m/s
Therefore, the recoil velocity of the gun after firing the bullet is approximately 3.33 m/s.
v2=-m1,v1 dived by m2
v2=-5g*400m/s dived by 6 kg