A bullet of 29g is shot from a gun of mass 20kg with a muzzle velocity of 200ms if the bullet is 30cm long.determine. a)acceleration of the bullet b)the recoil velocity of the gun
v of a gun
Bullet momentum = gun momentum
0.02×200 = 20 × v
V= 0.2m/s
Solution
To determine the acceleration of the bullet and the recoil velocity of the gun, we can make use of the law of conservation of momentum.
a) Acceleration of the bullet:
The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system.
The momentum of an object is given by the product of its mass and velocity: Momentum = mass * velocity.
Before the bullet is fired, the total momentum of the system (bullet + gun) is zero since both are at rest.
After the bullet is fired, the bullet and the gun gain momentum in opposite directions. The momentum gained by the bullet is equal in magnitude but opposite in direction to the momentum gained by the gun.
To find the acceleration of the bullet, we can use the formula for momentum:
Momentum = mass * velocity
For the bullet:
Momentum of bullet = (mass of bullet) * (velocity of bullet)
For the gun:
Momentum of gun = (mass of gun) * (velocity of gun)
Since the total momentum before the event is zero, the total momentum after the event is also zero:
Momentum of bullet + Momentum of gun = 0
Therefore, (-mass of bullet * velocity of bullet) + (-mass of gun * velocity of gun) = 0
Substituting the known values:
(-0.029 kg * 200 m/s) + (-20 kg * velocity of gun) = 0
Solving for the unknown, we find:
Velocity of gun = (mass of bullet * velocity of bullet) / mass of gun
Substituting the given values:
Velocity of gun = (0.029 kg * 200 m/s) / 20 kg
Calculating, we find:
Velocity of gun = 0.29 m/s
b) The recoil velocity of the gun is 0.29 m/s.
Therefore, the acceleration of the bullet is 0 m/s^2 (since the bullet is in free space with no external forces acting on it), and the recoil velocity of the gun is 0.29 m/s.