A bullet of mass 0.045kg is fired from a gun of mass 9kg, the bullet moving with an initial velocity of 200m/s. Find the initial backward velocity of the gun.
conserve momentum
0.045*200 = 9v
To find the initial backward velocity of the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum of the bullet and the gun combined is:
Initial momentum = (mass of bullet × velocity of bullet) + (mass of gun × velocity of gun)
Let's represent the velocity of the gun as Vg.
Initial momentum = (0.045 kg × 200 m/s) + (9 kg × Vg)
Since the gun is initially at rest, the initial velocity of the gun (Vg) is zero. Thus, the equation becomes:
Initial momentum = (0.045 kg × 200 m/s) + (9 kg × 0)
Initial momentum = 9 kg × 0.045 kg × 200 m/s
Initial momentum = 9 × 0.045 × 200 kg·m/s
Initial momentum = 81 kg·m/s
The total momentum after the bullet is fired will be the momentum of the bullet plus the momentum of the gun. Since the bullet is moving forward, its momentum is positive. Therefore, the backward velocity of the gun will be negative.
The final momentum = (mass of bullet × velocity of bullet) + (mass of gun × velocity of gun)
The final momentum = (0.045 kg × 0 m/s) + (9 kg × Vg)
The final momentum = 0 kg·m/s + (9 kg × Vg)
The final momentum = 9 kg × Vg
According to the principle of conservation of momentum, the initial momentum is equal to the final momentum:
Initial momentum = Final momentum
81 kg·m/s = 9 kg × Vg
To find the initial backward velocity of the gun, we divide both sides of the equation by 9 kg:
81 kg·m/s ÷ 9 kg = Vg
9 m/s = Vg
Therefore, the initial backward velocity of the gun is 9 m/s.