To calculate the momentum of the gun and the velocity of the recoiling gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event.
Let's denote the mass of the bullet as m₁ (10 g = 0.01 kg) and the mass of the gun as m₂ (2.0 kg). The initial velocity of the bullet is 0 m/s since it is at rest before being fired. The final velocity of the bullet is 400 m/s.
The momentum of an object is calculated by multiplying its mass by its velocity:
Momentum (p) = mass (m) × velocity (v)
Using the conservation of momentum, we can set up the equation:
Initial momentum of the system = Final momentum of the system
(m₁ × 0) + (m₂ × 0) = (m₁ × 400) + (m₂ × V)
Since the gun is initially at rest (velocity = 0), the initial momentum of the gun is 0. Therefore, the equation simplifies to:
0 = (m₁ × 400) + (m₂ × V)
Substituting the given values, we have:
0 = (0.01 kg × 400 m/s) + (2.0 kg × V)
0 = 4 kg·m/s + (2.0 kg × V)
To solve for V, we rearrange the equation:
2.0 kg × V = -4 kg·m/s
V = (-4 kg·m/s) / (2.0 kg)
V = -2 m/s
Therefore, the velocity of the recoiling gun is -2 m/s, indicating that the gun moves in the opposite direction to the bullet. The negative sign indicates the opposite direction of the bullet's velocity.
To calculate the momentum of the gun, we use the equation:
Momentum of the gun = mass of the gun × velocity of the gun
Momentum of the gun = 2.0 kg × (-2 m/s)
Momentum of the gun = -4 kg·m/s
The momentum of the gun is -4 kg·m/s, indicating that the direction of momentum is opposite to the direction of the bullet's momentum.