Lecture Notes: Recoil of a Gun and Momentum

Introduction

• Focus on the concept of recoil in guns as part of momentum studies.
• In gun recoil or an explosion, a force is exerted on both the bullet and the gun.
• Key principle: Conservation of Momentum.

Fundamental Concepts

• Initial Momentum: Zero, as neither the bullet nor the gun is moving.
• Post-Explosion: The momentum of the bullet and gun are equal and opposite.

Example 1: Bullet Fired from a Gun

• Bullet Velocity: 400 m/s
• Gun Mass: 3 kg
• Bullet Mass: 60 g (0.06 kg)

Momentum Before and After

• Before Explosion: Combined mass of gun and bullet is 3.06 kg, momentum is zero.
• After Explosion:
  • Gun moves backward with speed V.
  • Bullet moves forward with a velocity of 400 m/s.

Calculations

• Equation: Momentum before = Momentum after:
  • (3V + 400 \times 0.06 = 0)
  • Solving gives gun recoil speed (V = 8 m/s).

Real-World Implications

• Despite the calculated speed, the recoil is absorbed by the shooter's body, preventing actual movement of 8 m/s backwards.

Example 2: Recoil Speed Known, Find Bullet Speed

• Gun Mass: 4 kg
• Recoil Speed: 6 m/s
• Bullet Mass: 50 g (0.05 kg)

Momentum Calculations

• Initial Momentum: Zero
• Equation:
  • (0.05V - 6 \times 4 = 0)
  • Solving gives bullet speed (V = 480 m/s).

Conclusion

• Initially, both gun and bullet have zero momentum.
• Post-firing, they have equal and opposite momentum due to the conservation of momentum principle.
• Practical understanding requires considering external forces like the shooter's stance and grip.