Step 1: Understanding the Concept:
This problem involves Newton's Third Law (action-reaction) and the conservation of momentum.
The momentum gained by the rifle (recoil) is equal to the momentum of the bullet.
: Key Formula or Approach:
1. Recoil Momentum \( p_{recoil} = p_{bullet} \).
2. Kinetic Energy of recoil \( K = \frac{p^2}{2M} \).
Step 2: Detailed Explanation:
When a bullet is fired, the rifle experiences a backward force and moves with a recoil velocity.
Since the momentum \( p \) imparted to both rifles is the same (due to equal forces over the same time), we look at the kinetic energy transferred to the shooter's shoulder.
Kinetic energy \( K = \frac{p^2}{2M} \).
Since the momentum \( p \) is constant, \( K \propto \frac{1}{M} \).
- A light rifle has a smaller mass \( M \), therefore it will have a much higher recoil kinetic energy.
- A heavy rifle has a larger mass \( M \), leading to a lower recoil kinetic energy.
Because the light rifle carries more energy and moves backward with a greater speed, it delivers a harder "kick" to the shoulder, causing more injury.
Step 3: Final Answer:
The light rifle will cause more injury to the shoulder.