Final answer:
The M4 carbine utilizes recoil mechanisms to reduce the force on the shooter, calculated by utilizing conservation of momentum for recoil velocity, work-energy principle for the average force during plunger stoppage, and impulse for the force during bullet acceleration.
Step-by-step explanation:
The characteristics of the M4 carbine include features designed to reduce recoil when the weapon is fired. Using physics, we can analyze the recoil velocity, the average force exerted upon internal parts, and the force exerted on the gun during a bullet's acceleration.
- (a) To calculate the recoil velocity of a 1.00-kg plunger interacting with a 0.0200-kg bullet fired at 600 m/s, we use the principle of conservation of momentum. Since there is no external horizontal force, we set the initial momentum equal to the final momentum: (0.0200 kg) × (600 m/s) = (1.00 kg) × (recoil velocity). Solving for recoil velocity, v = (0.0200 kg × 600 m/s) / 1.00 kg, which gives us v = 12 m/s.
- (b) If this plunger is stopped over a distance of 20.0 cm (0.20 m), we can use the work-energy principle to calculate the average force. The work done to stop the plunger is equal to the kinetic energy of the plunger: ½ mv² = Fd. Plugging in the values, we get ½ (1.00 kg)(12 m/s)² = F(0.20 m). Solving for F gives an average force of 360 N exerted by the gun.
- (c) To compare this to the force exerted on the gun if the bullet is accelerated to its velocity in 10.0 ms, we'll use impulse, which is equal to the change in momentum. The impulse experienced by the gun is the force times the time interval, F × t = m × Δv. So, the force exerted on the gun is (0.0200 kg × 600 m/s) / 0.010 s, giving us a force of 1200 N.
In summary, recoil mechanisms in military rifles, such as the M4 carbine, are designed to handle the forces upon firing, safeguarding the user from excessive recoil and improving accuracy.