Final answer:
Calculations show that the recoil velocity of a 1.00-kg plunger in response to a bullet fired at 600 m/s is 12 m/s. The average force exerted upon the plunger by the gun when stopped over 20 cm is 360 N. This is compared to the higher force of 1200 N exerted on the gun when a bullet is accelerated to its velocity in 10 ms.
Step-by-step explanation:
The recoil a shooter experiences when firing a rifle is due to the conservation of momentum principle in physics. Military rifles have advanced designs which include mechanisms to reduce the recoil felt by the shooter, making the rifle more comfortable and safer to use.
a) Recoil Velocity Calculation:
To calculate the recoil velocity of a 1.00-kg plunger in a rifle that fires a 0.0200-kg bullet at 600 m/s, we apply the conservation of momentum:
Momentum before firing = Momentum after firing
m_bullet ∙ v_bullet = m_plunger ∙ v_plunger
0.0200 kg ∙ 600 m/s = 1.00 kg ∙ v_plunger
v_plunger = (0.0200 kg ∙ 600 m/s) / 1.00 kg = 12 m/s
b) Average Force Exerted on the Plunger:
The average force exerted on the plunger while it is stopped over a 20.0 cm (or 0.20 m) distance can be found using the work-energy principle:
Work = Force ∙ Distance
Work = ½ m_plunger (v_plunger^2)
= ½ ∙ 1.00 kg ∙ (12 m/s)^2
Force = Work / Distance = (72 J) / 0.20 m = 360 N
c) Comparison of Forces:
The force exerted on the gun if the bullet is accelerated to its velocity in 10.0 ms (milliseconds) can be derived from Newton's second law (F = ma) and assuming constant acceleration:
Acceleration (a) = Δv / Δt
Force = m_bullet ∙ a = m_bullet ∙ (v_bullet / Δt)
= 0.0200 kg ∙ (600 m/s) / (10 ∙ 10^-3 s)
= 1200 N, which is significantly higher than the average force exerted on the plunger.