A machine gun fires 60.0 gram bullets at a rate of 6 bullets per second. If the speed of the bullets is 600 m/s, then the magnitude of the average recoil force on the machine gun is
Question
A machine gun fires 60.0 gram bullets at a rate of 6 bullets per second. If the speed of the bullets is 600 m/s, then the magnitude of the average recoil force on the machine gun is
Solution
To solve this problem, we need to use the concept of momentum and Newton's second law.
Step 1: Calculate the momentum of each bullet Momentum (p) = mass (m) * velocity (v) The mass needs to be in kg, so 60.0 g = 0.06 kg So, p = 0.06 kg * 600 m/s = 36 kg*m/s
Step 2: Calculate the total momentum per second (which is also the force) The gun fires 6 bullets per second, so the total momentum per second is 6 * 36 kgm/s = 216 kgm/s^2
According to Newton's second law, Force = rate of change of momentum. Here, the momentum is changing every second by 216 kg*m/s^2. So, this is also the force.
Therefore, the magnitude of the average recoil force on the machine gun is 216 Newtons.
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