A machine gun has mass of 5kg.it fires 50g bullets at rate of 60 bullets per minute at a speed of 400 m/s what force is required to keep gun in its position

To determine the force required to keep the machine gun in its position while it fires bullets, we need to consider the concept of momentum and how it relates to the recoil of the gun. When a bullet is fired, it generates a backward force on the gun due to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. Let's break this down step by step.

Understanding the Problem

We have the following information:

• Mass of the machine gun (m_g) = 5 kg
• Mass of each bullet (m_b) = 50 g = 0.05 kg
• Rate of fire = 60 bullets per minute
• Speed of each bullet (v) = 400 m/s

Calculating the Momentum of the Bullets

The momentum (p) of a single bullet can be calculated using the formula:

p = m_b * v

Substituting the values:

p = 0.05 kg * 400 m/s = 20 kg·m/s

Finding the Total Momentum per Minute

Since the gun fires 60 bullets per minute, we can find the total momentum imparted by the bullets in one minute:

Total momentum per minute = 60 bullets * 20 kg·m/s = 1200 kg·m/s

Calculating the Average Force

Force can be defined as the rate of change of momentum. To find the average force exerted by the bullets on the gun, we can use the formula:

Force (F) = Change in momentum / Time

Here, the change in momentum is 1200 kg·m/s, and the time interval is 60 seconds (since we are considering one minute).

F = 1200 kg·m/s / 60 s = 20 N

Conclusion

The force required to keep the machine gun in its position while it fires is 20 Newtons. This force counteracts the recoil generated by the bullets being fired, ensuring that the gun remains stable. Understanding these principles of momentum and force helps us appreciate the dynamics involved in firing a weapon.