Explanation:

To find the force required to keep the machine gun in position while firing, we can use the principle of conservation of momentum. The force required will be equal in magnitude and opposite in direction to the momentum produced by the fired bullets.

Step 1: Calculate the momentum of one bullet.

Momentum (p) = mass (m) × velocity (v)

Given mass of one bullet (m_bullet) = 35 grams = 0.035 kg

Given velocity of one bullet (v_bullet) = 400 m/s

Momentum of one bullet (p_bullet) = 0.035 kg × 400 m/s

Step 2: Calculate the total momentum produced by firing 400 bullets in one minute.

Total momentum = p_bullet × number of bullets fired per minute

Total momentum = 0.035 kg × 400 m/s × 400 bullets

Step 3: Calculate the rate of change of momentum (force) required to keep the gun in position.

Force = Rate of change of momentum

Force = Total momentum / Time (in seconds)

Since the machine gun fires 400 bullets per minute, the time (T) taken to fire one bullet is 60 seconds / 400 bullets = 0.15 seconds.

Force = (0.035 kg × 400 m/s × 400 bullets) / 0.15 seconds

Now, calculate the force:

Force = 37,333.33 N (approximately)

So, a force of approximately 37,333.33 Newtons must be applied to the machine gun to keep it in position while firing at the given rate.