Question

A machine gun fires 50gm bullets at a speed of 1000m/s. the Gunner, holding the machine gun in his hand,can exert an average force of 180N against the gun. determine the maximum number of bullets he can fire per minute.

Answer 1

We are given:

m = 50g OR 0.05 kg

v = 1000 m/s

Force applied by the gunner in a second = 180 N

Momentum(p) of the bullet:

p = mv

p = 0.05 * 1000

p = 50 kg m/s

Finding the recoil force:

The units kg m/s are also known as 'N' (newtons)

So, we can say that the force exerted on every bullet is 50 N

According to the law of conservation of momentum, every bullet fired applies a force of 50N towards the gunner

Hence, we can say that the recoil force of every bullet is 50N

Finding the number of bullets fired in a minute:

We are given that the gunner applied an average force of 180N on the gun

we know that that can also be written as 180 kg m/s. Notice the 's' in the units of the momentum, it tells us that this force is applied every second

So, to find the amount of force applied in a minute, we can multiply it by 60

Force applied by the gunner in a minute = (60 * 180) = 10800 N

Let n be the number of bullets fired in a minute

We can say that the force applied by the gunner is equal to the force applied by a bullet times the number of bullets fired

F(gunner) = n * F(bullet)

10800 = n * 50

n = 10800/50

n = 216 bullets / minute

The gunner shoots 216 bullets in a minute